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During the past three decades, motion planning has emerged as a crucial and productive research area in robotics. In the mid-1980s, the most advanced planners were barely able to compute collision-free paths for objects crawling in planar workspaces. Today, planners efficiently deal with robots with many degrees of freedom in complex environments. Techniques also exist to generate quasi-optimal trajectories, coordinate multiple robots, deal with dynamic and kinematic constraints, and handle dynamic environments. This paper describes some of these achievements, presents new problems that have recently emerged, discusses applications likely to motivate future research, and finally gives expectations for the coming years. It stresses the fact that nonrobotics applications (e.g., graphic animation, surgical planning, computational biology) are growing in importance and are likely to shape future motion-planning research more than robotics itself.

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... The second era of motion planning comprises the years 1990 until 2000, where samplingbased algorithms were first pioneered and showed remarkable results in terms of efficiency of computation (26). This era roughly starts with the works of Barraquand (27), who improved the potential field approach using a Monte-Carlo random walking method which were instrumental for subsequent sampling-based planners. ...

... In the last decades, researchers in sampling-based motion planning have published several comprehensive review papers. An early account of the history of the field is found in the treatise by Latombe (26). Focusing more on sampling-based approaches, the work by Tsianos et al. (140) discusses developments of the field during the early 2000's. ...

Sampling-based motion planning is one of the fundamental paradigms to generate robot motions, and a cornerstone of robotics research. This comparative review provides an up-to-date guide and reference manual for the use of sampling-based motion planning algorithms. It includes a history of motion planning, an overview of the most successful planners, and a discussion of their properties. It also shows how planners can handle special cases and how extensions of motion planning can be accommodated. To put sampling-based motion planning into a larger context, a discussion of alternative motion generation frameworks highlights their respective differences from sampling-based motion planning. Finally, a set of sampling-based motion planners are compared on 24 challenging planning problems in order to provide insights into which planners perform well in which situations and where future research would be required. This comparative review thereby provides not only a useful reference manual for researchers in the field but also a guide for practitioners to make informed algorithmic decisions.
Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 7 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

... Input: Initial position: X 0 = (x 0 , y 0 ), size of RRT: N, step: δ, radius: ξ, list of obstacle points: L Output: RRT Graph: G 1 Add vertex X 0 to G 2 for i = 1 to N do 3 X rand ← random point on the map 4 X near ← nearest vertex from G to X rand 5 X new ← point situated at distance δ from X near when moving towards X rand 6 if ∃p ∈ L with the distance between p and X near X new < ξ, then 7 go to step 3 8 Add vertex X new to G 9 Add edge (X near , X new ) to G Figure 1. A Rapidly-exploring Random Tree covers the free-obstacle space. ...

... In the particular case of mobile robots, one crucial problem to be solved by this type of algorithm is the motion planning problem. This problem demands finding a sequence of commands that allow moving an agent from an initial state (usually a position in a 2D plane) to a final one, while avoiding obstacles [8]. In [9], the mentioned problem is demonstrated to be PSPACE-hard. ...

This paper investigates an FPGA architecture whose primary function is to accelerate parallel computations involved in the rapid-exploring random tree (RRT) algorithm. The RRT algorithm is inherently serial, while in each computing step there are many computations that can be executed simultaneously. Nevertheless, how to carry out these parallel computations on an FPGA so that a high degree of acceleration can be realized is the key issue. Membrane computing is a parallel computing paradigm inspired from the structures and functions of eukaryotic cells. As a newly proposed membrane computing model, the generalized numerical P system (GNPS) is intrinsically parallel; so, it is a good candidate for modeling parallel computations in the RRT algorithm. Open problems for the FPGA implementation of the RRT algorithm and GNPS include: (1) whether it possible to model the RRT with GNPS; (2) if yes, how to design such an FPGA architecture to achieve a better speedup; and (3) instead of implementing GNPSs with a fixed-point-number format, how to devise a GNPS FPGA architecture working with a floating-point-number format. In this paper, we modeled the RRT with a GNPS at first, showing that it is feasible to model the RRT with a GNPS. An FPGA architecture was fabricated according to the GNPS-modeled RRT. In this architecture, computations, which can be executed in parallel, are accommodated in different inner membranes of the GNPS. These membranes are designed as Verilog modules in the register transfer level model. All the computations within a membrane are triggered by the same clock impulse to implement parallel computing. The proposed architecture is validated by implementing it on the Xilinx VC707 FPGA evaluation board. Compared with the software simulation of the GNPS-modeled RRT, the FPGA architecture achieves a speedup of a 104 order of magnitude. Although this speedup is obtained on a small map, it reveals that this architecture promises to accelerate the RRT algorithm to a higher level compared with the previously reported architectures.

... This might also mean that time for computation that is used in solving path planning problem, increased and it dependent on problem size increase. The implication is that implementation become difficult considering traditional optimisation method [6]. The best solution searching and determination may become problematic due constraints, the searching process is achievable by utilising many agents that are evolving agents. ...

... The green specks in Figure 2B show the underlying portable robot climate's free space. The briefest free-crash way for the portable robot from the beginning point (6, -8) to the objective point (6,8) is displayed in Figure 2C, with a wellness work cost of 22.1503. Yellow and green stars mark the beginning and objective focuses, individually. ...

The emergence of mobile robot cannot be overemphasized as it is seen as essential but extreme technology taking into considerations, recent industrialisation. Automation has become a part of the process in order to obtain pathway of collision. The firefly algorithm has been identified to work on the principles of behaviour simulation. Two algorithms are implemented in this regard: Pseudo code of the basic firefly and Pseudo code of the firefly algorithm method that is proposed. To be considered for integration, the firefly algorithm method proposed is taken into consideration. A run of suggested mobile robot environment have been run. In conclusion, metaheuristic algorithms, is inspired by nature and are known as powerful tools especially in tackling global optimisation problem.

... In this paper, we introduce a new motion planning algorithm which falls under a type of deliberative motion planning known as sampling-based motion planning. The application of motion planning varies over a wide area which includes Industrial robot arms, planetary exploration, robotic surgery, animation, transportation systems, etc A part from robotics, the sampling-based motion planners are also used in computational biology and animations [1]. ...

... Here, we are interested in determining the distance of point q i to the line L(s, g), say d(q i , b) as depicted in Fig. 3. Let the distance between point g and b be d b . We can deduce that (1) The line L n is normal to L(s, g) forming a right triangle Δgbq i . We have: ...

Sampling-based motion planning in the field of robot motion planning has provided an effective approach to finding path for even high dimensional configuration space and with the motivation from the concepts of sampling based-motion planners, this paper presents a new sampling-based planning strategy called Optimistic Motion Planning using Recursive Sub-Sampling (OMPRSS), for finding a path from a source to a destination sanguinely without having to construct a roadmap or a tree. The random sample points are generated recursively and connected by straight lines. Generating sample points is limited to a range and edge connectivity is prioritized based on their distances from the line connecting through the parent samples with the intention to shorten the path. The planner is analysed and compared with some sampling strategies of probabilistic roadmap method (PRM) and the experimental results show agile planning with early convergence.

... Generalized Voronoi Diagram (GVD) 4 is another way to store the static or dynamic environments into the diagram structure. The cell decomposition method 5 divides the configuration space into small cells and constructs the connectivity graph. However, above mentioned methods are computationally too expensive to extend for higher dimension cluttered space. ...

... The reason behind the high computation load is well addressed in the literature. [5][6][7] The cell decomposition method divides the configuration space into regular and irregular grids or navigation meshes, but such representations for high-density obstacles space lack path accuracy and increase memory requirement for higher resolution. Latombe 5 has discussed that none of the cell decomposition-based approaches extends well to robots with higher dimensional configuration space as the number of cells becomes too large and offers no formal guarantee of performance even for simple problems. ...

Path planning of All-Terrain Rover over 3D terrains is one of the most challenging robotics problems. Prior research has been carried out over 2D static and dynamic configuration space. Currently, all available algorithms for 3D path planning of articulated rover require optimization for wheel-terrain interaction. In this comparative analysis, the path planning is carried out over the 10 degrees of freedom Rover CG-Space instead of ground. CG-Space is the collection of all possible center of gravity locations of the Rover while traversing on terrain. The introduction of preobtained CG-Space eliminates the need for optimization during the planning stage. In this work, a comprehensive path planning comparison has been obtained among modified artificial potential field (APF) method, sampling-based technique (RRT*), and particle swarm optimization (PSO) algorithm based on path length, path smoothness, and computational time. All algorithms are applied over CG-Space associated with two categories of terrains: even and uneven. Even terrains have a well-defined surface equation, while uneven terrains are generated using Kinect V2 sensor mounted over the sand arena. A continuous surface from CG-Space is generated using cubic spline interpolation. The simulation results show that all three algorithms generate obstacle-free paths in a different time span. Although sampling-based and APF-based techniques take about five times lesser time, the obtained paths have moderate smoothness. PSO performs better than RRT* and modified APF for the requirements of optimal path length and smoothness. Thus, PSO is the optimal way to plan the path if the computational cost associated is acceptable. On the other hand, if time is the major planning concern, then RRT* is the best because the path smoothening takes very little time when using separate cubic spline techniques after obtaining the path nodes. This comparative analysis is useful in selecting an appropriate algorithm depending on the terrain complexity and obstacle conditions.

... The resulting path commencing by RRT is not optimal all the time. Nonetheless, it remains pretty easy to find a path for a vehicle with dynamic and physical constrictions and it also creates least number of edges [19][20]. Probabilistic roadmap (PRM) method is a path-planning algorithm that takes random samples from the configuration space by examining the accessible free space and dodging the crashes to find a way. ...

... PRM is costly without any possibilities to acquire the path. [19][20]. ...

An Unmanned Aerial Vehicle (UAV) or robot is guided towards its goal through path planning that helps it in avoiding obstacles. Path planning generates a path between a given start and an end point for the safe and secure reach of the robot with required criteria. A number of path planning methods are available such as bio-inspired method, sampling based method, and combinatorial method. Cell decomposition technique which is known as one of the combinatorial methods can be represented with configuration space. The aim of this paper is to study the results obtained in earlier researches where cell decomposition technique has been used with different criteria like shortest traveled path, minimum computation time, memory usage, safety, completeness, and optimal. Based on the classical taxonomy, the studied methods are classified.

... Motion planning is a widely studied problem with applications in many fields such as robotics, computer graphics and medicine [1]. Early planning methods such as Djikstra's operate by searching a discretized version of the space of interest. ...

... We consider a two dimensional space populated with corridors as seen in Fig 3. such that all points in the space exist between (0,0) to (1,1). The walls are randomly generated resulting in random narrow corridors. ...

This paper investigates the feasibility of using Graph Neural Networks (GNNs) for classical motion planning problems. Planning algorithms that search through discrete spaces as well as continuous ones are studied. This paper proposes using GNNs to guide the search algorithm by exploiting the ability of GNNs to extract low level information about the topology of a planning space. We present two techniques, GNNs over dense fixed graphs for low-dimensional problems and sampling-based GNNs for high-dimensional problems. We examine the ability of a GNN to tackle planning problems that are heavily dependent on the topology of the space such as identifying critical nodes, learning a heuristic that guides exploration in $\text{A}^*$, and learning the sampling distribution in Rapidly-exploring Random Trees (RRT). We demonstrate that GNNs can offer better results when compared to traditional analytic methods as well as learning-based approaches that employ fully-connected networks or convolutional neural networks.

... M OTION planning problems have various applications such as Self-driving cars, Unmanned Aerial Vehicles (UAVs), medical surgery, computational biology, graphics animation and virtual prototyping [1][2][3][4][5][6][7]. Motion planners are mostly divided into two groups: graph-based and samplingbased methods. ...

... Instead, a heuristic function,f (·), can be considered as an estimation which must not overestimate the actual cost of the path. The definition off (·) is similar to (2). ...

Rapidly-exploring Random Trees (RRTs) are successful in single-query motion planning problems. The standard version of RRT grows a tree from a start location and stops once it reached the goal configuration. RRT-Connect is the bidirectional version of RRT, which grows two trees simultaneously. These two trees try to establish a connection to stop searching. RRT-Connect finds solutions faster than RRT. Following that, an asymptotically optimal version of RRT-Connect called RRT*-Connect has been introduced. It not only rewires both trees while they are growing, but also it keeps searching the state space for better solutions than the current one. However, it is inefficient and inconsistent to search all over the state space in order to find better solutions than the current one concerning its single-query nature. The better way is to look through states that can provide a better solution. In this paper, we propose Informed RRT*-Connect, which is the informed version of RRT*-Connect that uses direct sampling after the first solution found. Unlike RRT*-Connect, the proposed method checks only the states that can potentially provide better solutions than the current solution. The proposed method benefited from the properties of RRT*-Connect and informed sampling, which offers low-cost solutions with fewer iterations in comparison to RRT*-Connect. Different simulations in OMPL have been carried out to show the significance of Informed RRT*-Connect in comparison with RRT*, Informed RRT*, and RRT*-Connect.

... That means, the necessary computational time for solving the path planning problem increases dramatically depending on the increase of problem size. therefore, it is difficult to implement the traditional optimization methods for determining the shortest robot path in real time [6]. Searching and determining the best solution or values, to give problems according to certain constraints, is by adjusting the restricted variables to desired characteristics that optimize the objective is known as the optimization process. ...

... While in Figure 2B, the green points demonstrate the free space of the first mobile robot environment. And Figure 2C depicted the free-collision shortest path of the mobile robot from the start point (6, -8) to the goal point (6,8) with a fitness function cost equal to 22.1503. The yellow and green stars indicate to start and goal points respectively. ...

Mobile Robot has emerged as an extremely essential technology in the recent industrialization world. Present-days, one of the hot research areas in Mobile Robot are dealing with Path planning problems. Path planning problems encompass determining the best feasible path from the start point to the target point. From the other hand, the firefly algorithm has been deemed as an increasingly promising tool of Swarm Intelligence and employed in versatile optimization areas. The current research implemented the firefly algorithm to resolve the mobile robot problem of best planning. The major concern of the adopted method is looking for free-collision points in Mobile Robot environment and generate the optimal path based on the firefly algorithm. The algorithm was utilized to specify the optimal control points of the shortest path. Quintic Polynomial equation has been applied to roughly generate a free path from an initial to goal configurations within a specified period. the findings of computer simulation. The findings of computer simulation affirmed the efficiently of the firefly algorithm in generating an optimal path of Mobile Robot in an environment of moving obstacles.

... A local planner is used to join these configurations with close-by configurations. A graph search algorithm is applied after adding the initial and goal configurations to determine a path [14][15]. ...

... The main idea of this technique is to cluster small obstacles and merge the polygons after clustering. Further, in [14], an algorithm was proposed to separate the C-spaces in many parts and VG was utilized to assemble each part at parallel direction. The shortest path was determined by integrating each partial minimum distance path. ...

The use of autonomous vehicle/robot has been adopted widely to replace human beings in performing dangerous missions in adverse environments. Keeping this in mind, path planning ensures that the autonomous vehicle must safely arrive to its destination with required criteria like lower computation time, shortest travelled path and completeness. There are few kinds of path planning strategies, such as combinatorial method, sampling based method and bio-inspired method. Among them, combinatorial method can accomplish couple of criteria without further adjustment in conventional algorithm. Configuration space provides detailed information about the position of all points in the system and it is the space for all configurations. Therefore, C-space denotes the actual free space zone for the movement of robot and guarantees that the vehicle or robot must not collide with the obstacle. This paper analyses different C-Space representation techniques under combinatorial method based on the past researches and their findings with different criteria such as optimality, completeness, safety, memory uses, real time and computational time etc. Visibility Graph has optimality which is a unique from other 1. INTRODUCTION (10 PT) Path planning algorithm is important to produce an optimal path that enables the shortest distance movement of a vehicle or robot from a starting point to a target point with minimum computational time. The path planning algorithm should also hold complete criterion so that it is able to find a path, if one exists. Besides that, the vehicle's safety, memory usage for computing and the real-time applicable algorithm are also significant [1-6]. Path planning approaches, in general, can be classified in three ways, such as combinatorial method, sampling-based method, and bio-inspired method. The combinatorial path planning creates a route by resolving queries along the way. Figure 1 illustrates the classification of path planning approaches. It comprises mainly two methods like C-space representation technique and graph search algorithm. This paper focuses on C-space representation techniques. Road map (RM), cell decomposition (CD) and potential field (PF) techniques are among the ways of space representation. Road map technique is also divided into two categories-visibility graph (VD) and Voronoi diagram (VD) [7]. Visibility graph (VG) algorithm finds a path by connecting all the visible vertices of an obstacle including a starting and an ending point. After that, a shortest path is searched from the connected graph. In cell decomposition (CD) method, the first step is to decompose the configuration space into cells and then it finds a cell which is not occupied by any obstacle. The Voronoi diagram (VD) is an equidistant point from two or all the nearest obstacles and by connecting all these points, a path can be found [6], [8] and [9]. PF algorithm is a path planning technique based on attractive and repulsive potential [9-10].

... In the motion planning problem, given the initial and goal configuration of the robot, the objective is to plan from the initial state to the goal region while avoiding obstacles along the way. Motion planning finds its application in our everyday life, in fields such as smart cars [2], robotic surgery [3], aerial, underwater and amphibious robotics [2], humanoid robotics [4] and in countless others [5] [6] [7] [8]. As humans explore the outer-space more and more, motion planning in outer-space [9] is also a becoming a challenging task. ...

... In the motion planning problem, given the initial and goal configuration of the robot, the objective is to plan from the initial state to the goal region while avoiding obstacles along the way. Motion planning finds its application in our everyday life, in fields such as smart cars [2], robotic surgery [3], aerial, underwater and amphibious robotics [2], humanoid robotics [4] and in countless others [5] [6] [7] [8]. As humans explore the outer-space more and more, motion planning in outer-space [9] is also a becoming a challenging task. ...

Rapidly-exploring Random Tree star (RRT*) has recently gained immense popularity in the motion planning community as it provides a probabilistically complete and asymptotically optimal solution without requiring the complete information of the obstacle space. In spite of all of its advantages, RRT* converges to an optimal solution very slowly. Hence to improve the convergence rate, its bidirectional variants were introduced, the Bi-directional RRT* (B-RRT*) and Intelligent Bi-directional RRT* (IB-RRT*). However, as both variants perform pure exploration, they tend to suffer in highly cluttered environments. In order to overcome these limitations, we introduce a new concept of potentially guided bidirectional trees in our proposed Potentially Guided Intelligent Bi-directional RRT* (PIB-RRT*) and Potentially Guided Bi-directional RRT* (PB-RRT*). The proposed algorithms greatly improve the convergence rate and have a more efficient memory utilization. Theoretical and experimental evaluation of the proposed algorithms have been made and compared to the latest state of the art motion planning algorithms under different challenging environmental conditions and have proven their remarkable improvement in efficiency and convergence rate.

... The traditional obstacle avoidance path planning algorithm has a simple structure, but it depends on the accuracy of the obstacle expression in the environment (Karaman and Frazzoli, 2011). Moreover, constructing the environment graph or traversing the global nodes also makes the algorithm suffer from more complex calculations and low efficiency (Latombe, 1999;Huang and Teo, 2019). Traditional obstacle avoidance planning algorithms can be applied to 2-dimensional or 3-dimensional Euclidean space, and as to whether they are suitable for high-dimensional path planning of industrial robots, the paper (Tamaki et al., 2023) proved that by limiting the joint Angle of industrial robots to a certain range, the local surface of the ring space of industrial robots and N-dimensional Euclidean space can realize local differential homeomorphism. ...

Path planning is an essential part of robot intelligence. In this paper, we summarize the characteristics of path planning of industrial robots. And owing to the probabilistic completeness, we review the rapidly-exploring random tree (RRT) algorithm which is widely used in the path planning of industrial robots. Aiming at the shortcomings of the RRT algorithm, this paper investigates the RRT algorithm for path planning of industrial robots in order to improve its intelligence. Finally, the future development direction of the RRT algorithm for path planning of industrial robots is proposed. The study results have particularly guided significance for the development of the path planning of industrial robots and the applicability and practicability of the RRT algorithm.

... Motion planning has varied applications in several fields [Latombe 1999], but robotics remains the core field of development. The intention behind any motion planning problem in robotics (manipulation or navigation) is to plan a continuous motion sequence for a robot to reach the final goal configuration from its initial configuration in a given environment while avoiding collisions. ...

... In order to make AVs function in urban situations with unpredictable traffic, several real-time systems must interoperate [3], including highdefinition maps (HD-Maps) [4,5], perception [6], localization [7,8], motion planning and control [9,10]. Motion planning, a basic component of autonomous driving, acts as a bridge between the decision and control modules and is indispensable for the safe and stable operation of AVs [11], by generating smooth and safe trajectories in the locally feasible solution space provided by the decision-making system. ...

On campus, the complexity of the environment and the lack of regulatory constraints make it difficult to model the environment, resulting in less efficient motion planning algorithms. To solve this problem, HD-Map-guided sampling-based motion planning is a feasible research direction. We proposed a motion planning algorithm for autonomous vehicles on campus, called HD-Map-guided rapidly-exploring random tree (HDM-RRT). In our algorithm, A collision risk map (CR-Map) that quantifies the collision risk coefficient on the road is combined with the Gaussian distribution for sampling to improve the efficiency of algorithm. Then, the node optimization strategy of the algorithm is deeply optimized through the prior information of the CR-Map to improve the convergence rate and solve the problem of poor stability in campus environments. Three experiments were designed to verify the efficiency and stability of our approach. The results show that the sampling efficiency of our algorithm is four times higher than that of the Gaussian distribution method. The average convergence rate of the proposed algorithm outperforms the RRT* algorithm and DT-RRT* algorithm. In terms of algorithm efficiency, the average computation time of the proposed algorithm is only 15.98 ms, which is much better than that of the three compared algorithms.

... Using a weighted graph to model a workspace, configuration space, and, more generally, the geometry of a lowerdimensional manifold embedded in high-dimensional ambient space is a well-known strategy for both path planning and manifold learning (e.g., [10], [11], [12], [13], [14]). This is generally more computationally expensive than computing a single path between just a single pair of configurations (e.g., [15], [16]), but a robust graph model allows us to analyze more optimal paths and make repeated queries to investigate the geometry of output and input modes. ...

The configuration manifolds of parallel manipulators exhibit more nonlinearity than serial manipulators. Qualitatively, they can be seen to possess extra folds. By projecting such manifolds onto spaces of engineering relevance, such as an output workspace or an input actuator space, these folds cast edges that exhibit nonsmooth behavior. For example, inside the global workspace bounds of a five-bar linkage appear several local workspace bounds that only constrain certain output modes of the mechanism. The presence of such boundaries, which manifest in both input and output projections, serve as a source of confusion when these projections are studied exclusively instead of the configuration manifold itself. Particularly, the design of nonsymmetric parallel manipulators has been confounded by the presence of exotic projections in their input and output spaces. In this paper, we represent the configuration space with a radius graph, then weight each edge by solving an optimization problem using homotopy continuation to quantify transmission quality. We then employ a graph path planner to approximate geodesics between configuration points that avoid regions of low transmission quality. Our methodology automatically generates paths capable of transitioning between non-neighboring output modes, a motion which involves osculating multiple workspace boundaries (local, global, or both). We apply our technique to two nonsymmetric five-bar examples that demonstrate how transmission properties and other characteristics of the workspace can be selected by switching output modes.

... R OBOT path planning refers to the process of finding a sequence of configurations that lead a robot system from a starting configuration to a goal configuration without violating task constraints. Path planning is a crucial component in robotics [1], autonomous driving [2] and other domains such as surgical planning, computational biology, and molecules [3]. In robotics, path planning is an integral tool for manipulation tasks with robotic manipulator arms [4]- [6] and mobile robots [7]- [9]. ...

Path planning is a crucial algorithmic approach for designing robot behaviors. Sampling-based approaches, like rapidly exploring random trees (RRTs) or probabilistic roadmaps, are prominent algorithmic solutions for path planning problems. Despite its exponential convergence rate, RRT can only find suboptimal paths. On the other hand, $\textrm{RRT}^*$, a widely-used extension to RRT, guarantees probabilistic completeness for finding optimal paths but suffers in practice from slow convergence in complex environments. Furthermore, real-world robotic environments are often partially observable or with poorly described dynamics, casting the application of $\textrm{RRT}^*$ in complex tasks suboptimal. This paper studies a novel algorithmic formulation of the popular Monte-Carlo tree search (MCTS) algorithm for robot path planning. Notably, we study Monte-Carlo Path Planning (MCPP) by analyzing and proving, on the one part, its exponential convergence rate to the optimal path in fully observable Markov decision processes (MDPs), and on the other part, its probabilistic completeness for finding feasible paths in partially observable MDPs (POMDPs) assuming limited distance observability (proof sketch). Our algorithmic contribution allows us to employ recently proposed variants of MCTS with different exploration strategies for robot path planning. Our experimental evaluations in simulated 2D and 3D environments with a 7 degrees of freedom (DOF) manipulator, as well as in a real-world robot path planning task, demonstrate the superiority of MCPP in POMDP tasks.

... Designing a feasible trajectory that satisfies global obstacles constraints for a robot from the start state to the goal state is the main underlying idea of robot motion planning [1]. Over the past few decades, the motion planning problem has been widely studied [2], and many well-known motion planning algorithms have been proposed. The graphbased planning algorithms, such as the A* [3] and Dijkstra's algorithm [4] are used to find an optimal trajectory through graphs. ...

Motion Planning is necessary for robots to complete different tasks. Rapidly-exploring Random Tree (RRT) and its variants have been widely used in robot motion planning due to their fast search in state space. However, they perform not well in many complex environments since the motion planning needs to simultaneously consider the geometry constraints and differential constraints. In this article, we propose a novel robot motion planning algorithm that utilizes multi-tree to guide the exploration and exploitation. The proposed algorithm maintains more than two trees to search the state space at first. Each tree will explore the local environment. The tree starts from the root will gradually collect information from other trees and grow towards the goal state. This simultaneous exploration and exploitation method can quickly find a feasible trajectory. We compare the proposed algorithm with other popular motion planning algorithms. The experiment results demonstrate that our algorithm achieves the best performance on different evaluation metrics.

... Turner and Penn (2002) argued that human movement is "natural movement" (p. 474), driven by affordances rather than the object-based approaches popularized in agent-based modeling that mimicked heuristics from robot motion planning (Latombe 1991(Latombe , 1999. ...

In this review paper, we aim to make the case that a concept from retail analytics and marketing—the customer journey —can provide promising new frameworks and support for agent-based modeling, with a broad range of potential applications to high-resolution and high-fidelity simulation of dynamic phenomena on urban high streets. Although not the central focus of the review, we consider agent-based modeling of retail high streets against a backdrop of broader debate about downtown vitality and revitalization, amid a climate of economic challenges for brick-and-mortar retail. In particular, we consider how agent-based modeling, supported by insights from consideration of indoor shopping, can provide planning and decision support in outdoor high street settings. Our review considers abstractions of customers through conceptual modeling and customer typology, as well as abstractions of retailing as stationary and mobile. We examine high-level agency of shop choice and selection, as well as low-level agency centered on perception and cognition. Customer journeys are most often trips through geography; we therefore review path-planning, generation of foot traffic, wayfinding, steering, and locomotion. On busy high streets, journeys also manifest within crowd motifs; we thus review proximity, group dynamics, and sociality. Many customer journeys along retail high streets are dynamic, and customers will shift their journeys as they come into contact with experiences and service offerings. To address this, we specifically consider treatment of time and timing in agent-based models. We also examine sites for customer journeys, looking in particular at how agent-based models can provide support for the analysis of atmospherics, artifacts, and location-based services. Finally, we examine staff-side agency, considering store staff as potential agents outdoors; and we look at work to build agent-based models of fraud from customer journey analysis.

... Many others, however, are standalone algorithms, such as KPIECE1 [9], PDST [10], and SBL [11]. Motion planning today is quite robust compared to what it was in the 1980s and 1990s, when planners were barely able to compute collision-free paths for objects translating and rotating in 2D workspaces [12]. ...

Vegetable greenhouse operations are labour intensive. Automating some of these operations can save growers significant costs in an industry with low-profit margins. One of the most demanding operations is harvesting. Harvesting a tomato is a complex operation due to the significant clutter inherent to a greenhouse and the fragility of the object being grasped. Improving grasp and motion planning requires setting up a realistic testbed or testing on-site, which is expensive and time-limited to the growing season and specific environment. As such, it is important to develop a simulation environment to model this operation to help test various strategies before field testing can be conducted. Using the method presented in this work, 3D images are taken from a commercial greenhouse and used to develop a physics-based realistic simulation environment. The environment is then used to simulate a picking operation using various path planning algorithms to investigate the best algorithm to use in this case. The results show that this environment can be used to explore the best approaches to automate harvesting solutions in a vegetable greenhouse environment.

... Bu gayretleri yapılandırma alanı kavramına yol açmıştır. Yapılandırma alanında robot, serbestlik derecelerini tanımlayan parametre uzayında tek bir nokta olarak temsil edilmesini ifade eder(J.C. Latombe, 1999). Yapılan çalışma robotun yapılandırma alanının çıkarılmasına da önemli avantajlar sağlayacaktır. ...

... Motion planning, finding a valid path for a movable object from one state to another, has applications in many domains including robotics, computer-aided design, and computational biology [14]. Problems in these applications are usually defined with conditions on the quality of the solution. ...

Motion planning algorithms often leverage topological information about the environment to improve planner performance. However, these methods often focus only on the environment's connectivity while ignoring other properties such as obstacle clearance, terrain conditions, and resource accessibility. We present a method that augments a skeleton representing the workspace topology with such information to guide a sampling-based motion planner to rapidly discover regions most relevant to the problem at hand. Our approach decouples guidance and planning, making it possible for basic planning algorithms to find desired paths earlier in the planning process. We demonstrate the efficacy of our approach in both robotics problems and applications in drug design. Our method is able to produce desirable paths quickly with no change to the underlying planner.

... Motion planning has since grown to become one of the most studied ield in robotics and automation [66][67][68][69][70][71]. It has various applications in other ields, including computational biology with protein folding algorithms [72], video games or movies with computer animation [73,74]. Historically, motion planning is often referred to as the piano mover's problem [75]. ...

L’utilisation de robots collaboratifs dans l’industrie de production est en plein essor. Ces robots, dont la puissance est limitée, sont dotés de capteurs leur permettant de détecter la présence d’obstacles, afin de garantir la sécurité des humains se trouvant aux alentours. On s’intéresse dans cette thèse à l’utilisation de systèmes redondants, collaboratifs et mobiles (bras articulés montés sur plateformes mobiles), dans un environnement de production aéronautique peuplé d’humains, pour la réalisation d’opérations d’assemblage. Du point de vue des process, l’utilisation de ces systèmes, souvent beaucoup moins imposants et rigides que leurs homologues non collaboratifs, est jalonnée de défis. La grande souplesse mécanique et les faibles couples qui les caractérisent peuvent induire des imprécisions de positionnement et une incapacité à soutenir l’intensité d’une interaction physique. Ce contexte induit également un besoin d’autonomie de ces systèmes, qui sont amenés à travailler dans des environnements en perpétuelle évolution. Dans cette thèse, une formulation de la redondance cinématique est d’abord présentée. Le formalisme associé permet de simplifier l’exploitation de la liberté que ces systèmes possèdent sur le choix des postures à utiliser pour réaliser des tâches de placement statique de l’effecteur. Ce formalisme est ensuite exploité pour améliorer et caractériser le comportement en déformation et la capacité d’application d’efforts des systèmes redondants sériels. Enfin, le sujet de la planification des mouvements de systèmes robotisés dans un environnement dynamique et encombré est considéré. La solution présentée adapte l’algorithme bien connu des Probabilistic RoadMaps pour y inclure une anticipation des trajectoires des obstacles dynamiques. Cette solution permet de planifier des mouvements sécuritaires, peu intrusifs et efficaces, jusqu’à la destination.

... Other algorithms such as Particle Swarm Optimization (Chakraborti et al. 2011, Mukund Nilakantan andPonnambalam 2016) and direct variational Method (Shukla et al. 2013) and double global optimum genetic algorithm-particle swarm optimization (Wang et al. 2016) have been used by researchers. The use of evolutionary algorithms to optimize redundant robotic systems has advantages such as the possibility of using multi-objective optimizations including a combination of runtime, energy consumption, jerk and so on (Saramago and Steffen 1998, Chettibi et al. 2004, Pires, Machado, and de Moura Oliveira 2004, Gasparetto and Zanotto 2007, Pires, de Moura Oliveira, and Machado 2007, Glorieux et al. 2017 or applying many constraints in the objective functions without affecting the problem-solving strategy (Latombe 1999), or even using direct kinematics instead of reversing the Jacobian matrix (Lin 2004). Nevertheless, it has a big problem, which is computational cost. ...

The main objective of this paper is to develop a redundancy-resolution algorithm to optimize the joint motion of a redundant robotic welding system. At first, the Joint Limit Avoidance (JLA) and Singularity Avoidance (SGA) optimizations are employed. Due to complicated geometry of the welding path, despite using JLA & SGA optimizations, some constraints like joint angles violate their allowable limits. Hence, functional redundancy (FNR) is employed as the best solution because it has no effect on the welding electrode direction. In this paper, the functional redundancy is used as an augmented task, which changes the desired path without effecting the electrode direction. To select the best functional redundancy angle, two indexes, i.e. the minimum joint angles movement and the singularity indexes, are introduced. Simulation results show that the planned path using FNR not only satisfies all constraints, but it also is smooth.

... These methods have found immediate applications in various robotic platforms. Variants of RRT algorithm were found to be very useful in motion planning of robotic manipulators with high degrees of freedom due to their relatively less computational complexity [14][15][16]. But the paths generated are not always optimal. ...

Due to high degrees-of-freedom of humanoids and induced redundancy, there are multiple ways of performing a given manipulation task. Finding optimal ways of performing tasks is one desirable property of any motion planning framework. This includes optimizing both the path with respect to a certain objective function and also the final pre-grasp or goal position. Additionally, a variety of constraints need to be satisfied such as stability, self-collision and collision with objects in the environment and also kinematic loop-closure formed during the task. In this paper, an asymptotically optimal sampling based approach for generating motion plans is presented. A novel constraint solver extension to the bidirectional Fast Marching Trees (BFMT*) algorithm in the form of a way-point generator is proposed such that it can be applied for whole-body motion planning of humanoids. Moreover, a comparison of the performance of the proposed extension of BFMT* and the state-of-art RRT* based motion planner is shown. A gradient based inverse kinematics solver has also been implemented in combination with an optimization technique to generate goal configurations in order to ensure optimality in the pre-grasp position. The efficacy of the proposed approach is evaluated in a simulation environment on Hubo+ robot model. The results show a significant improvement in path costs, as well as overall optimality of given tasks for the proposed approach. Additionally, rigorous analysis over the choice of planning algorithms considered in this paper is present for the considered scenarios.

... Motion planning, which has applications from robotics, biochemistry [2], video animations, artificial intelligence [3], to autonomous vehicle navigation [4], is the name of producing a plan that moves object from an initial configuration to a desired configuration while obeying the movement constraint [5]. A state (or configuration) space, either discrete or continuous, which includes all possible values of the variables, such as positions, orientations, velocities of objects like robots, targets, obstacles, is the first fundamental requirement of motion planning. ...

This chapter presents designs and implementations of cellular nonlinear network accelerators on field programmable gate array. A digital circuit architecture is introduced to handle computationally intensive active waves generation on locally coupled oscillatory network. This architecture is also implemented on FPGA and applied to the motion planning problem. Furthermore, in order to speed up real-time response of artificial olfaction systems, a system-on-chip architecture which is including reconfigurable cellular neural network as a feature extractor is presented.

... 3 Yet, as challenging as the physical design of hyperredundant robots is, planning their motions is an additional challenge. 4,5,6,7 Early motion planners for hyper-redundant robot motion planning were developed by Chirikjian. [8][9][10][11] In those works, the curvature of the robotic snake is approximated as a continuous modal function with obstacles expressed as boundary constraints on the robot's shape. ...

This article presents a motion planning method for a novel hyper-redundant robot with minimal actuation based on the principles of fractals and self-organizing systems. The robot consists of multiple links connected by passive joints and a movable actuator. The actuator travels over the links to a given joint and adjusts the relative angle between the two adjacent links allowing the robot to undergo the same wide range of motions of hyper-redundant robot but with only one actuator. A suitable objective of the motion planner is to minimize the number of actuator traversals, which translates into minimizing the number of bends in the c-space trajectory. To this end, we propose a novel method for motion planning using fractals and self-organizing systems. A self-similar pattern for the path is implemented to map a path from start to finish. Each iteration of path segments is of smaller dimension than the previous one and is appended to it, just as in classical fractals. This process continues until a feasible trajectory is calculated. Self-organizing systems are then applied to this trajectory post-processing to optimize it by eliminating bends in the path. Examples of the robot maneuvering around obstacles and through confined spaces are shown to demonstrate the efficacy of the motion planner.

... [12,16]) have been proposed and successfully applied to challenging problems that remained out of scope for previously existing techniques. They allow today to handle practical motion planning problems arising in such diverse fields as robotics, graphic animation, virtual prototyping or computational biology [14]. ...

Kinematic loop-closure constraints significantly increase the difficulty of motion planning for articulated mechanisms. Configurations of closed-chain mechanisms do not form a single manifold, easy to parameterize, as the configurations of open kinematic chains. In general, they are grouped into several subsets with complex and a priori unknown topology. Sampling-based motion planning algorithms cannot be directly applied to such closed-chain systems. This paper describes our recent work [7] on the extension of sampling-based planners to treat this kind of mechanisms.

... This method may also be incomplete, i.e., it is unable to figure out a path between two locations although the path exists connecting these locations in the presence of narrow passage. Moreover, it is tough to know about any existing path unless it is found [28,29]. On the other hand, PRM is probabilistically optimal and complete with reasonable computation time. ...

Unmanned Aerial Vehicle (UAV) is a type of autonomous vehicle for which energy efficient path planning is a crucial issue. The use of UAV has been increased to replace humans in performing risky missions at adversarial environments and thus, the requirement of path planning with efficient energy consumption is necessary. This study analyses all the available path planning algorithms in terms of energy efficiency for a UAV. At the same time, the con-sideration is also given to the computation time, path length and completeness because UAV must compute a stealthy and minimal path length to save energy. Its range is limited and hence, time spent over a surveyed territory should be minimal, which in turn makes path length always a factor in any algorithm. Al-so the path must have a realistic trajectory and should be feasible for the UAV.

This paper presents Ex-RRT*, a modification of the rapidly-exploring random tree star (RRT*) algorithm that allows the robot to avoid obstacles with a margin. RRT* generates the shortest path to a destination while avoiding obstacles. However, if the robot’s embedded trajectory generation algorithm interpolates the waypoints generated by the RRT* to make a motion, collisions may occur with the edges or overhang of obstacles. This algorithm adds a cost function for the distance from each node to the nearest obstacle to ensure that the waypoints generated by the path planner have an appropriate margin for obstacles. It is designed to provide safer control from collisions when each robot’s embedded trajectory generation algorithm operates by interpolating waypoints derived by path planning. Through simulation, we compare the proposed Ex-RRT* and conventional RRT* with performance indices such as total distance traveled and collision avoidance norm. Experiments are conducted on the task of moving an object inside a box with a commercial robot to validate the proposed algorithm. The proposed algorithm generates paths with improved safety and can be applied to various robotic arms and mobile platforms.

We study the problem of determining minimum-length coordinated motions for two axis-aligned square robots translating in an obstacle-free plane: Given feasible start and goal configurations, find a continuous motion for the two squares from start to goal, comprising only robot-robot collision-free configurations, such that the total Euclidean distance traveled by the two squares is minimal among all possible such motions. We present an adaptation of the tools developed for the case of discs by Kirkpatrick and Liu [Characterizing minimum-length coordinated motions for two discs. Proceedings 28th CCCG, 252-259, 2016; CoRR abs/1607.04005, 2016.] to the case of squares. Certain aspects of the case of squares are more complicated, requiring additional and more involved arguments over the case of discs. Our contribution can serve as a basic component in optimizing the coordinated motion of two squares among obstacles, as well as for local planning in sampling-based algorithms, which are often used in practice, in the same setting.KeywordsMotion planningCoordinated motionsGeometric algorithms

The most important field of robotics study is path planning. Path planning problem in general is an NP-complete problem. Though several attempts have been made using A*, PRM, RRT, and RRT* these algorithms explore too many nodes in the state space, not completely captured kinematic constraints, and are not optimal in real-time. In this paper, a Multi-Objective Hybrid Collision- free Optimal Path Finder (MOHC-OPF) is proposed which is an attempt to obtain a near-optimal solution by exploring fewer nodes compare to the above existing methods while considering kinematic constraints aiming to generate optimal drivable paths. The empirical study revealed that the proposed algorithm is capable of detecting static obstacles and finding a collision-free nearest-optimal, smooth and safe path to the destination in a static known environment. Multiple criteria, including path length, collision-free, execution time, and smooth path, are used to determine an optimal path.. The proposed algorithm shows efficiency in finding the shortest path length and execution time decreased in 90% of the experiments.

Motion Planning is necessary for robots to complete different tasks. Rapidly-exploring Random Tree (RRT) and its variants have been widely used in robot motion planning due to their fast search in the state space. However, they perform not well in many complex environments since the motion planning needs to simultaneously consider the geometry constraints and differential constraints. In this article, we propose a novel robot motion planning algorithm that utilizes multi-tree to guide the exploration and exploitation. The proposed algorithm maintains more than two trees to search the state space at first. Each tree will explore the local environments. The tree starts from the root will gradually collect information from other trees and grow towards the goal state. This simultaneous exploration and exploitation method can quickly find a feasible trajectory. We compare the proposed algorithm with other popular motion planning algorithms. The experiment results demonstrate that our algorithm performs better on different evaluation metrics.

Path planning is a crucial algorithmic approach for designing robot behaviors. Sampling-based approaches, like rapidly exploring random trees (RRTs) or probabilistic roadmaps, are prominent algorithmic solutions for path planning problems. Despite its exponential convergence rate, RRT can only find suboptimal paths. On the other hand,
$\text {RRT}^*$
, a widely-used extension to RRT, guarantees probabilistic completeness for finding optimal paths but suffers in practice from slow convergence in complex environments. Furthermore, real-world robotic environments are often partially observable or with poorly described dynamics, casting the application of
$\text {RRT}^*$
in complex tasks suboptimal. This letter studies a novel algorithmic formulation of the popular Monte-Carlo tree search (MCTS) algorithm for robot path planning. Notably, we study Monte-Carlo Path Planning (MCPP) by analyzing and proving, on the one part, its exponential convergence rate to the optimal path in fully observable Markov decision processes (MDPs), and on the other part, its probabilistic completeness for finding feasible paths in partially observable MDPs (POMDPs) assuming limited distance observability (proof sketch). Our algorithmic contribution allows us to employ recently proposed variants of MCTS with different exploration strategies for robot path planning. Our experimental evaluations in simulated 2D and 3D environments with a 7 degrees of freedom (DOF) manipulator, as well as in a real-world robot path planning task, demonstrate the superiority of MCPP in POMDP tasks.

In recent years, a large number of manipulator robots have been deployed to replace or assist humans in many repetitive and dangerous tasks. Yet, these robots have complex mechanisms, resulting in their non-linearity of kinematics and dynamics as well as intensive computations. Therefore, relying on soft computing techniques are a common and alternative key to model and control these systems. In particular, fuzzy logic approaches have proven to be simple, efficient, and superior to relevant well-known methods and have sparked greater interest in robotic applications. To help researchers meet their needs easily and quickly in finding relevant research works on fuzzy-based solutions, this article adapted to provide an in-depth review of the currently updated fuzzy logic approaches for collision-free path planning of serial manipulator robots operating in complex and cluttered workspaces. In addition to a comprehensive description of fuzzy hybridization with other artificial intelligence techniques description. Further, this article attempts to present the main solutions with a summary and visualization of all basic approaches that path-planning problems may subtend in the decision-making process. Finally, the paper suggests some potential challenges and explores research issues for future work.

This chapter presents two artificial intelligence tools: multi‐agent systems (MAS) and fuzzy logic to design and implement the control architecture for autonomous navigation of a mobile robot, taking into account the changing nature of the environment. It provides the key methods used for mobile robot navigation as related works. Navigation methods for mobile robots have two classes: classical approaches and advanced approaches. The chapter introduces the problem position, describes the control architecture based agent, and also provides a discussion on the methods for evaluating an agent system. A robot is a complex system that must meet varied and sometimes contradictory requirements. The global architecture developed is a fully distributed hybrid architecture and does not involve any supervisor. The system is designed around four agents (perception, locomotion, fuzzy controller and feasibility). The chapter presents the elements essential for understanding the principle of control by fuzzy logic. These are: fuzzy variables, and inference rules.

A mobile robot acting in a human environment should follow social conventions, keeping safety distances and navigating at moderate speeds, in order to respect people in its surroundings and avoid obstacles in real-time. The problem is more complex in differential-drive wheeled robots, with trajectories constrained by nonholonomic and kinematics restrictions. It is an NP-hard problem widely studied in the literature, combining disciplines such as Psychology, Mathematics, Computer Science and Engineering. In this work, we propose a novel solution based on Membrane Computing, Social Force Model and Dynamic Window Approach Algorithm. The resulting model is able to compute, in logarithmic time, the best motion command for the robot, given its current state, considering the surrounding people and obstacles. The model is compatible with other membrane computing models for robotics and suitable for an implementation on parallel hardware. Finally, a visual simulator was implemented in ROS and C++ for validation and testing.

Membrane computing is a broad and flexible paradigm, where many types of computing models have been conceived since the inception of the field—around 20 years ago. It was clear from its early days that a deep understanding of the dynamics of the computational devices of the discipline (so-called P systems) required the development of support simulation tools. Different approaches have been followed in this context, but a historical overview is out of scope here. This chapter mainly focuses on describing P-Lingua framework, probably the most widely used product for the specification and simulation of different types of P systems, consequently leading to a very prolific scientific production. A high-level tool for virtual experiments, MeCoSim, is also presented.

The performance of P system simulators is key when deploying these models in real applications, or when pushing the limits of efficiency. In this concern, HPC is the key technology to accelerate the simulation of P systems, and specially, GPU computing is a good alternative since they provide a highly parallel device with a shared memory system and a flexible programming. GPUs are currently the enabling technology for trending areas such as Deep Learning. So far, many GPU simulators have been developed using CUDA, the first general-purpose programming model for GPUs. In this chapter, we introduce the concepts behind GPU computing and a taxonomy of GPU-based simulators: generic, specific, and adaptive simulation.

The theoretical basis of membrane computing was established in the early 2000s with fundamental research into the computational power, complexity aspects and relationships with other (un)conventional computing paradigms. Although this core theoretical research has continued to grow rapidly and vigorously, another area of investigation has since been added, focusing on the applications of this model in many areas, most prominently in systems and synthetic biology, engineering optimization, power system fault diagnosis and mobile robot controller design. The further development of these applications and their broad adoption by other researchers, as well as the expansion of the membrane computing modelling paradigm to other applications, call for a set of robust, efficient, reliable and easy-to-use tools supporting the most significant membrane computing models. This work provides comprehensive descriptions of such tools, making it a valuable resource for anyone interested in membrane computing models.

This chapter presents several representative applications implemented with P systems software simulators, including automatic design of cell-like and spiking neural P systems with P-Lingua, modelling real ecosystems with MeCoSim, and robot motion planning. The automatic design of P systems uses evolutionary computing approaches to heuristically select the best models satisfying the predefined requirements from a population of candidate P systems, where each P system is evaluated on the P-Lingua platform according to an evaluation function. The models for investigating population dynamics of real ecosystems are realized with MeCoSim. Robot motion planning is implemented by simulating rapidly exploring random trees algorithm within the P system framework.

This paper proposes a robot teaching method using augmented and virtual reality technologies. Robot teaching is essential for robots to accomplish several tasks in industrial production. Although there are various approaches to perform motion planning for robot manipulation, robot teaching is still required for precision and reliability. Online teaching, in which a physical robot moves in the real space to obtain the desired motion, is widely performed because of its ease and reliability. However, actual robot movements are required. In contrast, offline teaching can be accomplished entirely in the computational space, and it requires constructing the robot’s surroundings as computer graphic models. Additionally, planar displays do not provide sufficient information on 3D scenes. Our proposed method can be employed as offline teaching, but the operator can manipulate the robot intuitively using a head-mounted device and the specified controllers in the virtual 3D space. We demonstrate two approaches for robot teaching with augmented and virtual reality technologies and show some experimental results.

This book explores how neural networks can be designed to analyze sensory data in a way that mimics natural systems. It introduces readers to the cellular neural network (CNN) and formulates it to match the behavior of the Wilson–Cowan model. In turn, two properties that are vital in nature are added to the CNN to help it more accurately deliver mimetic behavior: randomness of connection, and the presence of different dynamics (excitatory and inhibitory) within the same network. It uses an ID matrix to determine the location of excitatory and inhibitory neurons, and to reconfigure the network to optimize its topology.
The book demonstrates that reconfiguring a single-layer CNN is an easier and more flexible solution than the procedure required in a multilayer CNN, in which excitatory and inhibitory neurons are separate, and that the key CNN criteria of a spatially invariant template and local coupling are fulfilled. In closing, the application of the authors’ neuron population model as a feature extractor is exemplified using odor and electroencephalogram classification.

Rapidly-exploring Random Trees (RRTs) have been widely used for motion planning problems due to their ability to efficiently find solutions. Informed RRT* is an optimized version of RRT, which not only implements the rewiring process to optimize the tree but also limits the search area to a subset of the state space to return near-optimal solutions faster. However, limiting the state space is a function of the obtained shortest path so that before a solution is found, the planner cannot limit the state space to a subset. Moreover, unidirectional RRTs such as Informed RRT* take more time to find initial solutions in comparison to the bidirectional RRTs. In this paper, we propose Hybrid RRT, which divides the planning process into three parts: finding initial solutions by a dual-tree search, combining two trees into one, and optimizing the solution. In order to obtain an initial solution, Hybrid RRT implements a dual-tree search, which helps it find solutions faster than unidirectional searches. Then, it combines the start tree and the goal tree of the dual-tree search into one so as to implement informed sampling for a single tree to optimize the current solution. The simulation carried out in Open Motion Planning Library (OMPL), which shows that Hybrid RRT achieved outstanding improvement over RRT* and Informed RRT*.

In a human-robot coexisting environment, reaching the target place efficiently and safely is pivotal for a mobile service robot. In this paper, a Risk-based Dual-Tree Rapidly exploring Random Tree (Risk-DTRRT) algorithm is proposed for the robot motion planning in a dynamic environment, which provides a homotopy optimal trajectory on the basis of a heuristic trajectory. A dual-tree framework consisting of an RRT tree and a rewired tree is proposed for the trajectory searching. The RRT tree is a time-based tree, considering the future trajectory predictions of the pedestrians, and this tree is utilized to generate a heuristic trajectory. However, the heuristic trajectory is usually nonoptimal. Then, a line-of-sight (LoS) control checking algorithm is proposed to detect whether two time-based nodes can be rewired with the least cost. On the basis of the LoS control checking algorithm, a tree rewiring algorithm is proposed to optimize the heuristic trajectory. The tree generated in the tree rewiring process is called the rewired tree. The trajectory generated by the Risk-DTRRT algorithm proves to be optimal in the homotopy class of the heuristic trajectory. The navigation run time and the lengths of the planned trajectories are selected to demonstrate the effectiveness of the proposed algorithm. The experimental results in both simulation studies and real-world implementations reveal that our proposed method achieves convincing performance in both static and dynamic environments.

Modular self-reconfigurable robots consist of large numbers of identical modules that possess the ability to reconfigure into different shapes as required by the task at hand. For example, such a robot could start out as a snake to traverse a narrow pipe, then re-assemble itself into a six-legged spider to move over uneven terrain, growing a pair of arms to pick up and manipulate an object at the same time. This paper examines the self-reconfigurable problem and present a divide-and-conquer strategy to solve reconfiguration for a class of problems referred to as closed-chain reconfiguration. This class includes reconfigurable robots whose topologies are described by 1D combinatorial topology. A robot topology is first decomposed into a hierarchy of small 'substrates' belonging to a finite set. Basic reconfiguration operations between the substructures in the set are precomputed, optimized and stored in a lookup table. The entire reconfiguration then consists of an ordered series of simple, precomputed sub-reconfigurations happening locally among the substructures.

We propose a new approach to robot path planning that consists of building and searching a graph connecting the local minima of a potential function defined over the robot's configuration space. A planner based on this approach has been implemented. This planner is consider ably faster than previous path planners and solves prob lems for robots with many more degrees of freedom (DOFs). The power of the planner derives both from the "good" properties of the potential function and from the efficiency of the techniques used to escape the local min ima of this function. The most powerful of these tech niques is a Monte Carlo technique that escapes local min ima by executing Brownian motions. The overall approach is made possible by the systematic use of distributed rep resentations (bitmaps) for the robot's work space and configuration space. We have experimented with the plan ner using several computer-simulated robots, including rigid objects with 3 DOFs (in 2D work space) and 6 DOFs (in 3D work space) and manipulator arms with 8, 10, and 31 DOFs (in 2D and 3D work spaces). Some of the most significant experiments are reported in this article.

In which order can a product be assembled or disassembled? How many hands are required? How many degrees of freedom? What parts should be withdrawn to allow the removal of a specified subassembly? To answer such questions automatically, important theoretical issues in geometric reasoning must be addressed. This paper investigates the planning of assembly algorithms specifying (dis) assembly operations on the components of a product and the ordering of these operations. It also presents measures to evaluate the complexity of these algorithms and techniques to estimate the inherent complexity of a product. The central concept underlying these planning and complexity evaluation techniques is that of a “non-directional blocking graph”, a qualitative representation of the internal structure of an assembly product. This representation describes the combinatorial set of parts interactions in polynomial space. It is obtained by identifying physical criticalities where geometric interferences among parts change. It is generated from an input geometric description of the product. The main application considered in the paper is the creation of smart environments to help designers create products that are easier to manufacture and service. Other possible applications include planning for rapid prototyping and autonomous robots.

We apply manipulation planning to computer animation. A new path planner is presented that automatically computes the collision-free trajectories for several cooperating arms to manipulate a movable object between two configurations. This implemented planner is capable of dealing with complicated tasks where regrasping is involved. In addition, we present a new inverse kinematics algorithm for the human arms. This algorithm is utilized by the planner for the generation of realistic human arm motions as they manipulate objects. We view our system as a tool for facilitating the production of animation.

In robotics uncertainty exists at both planning and execution time. Effective planning must make sure that enough information becomes available to the sensors during execution, to allow the robot to correctly identify the states it traverses. It requires selecting a set of states, associating a motion command with every state, and synthesizing functions to recognize state achievement. These three tasks are often interdependent, causing existing planners to be either unsound, incomplete, and/or computationally impractical. In this paper we partially break this interdependence by assuming the existence of landmark regions in the workspace. We define such regions as “islands of perfection” where position sensing and motion control are accurate. Using this notion, we propose a sound and complete planner of polynomial complexity. Creating landmarks may require some prior engineering of the robot and/or its environment. Though we believe that such engineering is unavoidable in order to build reliable practical robot systems, its cost must be reduced as much as possible. With this goal in mind, we also investigate how some of our original assumptions can be eliminated. In particular, we show that sensing and control do not have to be perfect in landmark regions. We also study the dependency of a plan on control uncertainty and we show that the structure of a reliable plan only changes at critical values of this uncertainty. Hence, any uncertainty reduction between two consecutive such values is useless. The proposed planner has been implemented. Experimentation has been successfully conducted both in simulation and using a NOMAD-200 mobile robot.

A hierarchical representation for configuration space is presented, along with an algorithm for searching that space for collision-free paths. The detail of the algorithm are presented for polygonal obstacles and a moving object with two translational and one rotational degrees of freedom.

Programmable vector fields can be used to control a variety of
flexible planar parts feeders. When a part is placed on our devices, the
programmed vector field induces a force and moment upon it. Over time,
the part may come to rest in a dynamic equilibrium state. We demonstrate
lower bounds on what the devices cannot do, and results on a
classification of control strategies. We suggest sufficient conditions
for programmable fields to induce well-behaved equilibria on every part
placed on our devices. We define composition operators to build complex
strategies from simple ones, and show the resulting fields are also
well-behaved. We discuss whether fields outside this class can be useful
and free of pathology. Using these tools, we describe new manipulation
algorithms, and improve existing planning algorithms by a quadratic
factor, and the plan-length by a linear factor. We relax earlier dynamic
and mechanical assumptions to obtain more robust and flexible
strategies. Finally, we consider parts feeders that can only implement a
very limited “vocabulary” of vector fields. We discuss the
trade-off between mechanical complexity and planning complexity

A simple and efficient algorithm for finding the closest points
between two convex polynomials is described. Data from numerous
experiments tested on a broad set of convex polyhedra on
R <sup>3</sup> show that the running time is roughly constant
for finding closest points when nearest points are approximately known
and is linear in total number of vertices if no special initialization
is done. This algorithm can be used for collision detection, computation
of the distance between two polyhedra in three-dimensional space, and
other robotics problems. It forms the heart of the motion planning
algorithm previously presented by the authors (Proc. IEEE ICRA,
p.1554-9, 1990)

Programmable force fields are a representation of a class of
devices for distributed, nonprehensile manipulation for applications in
parts feeding, sorting, positioning, and assembly. They generate force
vector fields in which the parts move until they reach a stable
equilibrium pose. Research has yielded open-loop strategies to uniquely
position, orient, and sort parts. These strategies typically consist of
several fields employed in sequence to achieve a desired final pose. The
length of the sequence depends on the complexity of the part. We show
that unique part poses can be achieved with just one field. First, we
exhibit a single field that positions and orients any part (except
certain symmetric parts) into two stable equilibrium poses. Then, we
show that for any part there exists a field in which the part reaches a
unique stable equilibrium pose (again, except for symmetric parts).
Besides giving an optimal upper bound for unique parts positioning and
orientation, our work gives further evidence that programmable force
fields are a powerful tool for parts manipulation. Our second result
also leads to the design of “universal parts feeders”,
proving an earlier conjecture about their existence. We argue that
universal parts feeders are relatively easy to build, and we report on
extensive simulation results which indicate that these devices may work
very well in practice. We believe that the results in this paper could
be the basis for a new generation of efficient, open-loop, parallel
parts feeders

A new motion planning method for robots in static workspaces is
presented. This method proceeds in two phases: a learning phase and a
query phase. In the learning phase, a probabilistic roadmap is
constructed and stored as a graph whose nodes correspond to
collision-free configurations and whose edges correspond to feasible
paths between these configurations. These paths are computed using a
simple and fast local planner. In the query phase, any given start and
goal configurations of the robot are connected to two nodes of the
roadmap; the roadmap is then searched for a path joining these two
nodes. The method is general and easy to implement. It can be applied to
virtually any type of holonomic robot. It requires selecting certain
parameters (e.g., the duration of the learning phase) whose values
depend on the scene, that is the robot and its workspace. But these
values turn out to be relatively easy to choose, Increased efficiency
can also be achieved by tailoring some components of the method (e.g.,
the local planner) to the considered robots. In this paper the method is
applied to planar articulated robots with many degrees of freedom.
Experimental results show that path planning can be done in a fraction
of a second on a contemporary workstation (≈150 MIPS), after learning
for relatively short periods of time (a few dozen seconds)

This paper considers the problem of motion planning for a car-like
robot (i.e., a mobile robot with a nonholonomic constraint whose turning
radius is lower-bounded). We present a fast and exact planner for our
mobile robot model, based upon recursive subdivision of a collision-free
path generated by a lower-level geometric planner that ignores the
motion constraints. The resultant trajectory is optimized to give a path
that is of near-minimal length in its homotopy class. Our claims of high
speed are supported by experimental results for implementations that
assume a robot moving amid polygonal obstacles. The completeness and the
complexity of the algorithm are proven using an appropriate metric in
the configuration space R<sup>2</sup>×S<sup>1</sup> of the robot.
This metric is defined by using the length of the shortest paths in the
absence of obstacles as the distance between two configurations. We
prove that the new induced topology and the classical one are the same.
Although we concentrate upon the car-like robot, the generalization of
these techniques leads to new theoretical issues involving
sub-Riemannian geometry and to practical results for nonholonomic motion
planning

The use of motion strategies to eliminate uncertainty, without the
use of sensors, is considered. The approach is demonstrated within the
context of a simple method to orient planar objects. A randomly oriented
object is dropped into a tray. When the tray is tilted, the object can
slide into walls, along walls, and into corners, sometimes with the
effect of reducing the number of possible orientations. For some objects
a sequence of tilting operations exists that leaves the object's
orientation completely determined. An automatic planner is described
that constructs such a tilting program, using a simple model of the
mechanics of sliding. The planner has been implemented, the resulting
programs have been executed using a tray attached to an industrial
manipulator, and sometimes the programs work. The authors explore the
issue of sensorless manipulation, tray tilting in particular, within the
context of a formal framework described by T. Lozano-Perez, M.T. Mason,
and Rolf Taylor (1984). It is observed that sensorless motion strategies
perform conditional actions using mechanical decisions in place of
environmental inquiries

We study the following problem: Given a collection A of polyhedral parts in 3D, determine whether there exists a subset 5 of the parts that can be moved as a rigid body by infinitesimal translation and rotation, without colliding with the rest of the parts, A \ S. A negative result implies that the object whose constituent parts are the collection A cannot be taken apart with two hands. A positive result, together with the list of movable parts in S and a direction of motion for S, can be used by an assembly sequence planner (it does not, however, give the complete specification of an assembly operation). This problem can be transformed into that of traversing an arrangement of convex polytopes in the space of directions of rigid motions. We identify a special type of cells in that arrangement, which we call the maximally covered cells, and we show that it suffices for the problem at hand to consider a representative point in each of these special cells rather than to compute the entire arrangement. Using this observation, we devise an algorithm which is complete (in the sense that it is guaranteed to find a solution if one exists), simple, and improves significantly over the best previously known solutions. We describe an implementation of our algorithm and report experimental results obtained with this implementation.

A program has been developed which takes a specification of a set of bodies and of spatial relations that are to hold between them in some goal state, and produces expressions denoting the positions of the bodies in the goal state together with residual equations linking the variables in these expressions.

This paper continues the discussion, begun in J. Schwartz and M. Sharir [Comm. Pure Appl. Math., in press], of the following problem, which arises in robotics: Given a collection of bodies B, which may be hinged, i.e., may allow internal motion around various joints, and given a region bounded by a collection of polyhedral or other simple walls, decide whether or not there exists a continuous motion connecting two given positions and orientations of the whole collection of bodies. We show that this problem can be handled by appropriate refinements of methods introduced by A. Tarski ["A Decision Method for Elementary Algebra and Geometry," 2nd ed., Univ. of Calif. Press, Berkeley, 1951] and G. Collins [in "Second GI Conference on Automata Theory and Formal Languages," Lecture Notes in Computer Science, Vol. 33, pp. 134-183, Springer-Verlag, Berlin, 1975], which lead to algorithms for this problem which are polynomial in the geometric complexity of the problem for each fixed number of degrees of freedom (but exponential in the number of degrees of freedom). Our method, which is also related to a technique outlined by J. Reif [in "Proceedings, 20th Symposium on the Foundations of Computer Science," pp. 421-427, 1979], also gives a general (but not polynomial time) procedure for calculating all of the homology groups of an arbitrary real algebraic variety. Various algorithmic issues concerning computations with algebraic numbers, which are required in the algorithms presented in this paper, are also reviewed.

This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the artificial potential field concept. Collision avoidance, tradi tionally considered a high level planning problem, can be effectively distributed between different levels of control, al lowing real-time robot operations in a complex environment. This method has been extended to moving obstacles by using a time-varying artificial patential field. We have applied this obstacle avoidance scheme to robot arm mechanisms and have used a new approach to the general problem of real-time manipulator control. We reformulated the manipulator con trol problem as direct control of manipulator motion in oper ational space—the space in which the task is originally described—rather than as control of the task's corresponding joint space motion obtained only after geometric and kine matic transformation. Outside the obstacles' regions of influ ence, we caused the end effector to move in a straight line with an upper speed limit. The artificial potential field ap proach has been extended to collision avoidance for all ma nipulator links. In addition, a joint space artificial potential field is used to satisfy the manipulator internal joint con straints. This method has been implemented in the COSMOS system for a PUMA 560 robot. Real-time collision avoidance demonstrations on moving obstacles have been performed by using visual sensing.

This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based dynamical models and avoiding obstacles in the robot's environment. The authors consider generic systems that express the nonlinear dynamics of a robot in terms of the robot's high-dimensional configuration space. Kinodynamic planning is treated as a motion-planning problem in a higher dimensional state space that has both first-order differential constraints and obstacle based global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized path-planning techniques do not directly apply to planning trajectories in the state space. The authors have developed a randomized planning approach that is particularly tailored to trajectory planni ng problems in high-dimensional state spaces. The basis for this approach is the construction of rapidly exploring random trees, which offer benefits that are similar to those obtained by successful randomized holonomic planning methods but apply to a much broader class of problems. Theoretical analysis of the algorithm is given. Experimental results are presented for an implementation that computes trajectories for hovercrafts and satellites in cluttered environments, resulting in state spaces of up to 12 dimensions.

1 Introduction and Overview.- 2 Configuration Space of a Rigid Object.- 3 Obstacles in Configuration Space.- 4 Roadmap Methods.- 5 Exact Cell Decomposition.- 6 Approximate Cell Decomposition.- 7 Potential Field Methods.- 8 Multiple Moving Objects.- 9 Kinematic Constraints.- 10 Dealing with Uncertainty.- 11 Movable Objects.- Prospects.- Appendix A Basic Mathematics.- Appendix B Computational Complexity.- Appendix C Graph Searching.- Appendix D Sweep-Line Algorithm.- References.

Automatic programming of manipulator robots attracts in creasing interest within the context of mechanical assembly. In this paper we focus on the problem of mating two parts, which requires sensor-based strategies to deal with geometric uncertainty. We present a system that embodies a two-phase approach to build robot programs implementing such strate gies. First a training phase interacts with the robot actuators and sensors and produces traces of execution of a given part- mating operation. Next a purely computational induction phase transforms these traces into an executable manipula tor-level program for the operation. The system embedding this approach has been completely implemented, and it has been used experimentally on several assembly tasks.

An algorithm for the generation of all mechanical assembly sequences for a given product is presented. It uses a relational model of assemblies. In addition to the geometry of the assembly, this model includes a representation of the attachments that bind parts together. The problem of generating the assembly sequences is transformed into the problem of generating disassembly sequences in which the disassembly tasks are the inverse of feasible assembly tasks. The problem of disassembling one assembly is decomposed into distinct disassembly subproblems. The algorithm returns the AND/OR graph representation of assembly sequences. The correctness of the algorithm is based on the assumption that it is always possible to decide correctly whether two subassemblies can be joined, based on geometrical and physical criteria. An approach to computing this decision is presented. An experimental implementation for the class of products made up of polyhedral and cylindrical parts with planar or cylindrical contacts among themselves is described. Bounds for the amount of computation involved are presented

An abstract is not available.

We describe an approach for interactive collision detection and proximity computations on massive models composed of millions of geometric primitives. We address issues related to interactive data access and processing in a large geometric database, which may not fit into main memory of typical desktop workstations or computers. We present a new algorithm using overlap graphs for localizing the “regions of interest” within a massive model, thereby reducing runtime memory requirements. The overlap graph is computed off-line, pre-processed using graph partitioning algorithms, and modified on the fly as needed. At run time, we traverse localized sub-graphs to check the corresponding geometry for proximity and pre-fetch geometry and auxiliary data structures. To perform interactive proximity queries, we use bounding-volume hierarchies and take advantage of spatial and temporal coherence. Based on the proposed algorithms, we have developed a system called IMMPACT and used it for interaction with a CAD model of a power plant consisting of over 15 million triangles. We are able to perform a number of proximity queries in real-time on such a model. In terms of model complexity and application to large models, we have improved the performance of interactive collision detection and proximity computation algorithms by an order of magnitude.

We consider the problem of planning the motion of an arbitraryk-sided polygonal robotB, free to translate and rotate in a polygonal environmentV bounded byn edges. We present an algorithm that constructs a single component of the free configuration space ofB in timeO((kn)
2+ɛ), for any ɛ>0. This algorithm, combined with some standard techniques in motion planning, yields a solution to the underlying motion-planning problem, within the same running time.

This paper considers the automatic generation of motion paths for
several cooperating robot arms to manipulate a movable object between
two configurations among obstacles. To avoid collisions the robots may
have to change their grasp of the object, for example, by passing it
from one arm to another. The case where the movable object can only be
moved by two arms acting simultaneously is also considered. An approach
for solving this planning problem is described and illustrated with a
robot system made of three arms moving in a 3D environment. Experiments
with a planner implementing this approach show that it is not only fast,
but also reliable in finding collision-free paths

This paper describes an efficient algorithm for computing the
distance between nonconvex objects. Objects are modeled as the union of
a set of convex components. From this model we construct a hierarchical
bounding representation based on spheres. The distance between objects
is determined by computing the distance between pairs of convex
components using preexisting techniques. The key to efficiency is a
simple search routine that uses the bounding representation to ignore
most of the possible pairs of components. The efficiency can further be
improved by accepting a relative error in the returned result. Several
empirical trials are presented to examine the performance of the
algorithm

Maintainability is an important issue in design where the
accessibility of certain parts is determined for routine maintenance. In
the past its study has been largely manual and labor intensive. Either
by using physical mockup or computer animation with CAD models of a
design, the task relies on a human to provide an access path for the
part. In this paper, the authors present an automated approach to
replace this manual process. By applying results from and developing
extensions to research in motion planning and other fields, the authors
demonstrate that an automated maintainability study system is feasible.
The authors describe general extensions needed to adapt robotic motion
planning techniques in maintainability studies. The authors show results
from applying such a system to two classes of industrial application
problems

This paper describes an experimental very high level programming system for computer controlled mechanical assembly, AUTOPASS (AUTOmated Parts ASsembly System). The AUTOPASS language is oriented towards objects and assembly operations, rather than motions of mechanical assembly machines. It is intended to enable the user to concentrate on the overall assembly sequence and to program with English-like statements using names and terminology that are familiar to him. To relate assembly operations to manipulator motions, the AUTOPASS compiler uses an internal representation of the assembly world. This representation consists of a geometric data base generated prior to compilation and updated during compilation; it thus represents the state of the world at each assembly step. The level of the language has been chosen to provide a high degree of assistance to the user without the system's having to perform artificial intelligence type problem solving operations.

The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot path planning. The attractiveness of the scheme stems from its general applicability to virtually any path-planning problem, and its empirically observed success. In this paper we initiate a theoretical basis for explaining this empirical success. Under a simple assumption about the configuration space, we show that it is possible to perform preprocessing following which queries can be answered quickly. En route, we consider related problems on graph connectivity in the evasiveness model, and art-gallery theorems.

ABSTRACT A research,project,applying,artificial,intelligence,techniques,to the development($#$#$#CommaToBeDetermineabout the environment, and for planning the sequence of motor actions necessary to accomplish,tasks,in the,environment.,A typical,task,performed,by our present,system,requires,the,robot,vehicle,to rearrange,(by pushing),simple objects,in its,environment. A novel,feature,of our,approach,is the,use,of a,formal,theorem-proving

ABSTRACT - The ,problem ,of planning ,safe ,tra jectories,for ,computer ,controlled ,manipulators with,two ,movable ,links ,and ,multiple ,degrees ,of freedom is analyzed, and a solution to the problem,proposed. The,key ,features ,of the ,solution ,are: 1.the,identification ,of trajectory

A collision avoidance algorithm for planning a safe path for a polyhedral object moving among known polyhedral objects is described. The algorithm transforms the obstacles so that they represent the locus of forbidden positions for an arbitrary reference point on the moving object. A trajectory of this reference point which avoids all forbidden regions is free of collisions. Trajectories are found by searching a network which indicates, for each vertex in the transformed obstacles, which other vertices can be reached safely.

We consider mobile robots made of a single body (car-like robots) or several bodies (tractors towing several trailers sequentially hooked). These robots are known to be nonholonomic, i.e., they are subject to nonintegrable equality kinematic constraints involving the velocity. In other words, the number of controls (dimension of the admissible velocity space), is smaller than the dimension of the configuration space. In addition, the range of possible controls is usually further constrained by inequality constraints due to mechanical stops in the steering mechanism of the tractor. We first analyze the controllability of such nonholonomic multibody robots. We show that the well-known Controll- ability Rank Condition Theorem is applicable to these robots even when there are inequality constraints on the velocity, in addition to the equality constraints. This allows us to subsume and generalize several controllability results recently published in the Robotics literature concerning nonholonomic mobile robots, and to infer several new important results. We then describe an implemented planner inspired by these results. We give experimental results obtained with this planner that illustrate the theoretical results previously developed.

The use of active compliance enables robots to carry out tasks in the presence of significant sensing and control errors. Compliant motions are quite difficult for humans to specify, however. Furthermore, robot programs are quite sensitive to details of geometry and to error characteristics and must, therefore, be constructed anew for each task. These factors motivate the need for automatic synthesis tools for robot programming, especially for compliant motion. This paper describes a formal approach to the synthesis of compliant motion strategies from geometric descriptions of assembly operations and explicit estimates of errors in sensing and control. A key aspect of the approach is that it provides correctness criteria for compliant motion strategies.

Stereotactic radiosurgery is a minimally invasive procedure that uses a focused beam of radiation as an ablative instrument to destroy brain tumors. To deposit a high dose of radiation in a tumor, while reducing the dose to healthy tissue, a large number of beams are crossfired at the tumor from multiple directions. The treatment planning problem (also called the inverse dosimetry problem) is to compute a set of beams that produces the desired dose distribution. So far its investigation has focused on the generation of isocenter-based treatments in which the beam axes intersect at a common point, the isocenter. However this restriction limits the applicability of the treatments to tumors which have simple shapes. This paper describes CARABEAMER, a new treatment planner for a radiosurgical system in which the radiation source can be arbitrarily positioned and oriented by a six-degree-of-freedom manipulator. This planner uses randomized techniques to guess a promising initial set of beams. It then applies space partitioning and linear programming techniques to compute the energy to be delivered along each beam. Finally, it exploits the results of the linear program to iteratively adapt and improve the beam set. Experimental results obtained with CARABEAMER on both patient and synthetic cases are presented and discussed. These results demonstrate that a radiosurgical system with general kinematics can deliver treatments in which the region receiving a high dose closely matches the shape of the tumor, even in complicated cases. They also suggest new research directions which are discussed at the end of the paper.

This paper concerns the problem of moving a polyhedron through Euclidean space while avoiding polyhedral obstacles.

An autonomous robotic manipulator can reduce uncertainty in the locations of objects in either of two ways: by sensing, or by motion strategies. This paper explores the use of motion strategies to eliminate uncertainty, without the use of sensors. The approach is demonstrated within the context of a simple method to orient planar objects. A randomly oriented object is dropped into a tray. When the tray is tilted, the object can slide into walls, along walls, and into corners, sometimes with the effect of reducing the number of possible orientations. For some objects a sequence of tilting operations exists that leaves the object's orientation completely determined. The paper describes an automatic planner that constructs such a tilting program, using a simple model of the mechanics of sliding. The planner has been implemented, the resulting programs have been executed using a tray attached to an industrial manipulator, and sometimes the programs work. The paper also explores the issue of sensorless manipulation, tray-tilting in particular, within the context of a formal framework first described by Lozano-Pérez, Mason, and Taylor [1984]. It is observed that sensorless motion strategies perform conditional actions using mechanical decisions in place of environmental inquiries.

This paper presents a unique real-time obstacle avoidance approach for manipulators and mobile robots based on the "artificial potential field" concept. In this approach, collision avoidance, traditionally considered a high level planning problem, can be effectively distributed between different levels of control, allowing real-time robot operations in a complex environment. We have applied this obstacle avoidance scheme to robot arm using a new approach to the general problem of real-time manipulator control. We reformulated the manipulator control problem as direct control of manipulator motion in operational space-the space in which the task is originally described-rather than as control of the task's corresponding joint space motion obtained only after geometric and kinematic transformation. This method has been implemented in the COSMOS system for a PUMA 560 robot. Using visual sensing, real-time collision avoidance demonstrations on moving obstacles have been performed.

We introduce the notion of expansiveness to characterize a family
of robot configuration spaces whose connectivity can be effectively
captured by a roadmap of randomly-sampled milestones. The analysis of
expansive configuration spaces has inspired us to develop a new
randomized planning algorithm. This algorithm tries to sample only the
portion of the configuration space that is relevant to the current
query, avoiding the cost of precomputing a roadmap for the entire
configuration space. Thus, it is well-suited for problems where a single
query is submitted for a given environment. The algorithm has been
implemented and successfully applied to complex assembly maintainability
problems from the automotive industry

Constraints on assembly plans vary depending on product, assembly
facility, assembly volume, and many other factors. This paper describes
the principles and implementation of a framework that supports a wide
variety of user-specified constraints for interactive assembly planning.
Constraints from many sources can be expressed on a sequences level,
specifying orders and conditions on part mating operations in a number
of ways. All constraints are implemented as filters that either accept
or reject assembly operations proposed by the planner. For efficiency,
some constraints are supplemented with special-purpose modifications to
the planner's algorithms. Fast replanning enables a natural
plan-view-constrain-replan cycle that aids in constraint discovery and
documentation. We describe an implementation of the framework in a
computer-aided assembly planning system and experiments applying the
system to several complex assemblies

Presents a new approach to the multi-robot path planning problem,
where a number of robots are to change their positions through feasible
motions in the same static environment. The approach is
probabilistically complete. That is, any solvable problem is guaranteed
to be solved within a finite amount of time. The method, which is an
extension of previous work on probabilistic single-robot planners, is
very flexible in the sense that it can easily be applied to different
robot types. In this paper the authors apply it to non-holonomic
car-like robots, and present experimental results which show that the
method is powerful and fast

The authors consider the robot path planning problem in the
presence of nonintegrable kinematic constraints, known as nonholonomic
constraints. Such constraints are generally caused by one or several
rolling contacts between rigid bodies and express that the relative
velocity of two points in contact is zero. They make the dimension of
the space of achievable velocities smaller than the dimension of the
robot's configuration space. Using standard results in differential
geometry (Frobenius integrability theorem) and nonlinear control theory,
the authors first give a formal characterization of holonomy (and
nonholonomy) for robot systems subject to linear differential
constraints and state some related results about their controllability.
They then apply these results to `car-like' and `trailer-like' robots.
Finally, they present an implemented planner, which generates
collision-free paths with a minimal number of maneuvers for car-like and
trailer-like robots among obstacles

The authors present an algorithm for the generation of mechanical assembly sequences and a proof of its correctness and completeness. The algorithm uses a relational model which describes the geometry of the assembly and the attachments that bind one part to another. The problem of generating the assembly sequences is transformed into the problem of generating disassembly sequences, in which the disassembly tasks are the reverse of feasible assembly tasks. This transformation leads to a decomposition approach in which the problem of disassembling one assembly is decomposed into distinct subproblems, each involving the disassembly of one subassembly. It is assumed that at each assembly task exactly two subassemblies are mated and that all contacts between the parts in the two subassemblies are established. The algorithm yields an AND/OR graph representation of assembly sequences. The correctness of the algorithm is based on the assumption that it is always possible to decide correctly whether two subassemblies can be joined based on geometrical and physical criteria. An approach to compute this decision is given, and bounds for the amount of computation required are presented