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Motion planning using adaptive random walks
Abstract
We propose a novel single-shot motion-planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement, and the solution it produces can be easily and efficiently optimized. Furthermore, the algorithm can incorporate adaptive components, so the developer is not required to specify all the parameters of the random distributions involved, and the algorithm itself can adapt to the environment it is moving in. Proofs of the theoretical soundness of the algorithm are provided, as well as implementation details. Numerical comparisons with well-known algorithms illustrate its effectiveness.
... Contudo, os algoritmos completos se mostraram impraticáveis devido ao tempo de processamento que requerem (Barraquand et al., 1997), (Berg and Overmars, 2004). Apesar deste fato, recentemente houve umaênfase nas pesquisas de algoritmos não somente probabilisticamente completos (Barraquand et al., 1997) como também de solucão completa e até mesmo determinísticos, apesar de o grande enfoque ainda ser nas abordagens estocásticas (Carpin and Pillonetto, 2005). ...
... Este trabalho apresenta um algoritmo de planejamento de trajetória cujo enfoqueé a grande eficiência em tempo de execução. Ele foi baseado na fusão dos métodos PAA (Carpin and Pillonetto, 2005) e MRP (Kavraki et al., 1996), de forma a gerar trajetórias sem a necessidade de um pré-processamento do ambiente e armazenando-as em um mapa de rotas, podendo assim utilizá-las posteriormente. Portanto, o algoritmo proposto será referenciado por Mapa de Rotas criado por Passeio Aleatório Adaptativo (MRPAA). ...
... O Passeio Aleatório Adaptativo (ou Adaptive Random Walk, do inglês) apresentado em (Carpin and Pillonetto, 2005) se encontra na categoria dos algoritmos de planejamento de trajetória de questionamentoúnico, ou seja, dado um ponto de início e um ponto de destino, uma trajetóriaé gerada em função desta escolha, sem a etapa de préprocessamento que ocorre em outros tipos de algoritmos, como, por exemplo, o MRP. ...
... The path planning problem consists in finding a sequence of movements for enabling a robot to leave a start configuration q start and arrive at the goal q goal without collision with the obstacles in the workspace W. To tackle this problem, several feasible algorithms have been proposed in the last years. For instance, some of them are: Probabilistic Roadmaps (PRM) [2], Rapidly-Exploring Random Trees (RRT)[3], Expansive Space Trees (EST) [4], Randomized Potential Field Planner (RPP) [5] and a less known but nonetheless important, Adaptive Random Walks (ARW) [1]. More general surveys on path planning algorithms can be found in [6], [7], [8]. ...
... However, the final path can be smoothed on a post-processing phase [9]. The simplicity and good performance of ARW [10] together with its probabilistic completeness [1] have attracted our attention, although this algorithm has been disregarded by the path planning community. This motivated the investigations and developments presented in this work. ...
... In the Adaptive Random Walk path planner [1], given a configuration q k , a neighbor configuration q k+1 is generated accordingly to a normal distribution, q k+1 ∼ N (q k , Σ k ). The sample is accepted if it is generated in C f ree and otherwise is rejected. ...
This paper presents a new path planning algorithm that uses adaptive random walks to incrementally construct a roadmap in the robot's free configuration space. This algorithm, named Incremental Adaptive Random Walks (iARW), uses a modified version of the ARW algorithm proposed by Carpin and Pillonetto for exploring the configuration space and storing the discovered path in a roadmap. Thus, the main idea is to use bidirectional adaptive random walks to explore the configuration space but also to use and expand the roadmap whenever possible.With this approach it is possible to construct a roadmap that captures the connectivity of the free configuration space without a preprocessing phase. A comparison of our approach with other state of the art path planners illustrates the good performance of the proposed method.
... These approaches all assume that each robot is individually controlled and are not directly applicable when a robot swarm is controlled with a single global control input. In our case, random walks are employed to allow the robots to avoid the collision, similarly to [21], [22], but the approach is adapted to the case of a single global control signal. ...
... When the random-walk finishes the robots are apart from each other (or possible obstacles) for at least a distance d. The proof of the completeness of the resulting algorithm is similar to [22] and is omitted due to space constraints. ...
An important problem in microrobotics is how to control a large group of microrobots with a global control signal. This paper focuses on controlling a large-scale swarm of MicroStressBots with on-board physical finite-state machines. We introduce the concept of group-based control, which makes it possible to scale up the swarm size while reducing the complexity both of robot fabrication as well as swarm control. We prove that the group-based control system is locally accessible in terms of the robot positions. We further hypothesize based on extensive simulations that the system is globally controllable. A nonlinear optimization strategy is proposed to control the swarm by minimizing control effort. We also propose a probabilistically complete collision avoidance method that is suitable for online use. The paper concludes with an evaluation of the proposed methods in simulations.
... Examples of models based on analytical models include Gaussian distribution [34], [35], [42], random tree [35], and Monte Carlo sampling strategies [34], [36]. Current research [35], [36], [38], [44]- [46] indicates that the focus is primarily on the improvement of robotic path planning using different mathematical models. However, there is no substantial evidence of any mathematical form that can be used to calculate a process of creating random motion such as Simple Random Walk (SRW) for studying the effect of static and dynamic obstacles. ...
... New approaches based on Monte Carlo random walk such as bidirectional and optimizing planner Arvand are used to improve motion-planning performance by using simple random walk. The method uses the distance measurement between the goal point and the sampled states [44]. Fast random walk approach that determines diverse and efficient paths from different Homotopy class have also been proposed to improve robotic path planning [45]. ...
... It is then a practical issue of enormous importance to merge together such partially overlapping maps before they are used by the human operators. To solve the map matching problem we have borrowed some ideas from a recent randomized motion planning algorithm recently developed by one of the authors which have turned out to work very efficiently [4], [5]. The algorithm performs a Gaussian random walk, but its novel aspect is that it updates its distribution parameters so that it can take advantage from its recent history. ...
... As the optimal value of the dissimilarity is not known, practically the algorithm will be bounded to a certain number of iterations and it will return the transformation producing the lowest ψ value. We wish to outline that this algorithm is a modification of the Adaptive Random Walk motion planner we have recently introduced [4]. The fundamental difference is that in motion planning one has to explore the space of configurations in order to reach a known target point, while in this case this information is not available. ...
We address the problem of merging multiple noisy maps in the rescue environment. The problem is tackled by performing a stochas- tic search in the space of possible map transformations. The proposed technique has its roots in a motion planning algorithm we recent devel- oped, and turns out to be a generalization of other search techniques like hill-climbing or simulated annealing. We provide the proofs of its probabilistic convergence and we provide numerical examples of its per- formance while merging partial maps build by our rescue robots.
... They will be described in section 2.1 where they will be related to the technique we present in this section. The algorithm was inspired by a motion planning algorithm one of the authors recently developed [12],[13],[14] , and by the recent successful application of motion planning algorithms to bioinformatics problems like ligand binding and protein folding [9],[15]. In a sense, the problems of ligand binding and map merging are not so different. ...
... In addition, one is relieved from the daunting task of fine tuning the parameters, i.e. determining good values for µ k and Σ k . This was indeed the lesson that was learned while developing the motion planner described in [14]. Algorithm 1 illustrates how the stochastic machinery described before can be turned into an algorithmic searching procedure. ...
We illustrate our experience in developing and implementing algorithms for map merging, i.e., the problem of fusing two or more partial maps without common reference frames into one large global map. The partial maps may for example be acquired by multiple robots, or during several runs of a single robot from varying starting positions. Our work deals with low quality maps based on probabilistic grids, motivated by the goal to develop multiple mobile platforms to be used in rescue environments. Several contributions to map merging are presented. First of all, we address map merging using a motion planning algorithm. The merging process can be done by rotating and translating the partial maps until similar regions overlap. Second, a motion planning algorithm is presented which is particular suited for this task. Third, a special metric is presented which guides the motion planning algorithm towards the goal of optimally overlapping partial maps. Results with our approach are presented based on data gathered from real robots developed for the RoboCupRescue real robot league.
... After each step the list is resorted by pairs of neighbouring segments. Path smoothing can be performed using a divide-and-conquer algorithm which removes all path points between the first and the last point in one recursion step if the direct path between them is allowed, and otherwise bisects the path points list (Carpin, S.;Pillonetto G., 2006). However, these approaches are not valid for the application we envisage because they do not guarantee a similarity between the original and the smoothed path. ...
... After each step the list is resorted by pairs of neighbouring segments. Path smoothing can be performed using a divide-and-conquer algorithm which removes all path points between the first and the last point in one recursion step if the direct path between them is allowed, and otherwise bisects the path points list (Carpin, S.;Pillonetto G., 2006). However, these approaches are not valid for the application we envisage because they do not guarantee a similarity between the original and the smoothed path. ...
We present an anytime-capable fast deterministic greedy algorithm for smoothing piecewise linear paths consisting of connected linear segments. With this method, path points with only a small influence on path geometry (i.e. aligned or nearly aligned points) are successively removed. Due to the removal of less important path points, the computational and memory requirements of the paths are reduced and traversing the path is accelerated. Our algorithm can be used in many different applications, e.g. sweeping, path finding, programming-by-demonstration in a virtual environment, or 6D CNC milling. The algorithm handles points with positional and orientational coordinates of arbitrary dimension.
... If no collision is detected, the child node is expanded until a path connecting the start and end points is established, ensuring efficiency and asymptotic optimality. Common sampling-based planning algorithms include adaptive random walks (Carpin and Pillonetto 2005), Probabilistic Road Map (Velagic et al 2014), and rapidly-exploring random trees (RRT) (Sun and Chen 2015). Among sampling-based algorithms, the RRT algorithm excels in guiding the search direction through random sampling points to avoid redundant exploration of known areas, thereby conserving computing resources. ...
The technology of mining filling is of great significance in improving coal recovery rates, protecting the environment, and conserving land resources. The current efficiency of filling is constrained by single-method approaches. To address this issue, this study develops a path planning model based on underground fill space data, which comprehensively considers fill path length and material volume using a goal programming method, and designs corresponding constraints and adaptive weights. To further optimize search efficiency, an adaptive directional bidirectional rapidly-exploring random tree (AD-BIRRT) algorithm is proposed. This algorithm can intelligently adjust the optimal exploration direction based on current demand and state, significantly enhancing search efficiency and accuracy through the establishment of a dual-tree structure. Additionally, a novel greedy strategy is introduced to resolve path smoothing and redundancy issues. To verify the rationality and effectiveness of the proposed method, comparative tests were conducted in test scenarios, fill scenarios, and on experimental platforms against BIRRT, BIRRT*, Genetic algorithm, and artificial potential field algorithms. The results indicate that the proposed greedy AD-BIRRT algorithm exhibits significant advantages in terms of computation time, path quality, and material accumulation. This algorithm effectively enhances the efficiency and quality of the filling process.
... • SAs (Kavraki et al. 1996;LaValle 1998;Karaman and Frazzoli 2011;LaValle and Kuffner 2001;Elbanhawi and Simic 2014;Hsu and Zheng 2004;Bohlin and Kavraki 2000;Akbaripour et al. 2017;LaValle et al. 2004;Lengyel et al. 1990;Stentz 1994;Radhakrishnan 2014;Dale and Amato 2001;Dash et al. 2003;Carpin and Pillonetto 2005;Barraquand and Latombe 2016;Kuffner and LaValle 2000;Atramentov and LaValle 2002;Ferguson and Stentz 2006;Lee et al. 2008;Diankov and Kuffner 2007;Jaillet et al. 2010;Chu et al. 2012;Kavraki et al. 1998;Donald et al. 2001;Berenson et al. 2011;Jaillet and Porta 2012;Quinlan 1995;Quinlan and Khatib 1993;Ademovic and Lacevic 2016;Qureshi et al. 2013aQureshi et al. , b, 2016Lin and Saripalli 2017;Kuwata et al. 2008;Wang et al. 2017;Suh et al. 2017;Qureshi and Ayaz 2015;Noreen et al. 2017;Wei and Ren 2018;Kang et al. 2019;McMahon et al. 2018), such as PRM-and RRTbased algorithms. • OAs, such as APF in Khatib (1986), Siciliano (2009), Oriolo (2020, Rasekhipour et al. (2018), Khosla (1987, 1990), Faverjon and Tournassoud (1987), Koditschek (1987), Khosla and Volpe (1988), Leica et al. (2014) and Agirrebeitia et al. (2005) Montiel et al. (2015), EAs in Aghababa (2012), Wang et al. (2016Wang et al. ( , 2020 and Kim et al. (2018), and NF in Barraquand and Latombe (2016) (SA-based) and Campana et al. (2016), Koditschek and Rimon (1990), Quillen et al. (2019), Kowalczyk et al. (2017), Kowalczyk (2018) and Tao and Tan (2018). ...
Autonomous robotics has permeated several industrial, research and consumer robotic applications, of which path planning is an important component. The path planning algorithm of choice is influenced by the application at hand and the history of algorithms used for such applications. The latter is dependent on an extensive conglomeration and classification of path planning literature, which is what this work focuses on. Specifically, we accomplish the following: typical classifications of path planning algorithms are provided. Such classifications rely on differences in knowledge of the environment (known/unknown), robot (model-specific/generic), and constraints (static/dynamic). This classification however, is not comprehensive. Thus, as a resolution, we propose a detailed taxonomy based on a fundamental parameter of the space, i.e. its ability to be characterized as a set of disjoint or connected points. We show that this taxonomy encompasses important attributes of path planning problems, such as connectivity and partitioning of spaces. Consequently, path planning spaces in robotics may be viewed as simply a set of points, or as manifolds. The former can further be divided into unpartitioned and partitioned spaces, of which the former uses variants of sampling algorithms, optimization algorithms, model predictive controls, and evolutionary algorithms, while the latter uses cell decomposition and graph traversal, and sampling-based optimization techniques.This article achieves the following two goals: The first is the introduction of an all-encompassing taxonomy of robotic path planning. The second is to streamline the migration of path planning work from disciplines such as mathematics and computer vision to robotics, into one comprehensive survey. Thus, the main contribution of this work is the review of works for static constraints that fall under the proposed taxonomy, i.e., specifically under topology and manifold-based methods. Additionally, further taxonomy is introduced for manifold-based path planning, based on incremental construction or one-step explicit parametrization of the space.
... The interesting part is that new transformations are generated using a Gaussian distribution whose parameters are updated at each iteration. This idea comes from a recent motion planning algorithm we recent developed [8]. It is possible to prove that the proposed algorithm is probabilistic complete, i.e. if enough time is allotted it will find the optimal transformation which obtains the best overlapping between the maps being considered. ...
We illustrate our progresses in developing multi-robot systems to be used for mapping in rescue scenarios. The problem we are currently investigating is to combine poor quality multiple maps produced by different robots into a single map to be used by human operators. In particular we motivate our approach and we illustrate the different techniques we implemented and that are at the moment being compared.
... Besides, the potential field method can make an instantaneous and smooth robot movement path without an additional controller, but it has a local minima problem that is caused by positions with zero force value where the robot or agent stops and cannot move any further [11,12]. There are some techniques to overcome the local minima problem, such as random walk [13,14] or backtracking. In the case of the random walk technique, it is impossible to predict the path or the processing time because of randomness. ...
There are various motion planning techniques for robots or agents, such as bug algorithm, visibility graph, Voronoi diagram, cell decomposition, potential field, and other probabilistic algorithms. Each technique has its own advantages and drawbacks, depending on the number and shape of obstacles and performance criteria. Especially, a potential field has vector values for movement guidance to the goal, and the method can be used to make an instantaneous and smooth robot movement path without an additional controller. However, there may be some positions with zero force value, called local minima, where the robot or agent stops and cannot move any further. There are some solutions for local minima, such as random walk or backtracking, but these are not yet good enough to solve the local minima problem. In this paper, we propose a novel movement guidance method that is based on the water sink model to overcome the previous local minima problem of potential field methods. The concept of the water sink model is to mimic the water flow, where there is a sink or bathtub with a plughole and floating piece on the water. The plughole represents the goal position and the floating piece represents robot. In this model, when the plug is removed, water starts to drain out via the plughole and the robot can always reach the goal by the water flow. The water sink model simulator is implemented and a comparison of experimental results is done between the water sink model and potential field.
... These approaches attempt to capture free-space connectivity by constructing a graph. The roadmap approaches include the probabilistic roadmap method (Yuan et al., 2015), the rapidly exploring random tree (Kuffner and Latombe, 2000;Moon and Chung, 2015), the expansive space planner (Hsu et al., 1997) and the random walk planner (Carpin and Pillonetto, 2005;Lu et al., 2016). Computational geometry-based methods comprise another branch of roadmap-based approaches, which 2 H A N L I N N I U A N D O T H E R S include the Voronoi diagram (Wu et al., 2013) and the Visibility graph (Kaluder et al., 2011;Zimmermann and Konig, 2016). ...
In this paper, a novel Voronoi-Visibility (VV) path planning algorithm, which integrates the merits of a Voronoi diagram and a Visibility graph, is proposed for solving the Unmanned Surface Vehicle (USV) path planning problem. The VM (Voronoi shortest path refined by Minimising the number of waypoints) algorithm was applied for performance comparison. The VV and VM algorithms were compared in ten Singapore Strait missions and five Croatian missions. To test the computational time, a high-resolution, large spatial dataset was used. It was demonstrated that the proposed algorithm not only improved the quality of the Voronoi shortest path but also maintained the computational efficiency of the Voronoi diagram in dealing with different geographical scenarios, while also keeping the USV at a configurable clearance distance c from coastlines. Quantitative results were generated by comparing the Voronoi, VM and VV algorithms in 2,000 randomly generated missions using the Singapore dataset.
... Trajectory planning for robotic vehicles is a problem diversely analyzed in literature, with many examples of developed techniques to overcome it such as Probabilistic Roadmaps [2], Adaptive Random Walk [3], Potential Fields [4], among others using mainly probabilistic methods. ...
... The roadmap method attempts to capture the free-space connectivity with a graph. The sampling-based roadmap method includes probabilistic roadmap method (Amato and Wu, 1996) (Kavraki and Latombe, 1998), rapidly exploring random tree (Kuffner and Latombe, 2000) (Kuffner and LaValle, 2000), expansive space planner (Hsu et al., 1997) and random walk planner (Carpin and Pillonetto, 2005). Some other well known roadmap based approaches based on computational geometry include Visibility graph and Voronoi diagram (Pehli-vanoglu, 2012) (Candeloro et al., 2017). ...
The sea current state affects the energy consumption of Unmanned Surface Vehicles (USVs) significantly and the path planning approach plays an important role in determining how long the USV can travel. To improve the endurance of the USV, an energy efficient path planning approach for computing feasible paths for USVs that takes the energy consumption into account based on sea current data is proposed. The approach also ensures that the USV remains at a user-configurable safety distance away from all islands and coastlines. In the proposed approach, Voronoi diagram, Visibility graph, Dijkstra's search and energy consumption function are combined, which allows USVs to avoid obstacles while at the same time using minimum amount of energy. The Voronoi-Visibility (VV) energy-efficient path and the corresponding shortest path were simulated and compared for ten missions in Singapore Strait and five missions for islands off the coast of Croatia. Impact of parameters such as mission time, the USV speed and sea current state on the results were analysed. It is shown that the proposed VV algorithm improves the quality of the Voronoi energy efficient path while keeping the same level of computational efficiency as that of the Voronoi energy efficient path planning algorithm.
... Numerous methods for flight trajectory planning in no-wind cases have been proposed. There are algorithms based on randomness, e.g., random-walk [3], rapidly exploring random trees (RRT) [8] or randomized potential fields [2]. These methods are fast but they are still based on random sampling and generally cannot find optimal solutions with respect to given criteria. ...
When operating autonomous unmanned aerial vehicles (UAVs) in real environments it is necessary to deal with the effects of wind that causes the aircraft to drift in a certain direction. In such conditions it is hard or even impossible for UAVs with a bounded turning rate to follow certain trajectories. We designed a method based on an Accelerated A* algorithm that allows the trajectory planner to take the wind effects into account and to generate states that are reachable by UAV. This method was tested on hardware UAV and the reachability of its generated trajectories was compared to the trajectories computed by the original Accelerated A*.
... The problem is still topical as all intelligent autonomous vehicles have to include path planning into their deliberation mechanisms. There exist very efficient (fast) algorithms based on randomness, e.g. the random-walk planner (Carpin and Pillonetto 2005b), the rapidly exploring random tree Copyright c 2009, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. ...
The paper describes an application of the A* algorithm for flight path planning for airplanes with defined motion dy-namics operating in a continuous three-dimensional space constrained by existing physical obstacles. The presented A* algorithm modification provides significant acceleration (reduction of the state space) of the path planning process. The described algorithm is able to find a path through small gaps between obstacles using a pre-defined searching preci-sion. The paper documents a set of path planning benchmarks where the solution quality and internal algorithm properties are compared against the A* algorithm for flight trajectory path planning.
... Furthermore, the algorithm can incorporate adaptive components in order to be adapted to particular problems. Proofs of the theoretical soundness of the algorithm are provided in [4]. After the kinematic evaluation, the optimization algorithms will edit the keypoints in order to make a smoother robot trajectory. ...
This paper presents a motion optimization system for an industrial quality inspection process where a vision device coupled with a manipulator robot arm is able to perform quality and completeness inspection on a complex solid part. In order to be deployed in an industrial production plant, the proposed system has been engineered and integrated as a module of an offline simulator, called WorkCellSimulator, conceived to simulate robot tasks in industrial environments. The novelty of the paper concerns the introduction of time constraints into the motion planning algorithms. Then, these algorithms have been deeply integrated with artificial intelligence techniques in order to optimize the inspection cycle time. This integration makes the application suitable for timeconstrained processes like, e.g., autonomous industrial painting or autonomous
thermo-graphic detection of cracks in metallic and composite materials.
... RPP used random walks to escape local minima of the potential field planner. Later on, a planner based entirely on random walks, with adaptive parameters, was proposed [52]. The work of Barraquand and Latombe [51] paved the way for a new generation of motion planning algorithms that employ randomization. ...
Motion planning is a fundamental research area in robotics. Sampling-based methods offer an efficient solution for what is otherwise a rather challenging dilemma of path planning. Consequently, these methods have been extended further away from basic robot planning into further difficult scenarios and diverse applications. A comprehensive survey of the growing body of work in sampling-based planning is given here. Simulations are executed to evaluate some of the proposed planners and highlight some of the implementation details that are often left unspecified. An emphasis is placed on contemporary research directions in this field. We address planners that tackle current issues in robotics. For instance, real-life kinodynamic planning, optimal planning, replanning in dynamic environments, and planning under uncertainty are discussed. The aim of this paper is to survey the state of the art in motion planning and to assess selected planners, examine implementation details and above all shed a light on the current challenges in motion planning and the promising approaches that will potentially overcome those problems.
... Thus this method is often used for multiple-query problems. Rapidly-Exploring Random Trees (RRT) were proposed later, as a single-query fast exploring method [23]. This method starts exploring from the start configuration, where a tree of connected configuration is incrementally grown. ...
Abstract— Sampling based algorithms provide efficient methods of solving robot motion planning problem. The advantage of these approaches is the ease of their implementation and their computational efficiency. These algorithms are probabilistically complete i.e. they will find a solution if one exists, given a suitable run time. The drawback of sampling based planners is that there is no guarantee of the quality of their solutions. In fact, it was proven that their probability of reaching an optimal solution approaches zero. A breakthrough in sampling planning was the proposal of optimal based sampling planners. Current optimal planners are characterized with asymptotic optimality i.e. they reach an optimal solutions as time approaches infinity. Motivated by the slow convergence of optimal planners, post-processing and heuristic approach have been suggested. Due to the nature of the sampling based planners, their implementation requires tuning and selection of a large number of parameters that are often overlooked. This paper presents the performance study of an optimal planner under different parameters and heuristics. We also propose a modification in the algorithm to improve the convergence rate towards an optimal solution.
... In this sense it differs from the major industrial robotics simulator, such that developed by KUKA, ABB or Fanuc [4-6], which are fully dedicated to a specific robotic manipulator. In detail, WorkCellSimulator has been developed by using the most advanced artificial intelligent algorithms, and motion and task planning approaches used to automatically generate the free obstacles trajectories, which optimize a given objective function (execution time, effort on the part, etc.) [7][8][9][10]. Moreover, its architecture allows the definition of algorithms for advanced task planning, such as for generating the optimal folding sequence in metal sheet bending process [11]. ...
This paper presents WorkCellSimulator, a software platform that allows to manage an environment for the simulation of robot tasks. It uses the most advanced artificial intelligence algorithms in order to define the production process, by controlling one or more robot manipulators and machineries present in the work cell. The main goal of this software is to assist the user in defining customized production processes which involve specific automated cells. It has been developed by IT+Robotics, a spin-off company of the University of Padua, founded in 2005 from the collaboration between young researchers in the field of Robotics and
a group of professors from the Department of Information Engineering, University of Padua.
... Once agent A 0 proves to be reliable and is thoroughly debugged, it remains unchanged and serves as the embryo for a cooperative society of agents, where higher levels of competence are pursued. In its primal phase, A 0 does not communicate with any other robot control agents, yet its neural reactor, acting as a compulsive behavior initiator, induces in the robot a class of behavior known as random walk [13]. The pursuing of random movement in isolated conditions confers the proposed route planning agents (RPA) their " proactiveness " [2]. ...
We have studied and developed the behavior of two specific neural processes, used for vehicle driving and path planning, in order to control mobile robots. Each processor is an independent agent defined by a neural network trained for a defined task. Through simulated evolution fully trained agents are encouraged to socialize by opening low bandwidth, asynchronous channels between them. Under evolutive pressure agents spontaneously develop communication skills (protolan-guage) that take advantages of interchanged information, even under noisy conditions. The emerged cooperative behavior raises the level of competence of vision guided mobile robots and allows a convenient autonomous exploration of the environment. The system has been tested in a simulated location and shows a robust performance.
... These approaches may be divided into two basic groups – algorithms optimizing the speed of the solution and algorithms optimizing the quality of the solution in terms of the length of the final plan. The first group uses random techniques to find the plan – the random walk planner [1], the rapidly exploring random tree (RRT) [2] and the randomized potential field [3], [4]. The other group of the planners is driven by an optimality criterion. ...
The paper provides a description of an iterative version of the Accelerated A* algorithm for path planning and its application in the air traffic domain for airplanes with defined motion dynamics operating in the Earth-centered, Earth-fixed coordinate system (GPS) on a spherical model of the Earth constrained by the landscape and special use airspaces (SUA). The motion dynamics of the airplanes is modeled using the Base of Aircraft Data (BADA) airplane performance models. The presented algorithm provides an extension of the A* algorithm that significantly reduces the search space and makes planning of the flight trajectories computationally tractable.
... In [13], where we introduced the general idea of brokenness, a map merging algorithm introduced in [32] was used for the steps in lines 5 to 7 of algorithm 1. This map merging algorithm builds upon a (dis)similarity measure of 2D raster data sets using Manhattan distances between nearest neighbors with the same cell property [34] combined with an Adaptive Random Walk [35], [36], [37] to stochastically search the space of possible transformations. In addition, a correlation metric is used to avoid convergence to local optima. ...
There are many common error sources that influence mapping, e.g., salt and pepper noise as well as other effects occurring quite uniformly distributed over the map. On the other hand, there are also errors, which occur very rarely but with severe effects. These errors influence not only the local accuracy but the overall spatial layout of the map. Concrete examples include bump noise in the robot's pose or residual errors in Simultaneous Localization and Mapping (SLAM). Brokenness is presented here to capture one form of structural errors in grid maps. Concretely, brokenness measures the degree with which a map can be partitioned into regions that are locally consistent with ground truth but “off” relative to each other. The concept of brokenness is presented in a formal way and it is shown how it can be computed in an efficient way using recursive spectral registrations. Experimental results show that the metric can indeed be used to automatically determine one structural quality aspect of a map in a quantitative way.
... After each step the list is re-sorted by pairs of neighbouring segments. Path smoothing can be performed using a divide-and-conquer algorithm which removes all path points between the first and the last point in one recursion step if the direct path between them is allowed, and otherwise bisects the path points list [7] . However, these approaches are not valid for the application we envisage because a similarity between the original and the smoothed path can not be guaranteed. ...
We present an anytime fast deterministic greedy method for smoothing piecewise linear paths consisting of con- nected linear segments by incrementally removing path points. First, points with only a small influence on path geometry are re- moved, i.e. aligned or nearly aligned points. Due to the removal of less important path points, the high computational and storage space requirements of the paths are reduced and traversal of the path is accelerated. Our algorithm can be used in the most diverse applications, i.e. sweeping, path finding or programming-by- demonstration in a virtual environment.
Autonomous exploration in unstructured indoor settings requires effective navigation approaches to manage obstacles, dead ends, and resource constraints. Conventional algorithms, like the TurtleBot3 Drive (TB3), frequently struggle with inadequate area coverage, inefficient obstacle management, and substantial computational demands. This study presents the Intelligent Exploration (IE) algorithm, an innovative method that integrates an improved random walk technique, real-time LiDAR-based obstacle avoidance, and a strategic back-off mechanism to optimize exploration efficiency. Detailed simulations using the TurtleBot3 Burger in the Gazebo simulator under the ROS Noetic framework, performed from various starting positions and over different time intervals (ranging from 2 to 15 minutes), demonstrated the efficiency of the proposed method when integrated with SLAM Gmapping. The IE algorithm consistently surpassed the baseline TurtleBot3 Drive (TB3) algorithm across critical metrics, attaining a 35% increment in coverage area (16.25 m² vs 11.99 m²), traversing 35% longer distances (113.95 m vs 84.07 m), and identifying 17% more obstacles (137.82 vs 118.11). The algorithm maintained a reliable average localization error of 0.005 m while exhibiting memory efficiency by the reduced memory usage by up to 13.7% relative to TB3. By addressing limitations in coverage, obstacle handling, and resource efficiency, the IE algorithm provides a scalable and lightweight solution for autonomous indoor exploration, particularly on resourceconstrained robotic systems.
Autonomous robotic path planning in partially known environments, such as warehouse robotics, deals with static and dynamic constraints. Static constraints include stationary obstacles, robotic and environmental limitations. Dynamic constraints include humans, robots and dis/appearance of anticipated dangers, such as spills. Path planning consists of two steps: First, a path between the source and target is generated. Second, path segments are evaluated for constraint violation. Sampling algorithms trade memory for maximal map representation. Optimization algorithms stagnate at non-optimal solutions. Alternatively, detailed grid-maps view terrain/structure as expensive memory costs. The open problem is thus to represent only constraint-free, navigable regions and generating anticipatory/reactive paths to combat new constraints. To solve this problem, a Constraint-Free Discretized Manifolds-based Path Planner (CFDMPP) is proposed in this paper. The algorithm’s first step focuses on maximizing map knowledge using manifolds. The second uses homology and homotopy classes to compute paths. The former constructs a representation of the navigable space as a manifold, which is free of apriori known constraints. Paths on this manifold are constraint-free and do not have to be explicitly evaluated for constraint violation. The latter handles new constraint knowledge that invalidate the original path. Using homology and homotopy, path classes can be recognized and avoided by tuning a design parameter, resulting in an alternative constraint-free path. Path classes on the discretized constraint-free manifold characterize numerical uniqueness of paths around constraints. This designation is what allows path class characterization, avoidance, and querying of a new path class (multiple classes with tuning), even when constraints are simply anticipatory.
The multi-robot system is employed to map the different parts of the indoor environment because it maps more quickly than a single robot. Two robots are used in the multi-robot system, each robot is equipped with 2D LIDAR and made to drive in an environment to develop occupancy grid maps. However, the main challenge in multi-robot mapping is to combine the occupancy grid map data from various robots into a single global map. Numerous studies have been conducted on ways to estimate the relative robot poses before or during the mapping process in multi-robot mapping. However, with map merging, the robots create local occupancy grid maps on their own without being aware of how they relate to one another. The next step is to find points where the local maps overlap to combine them. After finding the overlap between the two maps, the merging algorithm is implemented to combine the maps. Results from experiments with two robots are presented.
Lifting operations of mobile cranes are one of the commonly-seen and most important activities for prefabrication housing production (PHP) on sites. However, relevant operations are normally based on the experience of operators or project managers, this often leads to low efficiency as well as high accident rate due to dynamic and complex construction sites. Thus, it is important and necessary to develop an appropriate approach to the lifting planning of mobile cranes so as to guide on-site operations. This paper proposes an improved Rapidly-exploring Random Tree (RRT) algorithm for lifting path planning of mobile cranes. Considering the critical role of Nearest Neighbor Search (NNS) in the implementation of RRT algorithm, a novel strategy for searching the nearest neighbor is developed, i.e., Generalized Distance Method and Cell Method. Both methods are tested in simulation-based experiments. The results show that 1) the Generalized distance method not only reduces the search time, but also unifies the unit of distance measurement and clarifies the physical meaning of distance; 2) the Cell method dramatically reduces the traversal range as well as the search time; and 3) both methods improve the quality of lifting path planning of mobile cranes. This improved RRT algorithm enables rapid path planning of mobile cranes in a dynamic and complex construction environment. The outcomes of this research not only contribute to the body of knowledge in spatial path planning of crane lifting operations, but also have the potential of significantly improving efficiency and safety in crane lifting practices.
The main contribution of this article is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph search, i.e., a discrete roadmap method, with convex optimization, i.e., a complete path method. Contrary to past approaches, which have focused on using simple obstacle approximations, or suboptimal spatial discretizations, our approach is able to use the exact geometry of polygonal constraints in order to plan optimal trajectories. The performance and flexibility of the proposed method are evaluated via simulations by planning distance-optimal trajectories for a Dubins car model, as well as time-, distance-, and energy-optimal trajectories for a marine vehicle.
Autonomous industrial mobile manipulation systems (AIMMS) are widely used in manufacturing processes. AIMMS can help with part handling and delivering, part insertion and extraction, loading and unloading, and some other auxiliary tasks in a machine tending workshop environment. However, nowadays most AIMMS cannot truly realize the complete automation because the path for the mobile platform needs setting in advance in terms of different environment and inspection need to be executed to ensure safety due to lack of proper path planning algorithms. Therefore, this paper proposes an improved path-planning algorithm based on Rapidly-exploring Random Tree (RRT) and the quintic B-spline curve technique to generate a collision-free and smoother path for our designed Novel Self-adapting Intelligent Machine Tending Robotic System in the workspace. In the end, the proposed algorithm is demonstrated to generate paths for five different scenarios to test its performance and reliability.
Three algorithms that improve the performance of the asymptotically optimal Rapidly exploring Random Tree (RRT∗) are presented in this paper. First, we introduce the Goal Tree (GT) algorithm for motion planning in dynamic environments where unexpected obstacles appear sporadically. The GT reuses the previous RRT∗ by pruning the affected area and then extending the tree by drawing samples from a shadow set. The shadow is the subset of the free configuration space containing all configurations that have geodesics ending at the goal and are in conflict with the new obstacle. Smaller, well defined, sampling regions are considered for Euclidean metric spaces and Dubins' vehicles. Next, the Focused-Refinement (FR) algorithm, which samples with some probability around the first path found by an RRT∗, is defined. The third improvement is the Grandparent-Connection (GP) algorithm, which attempts to connect an added vertex directly to its grandparent vertex instead of parent. The GT and GP algorithms are both proven to be asymptotically optimal. Finally, the three algorithms are simulated and compared for a Euclidean metric robot, a Dubins' vehicle, and a seven degrees-of-freedom manipulator.
Currently there is growing interest in motion planning problems that play a key role in automation of technologically difficult processes in mechanical, power and transport engineering, medicine, construction and creation of new products and services. This interest particularly relates to the increasing role of computer simulation and such disciplines as complex planning of industrial projects, realistic 3D animation, robotic surgery, automotive products assembly and organization of movement of transport streams. This paper is devoted to the overview and analysis of modern motion planning methods.
This chapter first provides a formulation of the geometric path planning problem in Sect. 7.2 and then introduces sampling-based planning in Sect. 7.3. Sampling-based planners are general techniques applicable to a wide set of problems and have been successful in dealing with hard planning instances. For specific, often simpler, planning instances, alternative approaches exist and are presented in Sect. 7.4. These approaches provide theoretical guarantees and for simple planning instances they outperform sampling-based planners. Section 7.5 considers problems that involve differential constraints, while Sect. 7.6 overviews several other extensions of the basic problem formulation and proposed solutions. Finally, Sect. 7.8 addresses some important and more advanced topics related to motion planning.
This paper presents the combination of Potential Flow Field (PFF) and Virtual Force Field (VFF) methods to construct a viable means for UAS's to autonomously navigate and avoid collisions with obstacles. A validated flight dynamics model of a fixed-wing UAS was integrated with a heading hold autopilot that receives commanded heading angles from the selected output of the PFF and VFF methods. PFF primarily provides real-time heading angle commands derived from a velocity vector field. VFF provides collision avoidance heading angle commands when it calculates and determines that the UAS is in danger of collision with an obstacle. The combination of the two methods resulted in successful collision-free navigation in simulation through multiple scenarios including single obstacle, multiple obstacles, maze, and urban settings.
In this chapter, we describe an industrial inspection system composed by a 3D vision system, mounted on a manipulator robot arm
, able to perform quality and completeness inspection on a complex solid part. The novelty of the system is in the deep integration among three software modules: the visual inspection system
, the 3D simulation software, and the motion planning
engine of the manipulator robot. This enables an automatic off-line programming of the robot path by specifying in the system the desired inspection tasks. The system automatically generates the needed points of view in order to perform 3D reconstruction and automatic visual inspection. Moreover, the motion planning system can reorder the inspection points in order to optimize the inspection cycle time. The core of this system was developed in the European Project “Thermobot,” and currently, it is been engineered to be deployed in an industrial production plant.
To reach a fruit in an obstacle-dense crop environment, robotic fruit harvesting requires a collision-free motion of the manipulator and end-effector. A novel two-part analysis was conducted of a sweet-pepper harvesting robot based on data of fruit (N = 158) and stem locations collected from a greenhouse. The first part of the analysis compared two methods of selecting the azimuth angle of the end-effector. The new ‘constrained-azimuth’ method avoided risky paths and achieved a motion planning success similar to the ‘full-azimuth’ method. In the second part, a sensitivity analysis was conducted for five parameters specifying the crop (stem spacing and fruit location), the robot (end-effector dimensions and robot position) and the planning algorithm, to evaluate their effect on successfully finding a collision-free goal configuration and path. Reducing end-effector dimensions and widening stem spacing are promising research directions because they significantly improved goal configuration success, from 63% to 84%. However, the fruit location at the stem is the strongest influencing parameter and therefore provides an incentive to train or breed plants that develop more fruit at the front side of the plant stem. The two analyses may serve as useful tools to study motion planning problems in a dense obstacle environment.
Our planner allows the extraction of the metal sheets from a press-brake. Since the solution must respect safety standard, this operation can be very complex. For this reason it is useful to usean automatic system to plan these operations. Thus, we have developed a specific planning algorithm, called EFT (Exit from Tools), that utilizes a hybrid approach, combining a probabilistic roadmap with standard operations on the Cartesian configuration space. In addition, our algorithm has the important feature to be automatically reconfigurable. We performed several tests solving a set of critical real cases by WorkCellSimulator, an industrial software system for simulating manufacturing processing.
Path planning is a critical task for search and rescue mission in Mobile Ad-hoc Rescue Network in natural or unnatural catastrophes. However, most existing path planning schemes fail to cope with the challenges in post-disaster map environment due to its increased complexity and uncertainty. To address these issues, we propose a Hierarchical Random Walk based path Planner (HRWP). In HRWP, Regular Grid and Voronoi Diagram are used to model the map, and uncertain map segments are assigned uncertain cost using random variables. The hierarchical random walk is then designed to generate the optimal path using probabilistic accept-reject. In this way, results of HRWP can significantly reduce the risk of uncertainty and converge to the optimal path. Using a combination of analytical modeling and extensive simulations we show that HRWP outperforms existing path planer and mobility schemes, and performs well in complicated environments.
We present an approach to controlling multiple mobile robots without requiring system identification, geometric map building, localization, or state estimation. Instead, we purposely design them to execute wild motions, which means each will strike every open set infinitely often along the boundary of any connected region in which it is placed. We then divide the environment into a discrete set of regions, with borders delineated with simple markers, such as colored tape. Using simple sensor feedback, we show that complex tasks can be solved, such as patrolling, disentanglement, and basic navigation. The method is implemented in simulation and on real robots, which for many tasks are fully distributed without any mutual communication.
A smooth path generation scheme based on integrating rapidly-exploring random tree (RRT) with island parallel variable-length genetic algorithm with migration is presented for finding G3-continuous η3-spline paths that minimize a quality measure combining path length and curvature. By injecting RRT solutions into an isolated initial subpopulation and occasional migration to allow the competition and mixture of genetic information between the best individuals of subpopulations whenever feasible paths are discovered in other islands, the hybrid approach discovers smoother path more efficiently while maintaining the diversity of evolutionary optimizer and preventing the premature due to the RRT injection. The simulation results in complex maps demonstrated the advantage of RRT-injection in our implementation, and the hybrid approach is quite flexible and adaptive to generate paths with achievable smoother curvature profile at the expense of a little increased runtime and/or path length.
As a continuing work on G3-continuous path planning for nonholonomic wheeled unicycle-type nonholo-nomic mobile robot in the predefined static environment, this paper accounts for a multi-objective path optimization problem that directly incorporates the objectives of simultaneously minimizes the total path length and the maximum curvature along the path. Using easily customized variable-length Island-based Parallel Genetic Algorithm (IPGA) as a path computing framework and η3-splines as the path primitive for waypoint interpolation, a multi-objective genetic algorithm is implemented to find and optimize multiple collision-free paths to obtain a G3-continuous composite η3-spline path with each η3-spline segment shorter and a larger minimum turning radius along the whole path. By comparing with the corresponding single-objective implementation, the experimental result demonstrates the effectiveness of the evolutionary multi-objective path planner in finding paths of more practical value in complex environments.
This paper presents a novel evolutionary G3-continuous (continuous-differentiable curvature) path planner for nonholonomic wheeled mobile robots. The evolutionary path planner generates intermediate configurations connected via η3-splines that yields a collision-free G3-continuous path, which each point on the path has a closed-form expression. The path planner is implemented as architecture of island parallel genetic algorithm (IPGA) running a variable-length genetic algorithm in each island. The techniques of spatial fitness-sharing in search space and a crowded measure of generated paths are integrated in the planner to implement a high-diversity evolutionary optimizer of paths that could self-adjust the spacing and number of intermediate configurations. The experimental result demonstrates the robustness and self-adjusting capability of evolutionary path planner in discovering shorter and smoother composite η3-splines paths in complex environments.
The paper addresses the area of path planning for non-holonomic vehicles operating in a large-scale dynamic continuous three-dimensional space where the vehicle has to avoid given obstacles and restricted areas. For vehicles, motion dynamics is defined by means of constraints on the driving manoeuvres and restrictions on smoothness of the trajectory. The paper addresses only the basic spatial path planning problem -- a process searching for a spatial arrangement of the trajectory from the given start position and orientation to the given target position and orientation. Extended problems like incremental planning are not considered by this paper. The dynamic environment means that obstacles' and restricted areas' definitions are altered almost after each particular search.
Manipulator robots working in changing environments need special path planners that provide good solutions in short times. In this work we describe a sample-based path planning algorithm that is suitable for such environments. Our approach is based on two points. Firstly, unlike most sampling techniques, we have defined a non-random local sampling which reduces the computational time greatly. Secondly, a set of interpolated walks is obtained through cubic splines which guarantee the smoothness and continuity of the walks. This path planning algorithm is part of a full intelligent manipulation system based on D vision
... This paper provides foundations for understanding the effect of passages on the connectedness of probabilistic roadmaps. It also proposes a new random sampling scheme for finding such passages. An initial roadmap is built in a "dilated" free space allowing some penetration distance of the robot into the obstacles. This roadmap is then modified by resampling around the links that do not lie in the true free space. Experiments show that this strategy allows relatively small roadmaps to reliably capture the free space connectivity
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.
This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query—instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional—it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions—it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques and those of delayed collision checking reinforce each other. Experimental results show that this combination reduces planning time by a large factor, making it possible to efficiently handle difficult planning problems, such as problems involving multiple robots in geometrically complex environments. This paper specifically describes the application of the planner to multi-robot planning and compares results obtained when the planner uses a centralized planning approach (PRM planning is then performed in the joint configuration space of the robots) and when it uses a decoupled approach (the PRM planner is invoked several times, first to compute a path of each robot independent of the others, and then to coordinate those paths). On a simulated six-robot welding station combining 36 degrees of freedom, centralized planning has proven to be a much more effective approach than decoupled planning.
This paper presents a novel teleoperation scheme to control a PUMA robotic manipulator with a Phan-tom haptic device. Using local force control at the slave robot, contact with soft and hard surfaces is attained with high performance. The control design inserts a virtual spring between the master and slave control systems to generate the desired forces. The closed loop performance is increased by using an ac-tive observer and on-line stiffness adaptation to the slave contact environment in its forcefeedback con-troller.
This paper presents a new finite-dimensional Bayesian filter. The filter calculates the exact analytical expression for the posterior probability density function (pdf) of static systems with kind of nonlinear measurement equation subject to Gaussian measurement uncertainty. The paper also extends this filter to a limited class of dynamic systems. The filter is applied to the estimation of the inaccurately known position and orientation of two mating parts during autonomous robotic assembly. The sufficient statistics of the posterior pdf are obtained by Kalman Filter formulas, making online estimation possible.
A simple and efficient randomized algorithm is presented for
solving single-query path planning problems in high-dimensional
configuration spaces. The method works by incrementally building two
rapidly-exploring random trees (RRTs) rooted at the start and the goal
configurations. The trees each explore space around them and also
advance towards each other through, the use of a simple greedy
heuristic. Although originally designed to plan motions for a human arm
(modeled as a 7-DOF kinematic chain) for the automatic graphic animation
of collision-free grasping and manipulation tasks, the algorithm has
been successfully applied to a variety of path planning problems.
Computed examples include generating collision-free motions for rigid
objects in 2D and 3D, and collision-free manipulation motions for a
6-DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is
also presented
This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: (1) single- query -i.e., it does not pre-compute a roadmap, but uses the two input query configurations to explore as little space as possible; (2) bi-directional i.e., it searches the robot's free space by concurrently building a roadmap made of two trees rooted at the query configurations - and (3) applies a sys- tematic lazy collision-checking strategy -i.e., it postpones collision tests along connections in the roadmap until they are absolutely needed. Several observations motivated this collision-checking strategy: (1) PRM planners spend more than 90% of their time checking collision; (2) most connec- tions in a PRM are not on the final path; (3) the collision test for a connection is the most expensive when there is no collision; and (4) the probability that a short connection is collision-free is large. The strengths of single-query and bi- directional sampling techniques, and those of lazy collision checking reinforce each other. This combination reduces planning time by large factors, making it possible to han- dle more difficult planning problems, including multi-robot problems in geometrically complex environments.
We present, implement, and analyze a spectrum of closely-related planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on the quasi-random sampling literature, we have developed deterministic variants of the PRM that use Hammersley/Halton sequences and low-discrepancy lattices. Classical grid search is extended using subsampling for collision detection and also the optimal-dispersion Sukharev grid, which can be considered as a kind of lattice-based roadmap to complete the spectrum. Both multiple-query and lazy, single-query versions are considered for each planner. Our experimental results, ...
Given a robot and a workspace, probabilistic roadmap planners (PRMs) build a roadmap of paths sampled from the workspace. A roadmap node is a single collision-free robot configuration, randomly generated. A roadmap edge is a sequence of collision-free robot configurations which interpolate the path from one roadmap node to another. Queries to the roadmap are (start, goal) pairs. If both the start and goal of a pair can be connected to the same connected component of the roadmap, the query is solved. Many promising variants of the PRM have been proposed, each with their own strengths and weaknesses. We propose a meta-planner for using many PRMs in such a way that the strengths are combined and the weaknesses offset. Our meta-planner will perform the combination in the following manner: i) provide a framework in which different motion planners are available and to which new ones are easily added; ii) characterize subregions (possibly overlapping) based on sample characteristics and connection results; iii) assign subregions to one or more planners which are judged promising; and iv) provide stopping criteria for roadmap construction. We present experimental results for four characterization measures. A general technique we call 'filtering' is presented for keeping roadmaps compact.
Describes an approach to probabilistic roadmap planners (PRMs).
The overall theme of the algorithm, called Lazy PRM, is to minimize the
number of collision checks performed during planning and hence minimize
the running time of the planner. Our algorithm builds a roadmap in the
configuration space, whose nodes are the user-defined initial and goal
configurations and a number of randomly generated nodes. Neighboring
nodes are connected by edges representing paths between the nodes. In
contrast with PRMs, our planner initially assumes that all nodes and
edges in the roadmap are collision-free, and searches the roadmap at
hand for a shortest path between the initial and the goal node. The
nodes and edges along the path are then checked for collision. If a
collision with the obstacles occurs, the corresponding nodes and edges
are removed from the roadmap. Our planner either finds a new shortest
path, or first updates the roadmap with new nodes and edges, and then
searches for a shortest path. The above process is repeated until a
collision-free path is returned. Lazy PRM is tailored to efficiently
answer single planning queries, but can also be used for multiple
queries. Experimental results presented in the paper show that our lazy
method is very efficient in practice
Recognition of contact states is often necessary or preferred in
planning and executing contact-based assembly motions in the presence of
uncertainties. However, due to inevitable uncertainties, not all contact
states can be identified at all contact configurations. A crucial
question is what kinds of contact states at what kinds of configurations
are impossible to be distinguished or identified. We address the
question by analyzing the recognizability of contact states between
convex polyhedral objects with both position/orientation and
force/moment sensing in the presence of sensing uncertainties, i.e., by
characterizing configurations where contact states are intrinsically
indistinguishable with those sensing means. To reflect contact
recognizability in contact representation, we propose a fuzzy definition
of contact states. We further introduce a practical approach towards
real-time automatic contact state identification based on the
recognizability analysis
The efficiency of the automatic execution of complex assembly tasks can be enhanced by the identification of the contact state. In this paper we derive a new method for testing a hypothesized contact state using force sensing in the presence of sensing and control uncertainty. The hypothesized contact state is represented as a collection of elementary contacts. The feasibility of the elementary contacts is tested by solving a linear program. No knowledge of the contact pressure distribution or of the contact forces is required, so our method can be used even when the contact forces are statically indeterminate. We give a geometric interpretation of the contact identification problem using the theory of polyhedral convex cones. If more than one contact state is feasible, we use the geometric interpretation to determine the likelihood of each feasible contact formation
We provide an analysis of a path planning method which uses
probabilistic roadmaps. This method has proven very successful in
practice, but the theoretical understanding of its performance is still
limited. Assuming that a path γ exists between two configurations
a and b of the robot, we study the dependence of the failure probability
to connect a and b, on: 1) the length of γ; 2) the distance
function of γ from the obstacles; 3) the number of nodes N of the
probabilistic roadmap constructed. Importantly, our results do not
depend strongly on local irregularities of the configuration space, as
was the case with previous analysis. These results are illustrated with
a simple but illuminating example. In this example, we provide estimates
for N, the principal parameter of the method, in order to achieve
failure probability within prescribed bounds. We also compare, through
this example, the different approaches to the analysis of the planning
method
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 describes a rigorous Bayesian approach to model selection and state estimation for sensorbased robot tasks. The approach is illustrated with an example from autonomous compliant motion: simultaneous Contact Formation recognition and estimation of geometrical parameters. Previous research in this area tries to solve one of the two subproblems, or treats the Contact Formation recognition problem separately, avoiding interaction between the Contact Formation recognition and the geometrical parameter estimation problems. This limits the execution of the task to execution under small uncertainties. This research allows the robot to handle more uncertainty during the execution of its sensor-based task through the estimation of a hybrid joint density of both unknown model and state variables.
The choice of a suitable MCMC method and further the choice of a proposal distribution is known to be crucial for the convergence of the Markov chain. However, in many cases the choice of an effective proposal distribution is difficult. As a remedy we suggest a method called Adaptive Proposal (AP). Although the stationary distribution of the AP algorithm is slightly biased, it appears to provide an efficient tool for, e.g., reasonably low dimensional problems, as typically encountered in non-linear regression problems in natural sciences. As a realistic example we include a successful application of the AP algorithm in parameter estimation for the satellite instrument 'GOMOS'. In this paper we also present systematic performance criteria for comparing Adaptive Proposal algorithm with more traditional Metropolis algorithms.
This paper provides foundations for understanding the effect of passages on the connectedness of probabilistic roadmaps. It also proposes a new random sampling scheme for finding such passages. An initial roadmap is built in a "dilated" free space allowing some penetration distance of the robot into the obstacles. This roadmap is then modified by resampling around the links that do not lie in the true free space. Experiments show that this strategy allows relatively small roadmaps to reliably capture the free space connectivity
The main new feature of the fifth edition is the addition of a new chapter, Chapter 12, on applications to mathematical finance. I found it natural to include this material as another major application of stochastic analysis, in view of the amazing development in this field during the last 10-20 years. Moreover, the close contact between the theoretical achievements and the applications in this area is striking. For example, today very few firms (if any) trade with options without consulting the Black & Scholes formula! The first 11 chapters of the book are not much changed from the previous edition, but I have continued my efforts to improve the presentation through out and correct errors and misprints. Some new exercises have been added. Moreover, to facilitate the use of the book each chapter has been divided into subsections. If one doesn't want (or doesn't have time) to cover all the chapters, then one can compose a course by choosing subsections from the chapters. The chart below indicates what material depends on which sections. Chapter 6 Chapter IO Chapter 12 For example, to cover the first two sections of the new chapter 12 it is recom mended that one (at least) covers Chapters 1-5, Chapter 7 and Section 8.6. VIII Chapter 10, and hence Section 9.1, are necessary additional background for Section 12.3, in particular for the subsection on American options.
Meyn & Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
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.
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.
The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the algorithm is often used for non-linear systems by linearizing the system's process and measurement models. Different ways of linearizing the models lead to different filters. In some applications, these ‘Kalman filter variants’ seem to perform well, while for other applications they are useless. When choosing a filter for a new application, the literature gives us little to rely on. This paper tries to bridge the gap between the theoretical derivation of a Kalman filter variant and its performance in practice when applied to a non-linear system, by providing an application-independent analysis of the performances of the common Kalman filter variants. Correlated uncertainties can be dealt with by augmenting the state vector, this is the original formulation of the KF (Kalman 1960). Expressed in this new state vector, the process and measurement models are of the form (1) and (2) with uncorrelated uncertainties.This paper separates performance evaluation of Kalman filters into (i) consistency, and (ii) information content of the estimates; and it separates the filter structure into (i) the process update step, and (ii) the measurement update step. This decomposition provides the insights supporting an objective and systematic evaluation of the appropriateness of a particular Kalman filter variant in a particular application.
We present a new method for generating collision-free paths for robots operating in changing environments. Our approach is closely related to recent probabilistic roadmap approaches. These planners use preprocessing and query stages, and are aimed at planning many times in the same environment. In contrast, our preprocessing stage creates a representation of the configuration space that can be easily modified in real time to account for changes in the environment. As with previous approaches, we begin by constructing a graph that represents a roadmap in the configuration space, but we do not construct this graph for a specific workspace. Instead, we construct the graph for an obstacle-free workspace, and encode the mapping from workspace cells to nodes and arcs in the graph. When the environment changes, this mapping is used to make the appropriate modifications to the graph, and plans can be generated by searching the modified graph. After presenting the approach, we address a number of performance issues via extensive simulation results for robots with as many as twenty degrees of freedom. We evaluate memory requirements, preprocessing time, and the time to dynamically modify the graph and replan, all as a function of the number of degrees of freedom of the robot.
This paper presents an approach to estimating the contact state between a robot and its environment during task execution.
Contact states are modeled by constraint equations parameterized by time-dependent sensor data and time-independent object
properties. At each sampling time, multiple model estimation is used to assess the most likely contact state. The assessment
is performed by a Hidden Markov Model, which combines a measure of how well each set of constraint equations fit the sensor
data with the probability of specific contact state transitions. The latter is embodied in a task-based contact state network.
The approach is illustrated for a three dimensional peg-in-hole insertion using a tabletop manipulator robot. Using only position
sensing, the contact state sequence is successfully estimated. Property estimates are obtained for the peg dimensions as well
as the hole position and orientation.
When assembly tasks are accomplished by robot manipulators, it is
necessary to identify interactions between grasped objects and external
environments, such as contact positions and contact type, and also
contact directions. This paper discusses the identification of unknown
parameters such as mentioned above. Point contact, line contact and
plane contact are formulated in contact conditions. Applying this
formulation, a simple scheme is proposed for identification of contact
conditions by using active force sensing method. In this algorithm,
contact type, contact direction and contact point can be
identified
An approach to analyzing ambiguous contact situations in an
uncertain robotic environment is presented. When invoked by the
occurrence of a contact, the analysis proceeds by generating a set of
hypotheses on the contact, out of which the valid one is detected by
testing the feasibility of certain motions, i.e., performing movability
tests. Emphasis is placed on the generation of the hypotheses. All parts
of the analysis are based upon the same probabilistic uncertainty model,
which is given
The role of adaptive controllers for controlling the force as well
as the contact behavior of manipulators is examined. It is shown how the
standard model-reference adaptive control (MRAC) scheme can be employed
to explicitly control the force of contact for a linear system despite
unknown stiffness. This is extended to the impedance control of the
end-effector in contact with a similar environment. Also analyzed is an
interesting case where the system achieves explicit force control as
well as the desired impedance through adaptive control within the MRAC
framework. It is shown that similar results hold for an end-effector
with nonlinear dynamics, provided a specially-designed robust adaptive
controller is used. Both simulations and experiments are performed to
validate theoretical conclusions
This paper presents it novel analysis of the probabilistic roadmap method (PRM) for path planning. We formulate the problem in terms of computing the transitive closure of a relation over a probability space and give a bound in terms of the number of intermediate points for some path and the probability of choosing a point from a certain set. Explicit geometric assumptions are not necessary to complete this analysis and consequently it provides some unification of the previous work as well as generalizing new path planning problems, two of which, 2k-DOF kinodynamic point robots and deformable robots with force field control, are presented in this paper.
This paper uses (linearized) Kalman filters to estimate first-order geometric parameters (i.e., orientation of contact normals and location of contact points) that occur in force-controlled compliant motions. The time variance of these parameters is also estimated. In addition, transitions between contact situations can be monitored. The contact between the manipulated object and its environment is general, i.e., multiple contacts can occur at the same time, and both the topology and the geometry of each single contact are arbitrary. The two major theoretical contributions are 1) the integration of the general contact model, developed previously by the authors, into a state-space form suitable for recursive processing; and 2) the use of the reciprocity constraint between ideal contact forces and motion freedoms as the `measurement equation' of the Kalman filter. The theory is illustrated by full 3-D experiments. The approach of this paper allows a breakthrough in the state of the art dominated by the classical, orthogonal contact models of Mason that can only cope with a limited (albeit important) subset of all possible contact situations.
This article describes a new statistical, model-based approach to building a contact-state observer for time-invariant con straints for a point in three dimensions. Three-dimensional constraint estimation and selection, and the application of these procedures to a planar, two-dimensional maze is described in detail. The observer uses measurements of the contact force and position, and prior information about the task encoded in a network, to determine the current location of the robot in the task-configuration space. Each node represents what the measurements will look like in a small region of configuration space by storing a predictive, statistical, measurement model. Construction of the task network requires a model of both the grasped part and the environment. The model makes the system robust to alignment errors, however, gross errors can occur if the topology of the modeled configuration space differs from the true topology. Arcs in the task network represent possible transitions between models. Beam search is used to match the measurement history against possible paths through the model network to estimate the most likely path for the robot. The re sulting approach provides a new decision process that can be used as an observer for event-driven manipulation program ming.
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1995. Includes bibliographical references (p. 63-65). by Susan L. Ipri. M.S.
When a system is acted upon by exterior disturbances, its time-development can often be described by a system of ordinary differential equations, provided that the disturbances are smooth functions. But for sound reasons physicists and engineers usually want the theory to apply when the noises belong to a larger class, including for example "white noise." If the integrals in the system derived for smooth noises are reinterpreted as Itô integrals, the equations make sense; but in nonlinear cases they often fail to describe the time-development of the system. In this paper (extending previous work of the author) a calculus is set up for stochastic systems that extends to a theory of differential equations. When the equations are known that describe the development of the system when noises are smooth, an extension to the larger class of noises is proposed that in many cases gives results consistent with the smooth-noise case and also has "robust" solutions, that change by small amounts when the noises undergo small changes. This is called the "canonical" extension. Nevertheless, there are certain systems in which the canonical equations are inappropriate. A criterion is suggested that may allow us to distinguish when the canonical equations are the right choice and when they are not.
This paper concerns the problem of moving a polyhedron through Euclidean space while avoiding polyhedral obstacles.
Proposes an identification technique of constraint condition that the environment imposes on the robot's end-effector, based on position and force sensing during arbitrary manipulation. In the proposed method, the impedance that constrains the motion of the end-effector is estimated on-line; the uncertainties of the estimates are evaluated; and discontinuous changes of the impedance are detected. This method can be installed on robots as human-like perception of impedance, and can be used for monitoring human demonstration. Results of preliminary experiments are presented.
We present and implement an efficient algorithm for performing nearest-neighbor queries in topological spaces that usually arise in the context of motion planning. Our approach extends the Kd tree-based ANN algorithm, which was developed by Arya and Mount (1993) for Euclidean spaces. We argue the correctness of the algorithm and illustrate its efficiency through computed examples. We have applied the algorithm to both probabilistic roadmaps (PRMs) and rapidly-exploring random trees (RRTs). Substantial performance improvements are shown for motion planning examples.
Trajectory design for high-dimensional systems with nonconvex constraints has considerable success recently; however, the resolution completeness analysis for various methods is insufficient. In this paper, based on Lipschitz condition and the accessibility graph, conditions for resolution completeness are derived. By combining the systematic search with randomized technique, a randomized planner is transformed to be a deterministic resolution complete planner, which shows reliable performance in the simulation.
This paper discusses a method for identification of contact conditions from the information of 6-axes force sensor equipped with a robot hand. The previous paper (1999) has the following problems: the noise of sensing force was not considered, and hence the estimates obtained by the previous method are biased from true value, and the identification of contact types depends on an unknown contact position. In this paper we consider the noise of force. We propose a method of removing the bias from the estimates. Hence, it is guaranteed that asymptotically unbiased estimates are obtained. The contact types can be judged by eigenvalues of a covariance matrix, which is derived from estimates of the contact moment. The effectiveness of the algorithm is demonstrated by simulations.
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
Presents two simple and computationally efficient schemes for
force tracking using impedance control. The schemes generate the
reference position trajectory required to produce a desired contact
force despite lack of knowledge of the environmental stiffness and
location. The first scheme uses direct adaptive control to generate the
reference position online as a function of the force tracking-error. The
second scheme utilizes an indirect adaptive strategy in which the
environmental parameters are estimated online, and the required
reference position is computed based on these estimates. Simulation
studies are presented for a 7-DOF Robotics Research arm using full arm
dynamics and demonstrate that the adaptive schemes are able to
compensate for uncertainties in both the environmental stiffness and
location, so that the end-effector applies the desired contact force
while exhibiting the specified impedance dynamics
We present two methods of rapidly (less than 1 ms) identifying
contact formations from force sensor patterns, including friction and
measurement uncertainty. Both principally use force signals instead of
positions and detailed geometric models. First, fuzzy sets are used to
model patterns and sensor uncertainty; membership functions are
generated automatically from training data. Second, a neural network is
used to generate confidence levels for each contact formation.
Experimental results are presented for both classifiers, showing
excellent results. New insights into the data sets are discussed, and a
modified training method is presented that further improves the
performance. The classification techniques are discussed in the context
of robot programming by demonstration
This paper presents algorithms for computing constraints on the position of an object due to the presence of ther objects. This problem arises in applications that require choosing how to arrange or how to move objects without collisions. The approach presented here is based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object. The configurations forbidden to this object, due to the presence of other objects, can then be characterized as regions in the configuration space, called configuration space obstacles. The paper presents algorithms for computing these configuration space obstacles when the objects are polygons or polyhedra.
A new task-level adaptive controller is presented for the hybrid
dynamic control of constrained motion systems. Using a hybrid dynamic
model of the process, velocity constraints are derived from which
satisfactory velocity commands are obtained. Due to modeling errors and
parametric uncertainties, the velocity commands may be erroneous and may
result in suboptimal performance. A task-level adaptive control scheme,
based on the occurrence of discrete events, is used to change the model
parameters from which the velocity commands are determined. Automated
control of an assembly task is given as an example, and simulations and
experiments for this task are presented. These results demonstrate the
applicability of the method and also indicate properties for rapid
convergence
A simple and e#cient randomized algorithm is presented for solving single-query path planning problems in high-dimensional configuration spaces. The method works by incrementally building two Rapidly-exploring Random Trees (RRTs) rooted at the start and the goal configurations. The trees each explore space around them and also advance towards each other through the use of a simple greedy heuristic. Although originally designed to plan motions for a human arm (modeled as a 7-DOF kinematic chain) for the automatic graphic animation of collision-free grasping and manipulation tasks, the algorithm has been successfully applied to a variety of path planning problems. Computed examples include generating collision-free motions for rigid objects in 2D and 3D, and collision-free manipulation motions for a 6-DOF PUMA arm in a 3D workspace. Some basic theoretical analysis is also presented.
A process monitor for robotic assembly based on Hidden Markov Models (HMMs) is presented. The HMM process monitor is based on the dynamic force/torque signals arising from interaction between the workpiece and the environment. The HMMs represent a stochastic, knowledge-based system where the models are trained off-line with the Baum-Welch re-estimation algorithm. The assembly task is modeled as a discrete event dynamic system, where a discrete event is defined as a change in contact state between the workpiece and the environment. Our method 1) allows for dynamic motions of the workpiece, 2) accounts for sensor noise and friction and 3) exploits the fact that the amount of force information is large when there is a sudden change of discrete state in robotic assembly. After the HMMs have been trained, we use them on-line in a 2D experimental setup to recognise discrete events as they occur. Successful event recognition with an accuracy as high as 97% was achieved in 0.5-0.6 seconds with...
Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An alternative approach might be to allow the transition kernel to adapt whenever new features of π are encountered during the MCMC run. However, if such adaptation occurs infinitely often, then the stationary distribution of the chain may be disturbed. We describe a framework, based on the concept of Markov chain regeneration, which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages.