No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
On curves of Minimal lenght with a constraint on average curvature and with prescribed initial and terminal positions and tangents
... The next dichotomy results from the number of systems to which a planning method can be applied. In this scope we distinguish general purpose methods [2,5,6] and dedicated ones that work only for a specific model [7,8] or a small number of models [9]. General-purpose methods are computationally involved, solved or supported with an extensive usage of numerical methods and some numerical problems in high dimensional search spaces are to be expected. ...
... Dedicated methods can be suited into a particular system structure and use it to simplify a task to be solved. Sometimes even analytical solutions [7] can be obtained with the methods. ...
... Motion planning tasks can be motivated by practical necessity to control real objects or just a mathematical curiosity [7]. Recently numerous motion planning methods are based on graph-searching techniques able to find desired trajectories in obstacle-clutter environments. ...
... The kinematic control of a system moving from a pose to another along a desired trajectory is often done by dividing the path in motion segments composed by straight lines and segments of a circle (Siegwart et al., 2011). When considering mechanical constraints, Dubin's path generation approaches (Dubins, 1957) are often used and adapted for the definition of feasible trajectories in 3D space ( Ambrosino et al., 2009;Babaei and Mortazavi, 2010;Yu et al., 2015;Makdah et al., 2016). ...
... As in mobile robotics, we can identify a path from s 0 to s e composed by a sequence of turns and straight lines (Dubins, 1957;Siegwart et al., 2011), and obtain the transformation matrix i T (s t ) for each of the segments. The problem is to define a feasible path for the robot. ...
... To find feasible paths for growing robots, solutions based on Dubin's path generation can be adopted bringing the tip from X s to X e . Dubin's paths have been formalized for 2D motion planning of mobile robots and used to find optimal paths under curvature constraints (Dubins, 1957). In 2D, a minimum path is a path between a starting Y s = x s , y s , θ s and a final state Y e = x e , y e , θ e which can be composed by S straight segments or C curvatures, with several combinations: S, C, SC, CS, CSC, CC, CCC. ...
Growing robots are a new class of robots able to move in the environment exploiting a growing from the tip process (movement by growing). Thanks to this property, these robots are able to navigate 3D environments while negotiating confined spaces and large voids by adapting their body. During the exploration of the environment, the tip of the robot is able to move in any direction and can be kinematically considered as a non-holonomic mobile system. In this paper, we show the kinematics of robot growing at its tip level. We also present the affordable workspace analyzed by an evaluation of feasible trajectories toward target poses. The geometrical key parameters imposing constraints on growing robots' workspace are discussed, in view of facing different possible application scenarios. The proposed kinematics was applied to a plant-inspired growing robot moving in a 3D environment in simulation, obtaining ~2 cm error after 1 m of displacement. With appropriate parametrization, the proposed kinematic model is able to describe the motion from the tip in robots able to grow.
... The CSP is a generalization of the two point shortest path problem solved by L.E. Dubins [20] in 1957. Dubins [20] addressed the problem of finding a shortest path for a vehicle to travel from a point at (x 1 , y 1 ) with heading angle θ 1 to a point at (x 2 , y 2 ) with heading angle θ 2 such that the radius of curvature at any point along the path is at least equal to ρ ≥ 0. Dubins [20] showed that any shortest path to this two point problem must consist of at most three segments where each of the segments must be an arc of radius ρ (denoted by C) or a straight line segment (denoted by S). ...
... Dubins [20] in 1957. Dubins [20] addressed the problem of finding a shortest path for a vehicle to travel from a point at (x 1 , y 1 ) with heading angle θ 1 to a point at (x 2 , y 2 ) with heading angle θ 2 such that the radius of curvature at any point along the path is at least equal to ρ ≥ 0. Dubins [20] showed that any shortest path to this two point problem must consist of at most three segments where each of the segments must be an arc of radius ρ (denoted by C) or a straight line segment (denoted by S). Specifically, any shortest path is of type CSC or CCC, or a degenerate form of these paths. ...
... Dubins [20] in 1957. Dubins [20] addressed the problem of finding a shortest path for a vehicle to travel from a point at (x 1 , y 1 ) with heading angle θ 1 to a point at (x 2 , y 2 ) with heading angle θ 2 such that the radius of curvature at any point along the path is at least equal to ρ ≥ 0. Dubins [20] showed that any shortest path to this two point problem must consist of at most three segments where each of the segments must be an arc of radius ρ (denoted by C) or a straight line segment (denoted by S). Specifically, any shortest path is of type CSC or CCC, or a degenerate form of these paths. ...
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications involving unmanned aerial vehicles. There is currently no algorithm that can find an optimal solution to this problem. Therefore, heuristics that can find approximate solutions with guarantees on the quality of the solutions are useful. The best approximation algorithm currently available for the case when the distance between any two adjacent target points in the sequence is at least equal to twice the minimum radius of the vehicle has a guarantee of 3.04. This article provides a new approximation algorithm which improves this guarantee to 2.04. The developed algorithm is also implemented for hundreds of typical instances involving at most 30 points to corroborate the performance of the proposed approach.
... An important variation of this model is the case when v r is fixed. This is sometimes referred to as the Dubins car, after Lester Dubins who derived the minimum time motion between to points with prescribed tangents [57]. Another notable variation is the Reeds-Shepp car for which minimum length paths are known when v r takes a single forward and reverse speed [58]. ...
... A special case where a solution can be efficiently computed is the shortest curvature bounded path in an obstacle free environment. Dubins [57] has shown that the shortest path having curvature bounded by κ between given two points p 1 , p 2 and with prescribed tangents θ 1 , θ 2 is a curve consisting of at most three segments, each one being either a circular arc segment or a straight line. Reeds and Shepp [58] extended the method for a car that can move both forwards and backwards. ...
... Such a path corresponds to a solution of a 2-point boundary value problem. For some systems and cost functionals, such a path can be obtained analytically, e.g., a straight line for holonomic systems, a Dubins curve for forward-moving unicycle [57], or a Reeds-Shepp curve for bi-directional unicycle [58]. An analytic solution also exists for differentially flat systems [61], while for more complicated models, the exact steering can be obtained by solving the twopoint boundary value problem. ...
Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side-by-side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.
... Path planning for a non-holonomic vehicle is a fundamental problem of surveillance mission where an unmanned aerial vehicle (such as a fixed-wing) is requested to visit a given set of locations. The basic model of such a vehicle with the limited turning radius is called the Dubins vehicle [1] for which the combinatorial problem of finding optimal sequence of visits to the locations is known as the Dubins Traveling Salesman Problem (DTSP) [2]. ...
... The problem of curvature-constrained path planning has been studied years ago and the fundamental work has been published in 1957 by Dubins. In [1], he proved that the optimal path between two configurations q 1 , q 2 ∈ SE(2) consists of only straight line segments and segments with the minimum turning radius. He also showed that only 6 maneuvers can be optimal, which can be further divided into two main types: ...
... The addressed problem is motivated by surveillance missions with fixed-wing aerial vehicles, which are nonholonomic vehicles due to their kinodynamic constraints. These vehicles are often modeled as the Dubins vehicle [1], which can go only forward at a constant speed and has a minimum turning radius ρ. The configuration space of such a vehicle can be represented as SE (2), where each configuration q ∈ SE(2) is a triplet (x, y, θ), where (x, y) is the vehicle position in a plane and θ ∈ S 1 is the orientation of the vehicle. ...
In this paper, we address the problem of path planning to visit a set of regions by Dubins vehicle, which is also known as the Dubins Traveling Salesman Problem Neighborhoods (DTSPN). We propose a modification of the existing sampling-based approach to determine increasing number of samples per goal region and thus improve the solution quality if a more computational time is available. The proposed modification of the sampling-based algorithm has been compared with performance of existing approaches for the DTSPN and results of the quality of the found solutions and the required computational time are presented in the paper.
... The system studied is quite specific, compared to systems for which generalpurpose motion planning algorithms have been successfully applied, and the algorithm we present is much weaker than algorithms derived from exact analytical descriptions of time-optimal trajectories for specific systems (e.g. Dubins [4] , Reeds- Shepp [16], and others [18, 17, 11, 2, 1, 20, 9]). However, the theorems and results in this paper show, perhaps for the first time, that provably optimal motion planning is computationally feasible for a somewhat-general model of mobile robots in the plane. ...
... In previous work, we have been able to show some strong geometric necessary conditions on optimal trajectories for a general model of planar rigid bodies [6]. This rigid body might represent a simple model of a mobile robot (for example, the steered cars studied by Dubins, Reeds and Shepp, and others [4, 16, 18, 11, 19], differential drives [2] , omnidirectional vehicles [1, 20], or an object being manipulated in the plane by a robot arm, studied by e.g. Lynch [13]). ...
... Solving for the placement of the control line is an inverse kinematics problem. For some simple robot geometries (e.g., steered cars, differential drives, symmetric omnidirectional robots), an analytical solution can be found [4, 16, 2, 1, 20], but for other interesting variations of robot designs, we do not expect to be able to find analytical solutions. An approach to solving an inverse kinematics problem is to sample a forwards kinematics problem. ...
This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane. Previous work has used Pontryagin’s Principle to find strong necessary conditions on time-optimal trajectories of the rigid body; trajectories satisfying these conditions are called extremal trajectories. The main contribution of this paper is a method for sampling the extremal trajectories sufficiently densely to guarantee that for any pair of start and goal configurations, a trajectory can be found that (provably) approximately reaches the goal, approximately optimally; the quality of the approximation is only limited by the availability of computational resources.
... In the second stage, a curve (the path of the mobile robot) is constructed using the generated set of control waypoints. Another planning method is the construction of the shortest trajectory by the Dubins method [14,15]. However, such trajectories belong to a class C 1 and their implementation is quite laborious in practice [15]. ...
... For the implementation of control law (19), information is required about the state variables of control plant (12), (14), (16), reference actions, and their derivatives of the first and second order. ...
In the deterministic formulation, two problems are considered related to the generation of admissible reference actions for the automatic control of an autonomous mobile robot in the problem of path following stabilization. The first problem is the restoration of the derivatives of the reference vector signal without its analytical description. This signal sets the realizable trajectory for the robot. An easy-to-tune dynamic differentiator with piecewise linear corrective actions is proposed to solve that problem. The differentiator is constructed as a copy of the virtual canonical model with unknown input and provides an estimation of derivatives of any required order with any given accuracy. The second problem is the smoothing of composite spatial trajectories. For solution, a dynamic generator is presented. It is constructed as a copy of the motion equations of a specific robot. A decomposition procedure for the synthesis of S-shaped smooth and bounded corrective actions of the generator is developed. In the generator, a reference non-smooth vector signal is used to describe the path of the robot in the first approximation. For tuning the generator, the constraints on the state variables and controls of a specific robot are taken into account. It produces smooth output signals, as well as their derivatives, realizable by a particular robot. These algorithms can be implemented both at the planning stage and in real time since they do not require large computational costs. Their effectiveness is verified by numerical simulation for the movement of the center of mass of an unmanned aerial vehicle.
... In order to achieve a smooth transition between two straight-line paths, a circular arc path is inserted between the adjacent straight-line paths. The methods used to generate such circular arc path have been extensively studied in recent years, and the Dubins path is highly recognized in [9]. The curvature of the Dubins path is usually discontinuous at the intersection of a straight-line path and its adjacent circular arc path. ...
... Execution process of the path selecting method.9 Journal of Sensors where V d is the desired speed in the coordinate frame fng; β C 1 is the desired sideslip angle; u d and v d are the desired velocity components in the body coordinate frame, respectively. ...
A pipelaying control method is presented in this paper which includes path planning, path guidance, and path tracking controller for dynamically positioned (DP) surface vessels based on the characteristics of the predefined path in marine pipelaying operation. The pipelaying control method depends on path coding, path selection logic system, and a sliding matrix. The sliding matrix contains a vessel local path and its specified control requirements, which can be updated by sliding down the waypoint table line by line as the vessel is traveling from one path to the next. A line of sight (LOS) algorithm is developed to calculate the desired vessel position and heading on a circular arc path. The motion controller, which can simultaneously control the vessel speed at the directions of surge and sway, is designed by decomposing the desired inertial resulting velocity into the desired body velocity components. A DP simulator for pipelaying operation is developed, and in order to verify the proposed method, a pipelaying simulation is carried out. The simulation results show that the proposed method enables the vessel to move along the desired path while maintaining a set crab angle, a specified speed, and a turning radius. The pipeline can be laid onto the specified waypoints even when the vessel is subjected to drift forces caused by ocean currents, wind, and waves.
... There are several approaches to define the desired path. Dubins defines the path as a combination of circle's arcs and lines tangent to them [28] [8]. In the waypoint-based case the sequence of points is commonly connected by straightlines [21] [60] or splines [84] [27]. ...
... Where J 1 , J 2 and J 3 are inertial terms defined in Eqs. (28)(29)(30); R 1 , R 2 , R 3 and R 4 are auxiliary terms, Eqs. (31)(32)(33)(34); and C x , C y , C z are the inverse of the inertia in each coordinate axis, Eq. (35). ...
The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.
... Dubins [6] introduced the class of curves of bounded average curvature as the curves γ parameterized by arclength that are differentiable such that for all s 1 , s 2 , we have ...
... Since Arg y α + = 2π and z −→ Arg z α + is constant on Int α + , it follows that Arg x α + = 2π. We now get from (5) that Arg x γ[a, b] = θ x , and then by (6) that Arg x α − = 0, that is; x ∈ Ext α − . We conclude that Ext α − ∩ U = Int α + , as claimed. ...
We say that a simple, closed curve $\gamma$ in the plane has bounded convex curvature if for every point $x$ on $\gamma$, there is an open unit disk $U_x$ and $\varepsilon_x>0$ such that $x\in\partial U_x$ and $B_{\varepsilon_x}(x)\cap U_x\subset\text{Int}\;\gamma$. We prove that the interior of every curve of bounded convex curvature contains an open unit disk.
... Strongly motivated from robotics, particularly the surveillance domain for UAVs, the TSP has also been adapted for vehicles with nonholonomic/dubins constraints. Two variants of this problem have been studied: the Euclidean TSP (ETSP), where the Euclidean metric is used to measure the distance between adjacent nodes; and the Dubins Traveling Salesperson Problem (DTSP) [2], where the problem is to find a shortest tour composed of paths of bounded curvature [3]. ...
... 0.5), (9.0, 0.5) , i.e., the geofence is close to the targets, but the targets are far from each other; and problems of type 4 are (14.0, 0.5), (36.0, 0.5) , i.e., the geofence is far from the targets, and the targets are sparse 3 . ...
We introduce a variant of the multi-vehicle routing problem which accounts for nonholonomic constraints and dense, dynamic obstacles, called MVRP-DDO. The problem is strongly motivated by an industrial mining application. This paper illustrates how MVRP-DDO relates to other extensions of the vehicle routing problem. We provide an application-independent formulation of MVRP-DDO, as well as a concrete instantiation in a surface mining application. We propose a multi-abstraction search approach to compute an executable plan for the drilling operations of several machines in a very constrained environment. The approach is evaluated in terms of makespan and computation time, both of which are hard industrial requirements.
... In this paper, the robot is modelled as a unicycle moving at a constant speed with bounded angular velocity. This model is also called the Dubins car [11] and it is well known that the motion of many wheeled robots and unmanned aerial vehicles can be described by this model [12][13][14][15] . Recent studies have proposed various solutions to the path planning problem in data collection. ...
... Any path ( x ( t ), y ( t )) of the robot (1) is a plane curve satisfying the following constraint on its so-called average curvature (see [11] ): let P ( a ) be this path parametrized by arc length, then ...
Introducing mobile robots into wireless sensor networks to collect data can balance the energy dissipation through the entire network and then improve the network lifetime. In this context, path management is a crucial problem since it impacts on the system performance such as data delivery delay and energy consumption. In this paper, we consider the problem of planning paths for unicycle robots (with constant speed and bounded angular velocity) to visit a set of sensor nodes in a sensing field with obstacles while minimizing the path lengths. Several practical issues that have not been sufficiently addressed so far are taken into account. As the combination of concerns from robotics and sensor networks, a viable path is defined, which is smooth, collision free with sensor nodes and obstacles, closed and let the robot to read all the data from sensor nodes. To design the shortest viable path for the underlying robots, a Shortest Viable Path Planning (SVPP) algorithm is first developed for single robot. Due to the physical speed, using single robot to collect data in a large scale network may result in a long collection time. Then, a k-Shortest Viable Path Planning (k-SVPP) algorithm to construct k paths of approximately equal lengths is proposed. Through extensive simulations, we demonstrate the effectiveness of the proposed algorithms and show their advantages over the alternatives.
... The major trends have been focused on holonomic and non-holonomic kinematic path planning problems. Perhaps Dubins' seminal work [3] is one of the first ones in this area that characterizes shortest bounded-curvature paths for a vehicle in absence of obstacles. It is well-known that finding a shortest boundedcurvature path amidst polygonal obstacles in the plane is NP-hard [4]. ...
... In the following theorem, it is shown that by means of discontinuous elasticity functions one can actually prove that all unfavorable equilibria of the multi-particle dynamical system (8) are unstable. In other words, theorem (3) shows that for almost all initial conditions (except for those where the particles lie on a straight line passing through p 0 and p n which constitute a set of measure zero) the trajectories of the multi-particle dynamical system asymptotically converges to an equilibrium which is a feasible solution of problem (7). In the sequel, we consider the following class of discontinuous elasticity functions Proof: Without loss of generality, we may assume that ...
In this paper, we propose a path planning method for nonholonomic multi-vehicle system in presence of moving obstacles. The objective is to find multiple fixed length paths for multiple vehicles with the following properties: (i) bounded curvature (ii) obstacle avoidant (iii) collision free. Our approach is based on polygonal approximation of a continuous curve. Using this idea, we formulate an arbitrarily fine relaxation of the path planning problem as a nonconvex feasibility optimization problem. Then, we propound a nonsmooth dynamical systems approach to find feasible solutions of this optimization problem. It is shown that the trajectories of the nonsmooth dynamical system always converge to some equilibria that correspond to the set of feasible solutions of the relaxed problem. The proposed framework can handle more complex mission scenarios for multi-vehicle systems such as rendezvous and area coverage.
... ). 2) Optimal Trajectory in Fluidic Environment: For mobile robots evolving on the ground, a well-known result states that the shortest trajectory under constraint of maximal curvature, and with selected initial and final tangents, is a Dubins path [9], [10]. Such a path always starts with a rotation with maximal curvature (i.e., Sx 2 in our case), followed by a forward motion, and finally by a second rotation with maximal curvature. ...
... as given by (9). Remark 1: We note that the computed object transport trajectories are similar to Dubins paths for general nonholonomic vehicles with unicycle dynamics [9], [10]. Rather than trajectories composed of circular arcs of the same radii, our paths are composed of trajectories composed of two arcs of different radii. ...
We present a distributed control mechanism allowing a swarm of non-holonomic autonomous surface vehicles (ASVs) to synchronously arrange around a rectangular floating object in a grasping formation; the swarm is then able to collaboratively transport the object to a desired final position and orientation. We analytically consider the problem of synchronizing the ASVs' arrival at the object, with regard to their initial random positions. We further analytically construct a set of acceptable trajectories, allowing the transport of the grasped object to its final desired position. Numerical simulations illustrate the performance of the presented control mechanism. We present experimental results, to demonstrate the feasibility and relevance of our strategy.
... What follows is a review of these two problems. Some basic geometric and topological concepts primarily drawn from [5] and [9] are presented here in order to prepare the reader for subsequent sections. First, consider Fermat's problem, which is a 3-terminal special case of the Steiner prob- lem: ...
... Given an initial directed point p 1 and a final directed point p 2 , construct a shortest admissible path connecting these two directed points. Dubins [5] proved that such a path, called a Dubins path, necessarily exists and consists of not more than three components, each of which is either a straight segment, denoted by S, or an arc of a circle of radius ρ, denoted by C. Furthermore, such a path is necessarily a subpath of a path of type CSC or of type CCC. A well-known result states that if two points p 1 and p 2 are distance at least 4ρ apart, then a shortest Dubins path between any two directed points (p 1 , #» p 1 ) and (p 2 , #» p 2 ) is of type CSC (see, for example, [8]). ...
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be referred to as a minimum Dubins network, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins network appears in the context of underground mining optimisation, where the aim is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins network problem is similar to the Steiner tree problem, except that the terminals are directed and there is a curvature constraint. We propose the minimum curvature-constrained Steiner point algorithm for determining the optimal location of the Steiner point in a 3-terminal network. We show that when two terminals are fixed and the third varied, the Steiner point traces out a lima\c{c}on.
... Therefore, one is brought back to the Dubins car model [25]. Equation 7 can be written as follows: ...
... The first two equations represent the translation model. They are in the form of Dubins car model [25]. The rotation model (course derivativeψ V ) depends on two terms: the first is based on the roll (inclination) and the second is based on the roll and pitch derivatives. ...
Fixed-wing Unmanned Aerial Vehicles (UAVs) are a class of UAVs which present many advantages notably long range of action. However, design of this kind of UAVs requires heavy logistics like outdoor tests, runways and experimented pilots. These constraints impact the development of embedded systems for fixed-wing UAVs. The purpose of this paper is to present an experimental approach for evaluating an embedded sensors system of a micro-fixed-wing UAV. Our idea is to test the sensors system using a vehicle that emulate the behavior of this UAV but without the constraints imposed by flight experimentations. Looking for the best emulation vehicle, first a theoretical and then an experimental study is conducted on a mobile robot and a bicycle models. We also show that, contrary to trend in literature, a mobile robot is not the optimal choice to emulate a fixed-wing UAV.
... A more exhaustive list of path planning methods can be found in the surveys by Nygards and Forskningsinstitut (Nygå rds et al., 2005) and Goerzen et al. (Goerzen et al., 2009). The shortest curve that can be manoeuvred by a vehicle with constraints on the curvature of the path is known as a Dubins Path (Dubins, 1957). This is especially useful for generating smooth 2D paths for fixed-wing UAVs, as these can be well approximated as Ackerman-steered vehicles. ...
... To ensure the system remains flexible enough to be applied to a wide range of vehicles, such as the UAV and full-size Cessna 172 in this paper, a simple guidance and control algorithm is sought. For this reason, we implement a Dubins path (Dubins, 1957) based planner extended to compensate for wind and develop a control system that models the aircraft as a non-holonomic vehicle, taking into account roll-based turning manoeuvres. ...
A number of hurdles must be overcome in order to integrate unmanned aircraft into civilian airspace for routine operations. The ability of the aircraft to land safely in an emergency is essential to reduce the risk to people, infrastructure, and aircraft. To date, few field-demonstrated systems have been presented that show online replanning and repeatability from failure to touchdown. This paper presents the development of the guidance, navigation, and control (GNC) component of an automated emergency landing system (AELS) intended to address this gap, suited to a variety of fixed-wing aircraft. Field-tested on both a fixed-wing unmanned aerial vehicle (UAV) and Cessna 172R during repeated emergency landing experiments, a trochoid-based path planner computes feasible trajectories, and a simplified control system executes the required maneuvers to guide the aircraft toward touchdown on a predefined landing site. This is achieved in zero-thrust conditions with engine forced to idle to simulate failure. During an autonomous landing, the controller uses airspeed, inertial, and GPS data to track motion and maintains essential flight parameters to guarantee flyability, while the planner monitors glide ratio and replans to ensure approach at correct altitude. Simulations show reliability of the system in a variety of wind conditions and its repeated ability to land within the boundary of a predefined landing site. Results from field-tests for the two aircraft demonstrate the effectiveness of the proposed GNC system in live operation. Results show that the system is capable of guiding the aircraft to close proximity of a predefined keyhole in nearly 100% of cases.
... A smoothing algorithm provides motion continuity and reduces the execution time of coverage tasks. The first research on finding the shortest curvature constrained smooth paths consisting of straight lines and arcs was done by Dubin in [35]. The presence of discontinuities at the intersection of the straight lines and circular arcs makes them infeasible for real applications. ...
The complete coverage path planning is a process of finding a path which ensures that a mobile robot completely covers the entire environment while following the planned path. In this paper, we propose a complete coverage path planning algorithm that generates smooth complete coverage paths based on clothoids that allow a nonholonomic mobile robot to move in optimal time while following the path. This algorithm greatly reduces coverage time, the path length, and overlap area, and increases the coverage rate compared to the state-of-the-art complete coverage algorithms, which is verified by simulation. Furthermore, the proposed algorithm is suitable for real-time operation due to its computational simplicity and allows path replanning in case the robot encounters unknown obstacles. The efficiency of the proposed algorithm is validated by experimental results on the Pioneer 3DX mobile robot.
... There are several approaches to define the desired path. Dubins defines the path as a combination of circle's arcs and lines tangent to them [47] [10]. In the waypoint-based approach the sequence of points is commonly connected by straight-lines [35] [127] or splines [190] [43]. ...
This thesis presents contributions to the Guidance, Navigation and Control (GNC) systems for multirotor vehicles by applying and developing diverse control techniques and machine learning theory with innovative results. The aim of the thesis is to obtain a GNC system able to make the vehicle follow predefined paths while avoiding obstacles in the vehicle's route. The system must be adaptable to different paths, situations and missions, reducing the tuning effort and parametrisation of the proposed approaches.
The multirotor platform, formed by the Asctec Hummingbird quadrotor vehicle, is studied and described in detail. A complete mathematical model is obtained and a freely available and open simulation platform is built. Furthermore, an autopilot controller is designed and implemented in the real platform.
The control part is focused on the path following problem. That is, following a predefined
path in space without any time constraint. Diverse control-oriented and geometrical algorithms are studied, implemented and compared. Then, the geometrical algorithms are improved by obtaining adaptive approaches that do not need any parameter tuning. The adaptive geometrical approaches are developed by means of Neural Networks. To end up, a deep reinforcement learning approach is developed to solve the path following problem. This approach implements the Deep Deterministic Policy Gradient algorithm. The resulting approach is trained in a realistic multirotor simulator and tested in real experiments with success. The proposed approach is able to accurately follow a path while adapting the vehicle's velocity depending on the path's shape.
In the navigation part, an obstacle detection system based on the use of a LIDAR sensor is implemented. A model of the sensor is derived and included in the simulator. Moreover, an approach for treating the sensor data to eliminate the possible ground detections is developed.
The guidance part is focused on the reactive path planning problem. That is, a path planning algorithm that is able to re-plan the trajectory online if an unexpected event, such as detecting an obstacle in the vehicle's route, occurs. A deep reinforcement learning approach for the reactive obstacle avoidance problem is developed. This approach implements the Deep Deterministic Policy Gradient algorithm. The developed deep reinforcement learning agent is trained and tested in the realistic simulation platform. This agent is combined with the path following agent and the rest of the elements developed in the thesis obtaining a GNC system that is able to follow different types of paths while avoiding obstacle in the vehicle's route.
... Due to the differences in performance, functions, and roles of heterogeneous UAVs, their cooperation generally involves more problems, such as coalition formation and role assignment , which are closely related to their cooperative path planning. Also, UAVs may cooperate with other categories of vehicles, such as ground vehicles and underwater vehicles, to achieve multi-domain coordination in complex tasks (Sujit et al., 2009;Quintin et al., 2017;Ding et al., 2019b). Their coordination in various dimensions, e.g., task, time, and space, will bring about behavioral dependence and thus new constraints, posing more challenges to the CPP in a larger heterogeneous group (Chen J et al., 2016). ...
As a cutting-edge branch of unmanned aerial vehicle (UAV) technology, the cooperation of a group of UAVs has attracted increasing attention from both civil and military sectors, due to its remarkable merits in functionality and flexibility for accomplishing complex extensive tasks, e.g., search and rescue, fire-fighting, reconnaissance, and surveillance. Cooperative path planning (CPP) is a key problem for a UAV group in executing tasks collectively. In this paper, an attempt is made to perform a comprehensive review of the research on CPP for UAV groups. First, a generalized optimization framework of CPP problems is proposed from the viewpoint of three key elements, i.e., task, UAV group, and environment, as a basis for a comprehensive classification of different types of CPP problems. By following the proposed framework, a taxonomy for the classification of existing CPP problems is proposed to describe different kinds of CPPs in a unified way. Then, a review and a statistical analysis are presented based on the taxonomy, emphasizing the coordinative elements in the existing CPP research. In addition, a collection of challenging CPP problems are provided to highlight future research directions.
... Another common limitation for mobile vehicles that must be taken into account when developing trajectories for vehicles is the executability of a trajectory. The maximum curvature limitation for path planning is commonly addressed with the Dubins path, which is formed using a waypoint path planner that produces optimal distance paths between two oriented points using circular arcs and straight lines while taking into account maximum curvature constraints [6]. Dubins paths, however, require instantaneous changes in curvature which is often not achievable in physical systems due to actuator limitations and wheel slippage [15]. ...
This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in front of the vehicle can be controlled to track a desired trajectory, albeit with a steady-state error. To eliminate steady state error, a sufficiently smooth trajectory is reformulated for the new reference point such that, when tracking the new trajectory, the vehicle asymptotically converges to the original trajectory. The resulting zero-error tracking law is demonstrated through a novel framework for creating time-indexed Clothoids. The Clothoids can be planned to pass through arbitrary waypoints using traditional methods yet result in trajectories that can be followed with zero steady-state error. The results of the control method and planner are illustrated in simulation wherein zero-error tracking is demonstrated.
... It models indeed an unicycle (Aicardi et al., 1995) with ω and v being the angular and linear velocities, respectively. Several works proved that by opportunely using ω and v all the points in R 2 can be reached, even in presence of constraints on ω, and with strictly positive v (Dubins, 1957;Consolini et al., 2009). This assures that the map is well-posed. ...
Proportional and simultaneous control algorithms are considered as one of the most effective ways of mapping electromyographic signals to an artificial device. However, the applicability of these methods is limited by the high number of electromyographic features that they require to operate—typically twice as many the actuators to be controlled.Indeed, extracting many independent electromyographic signals is challenging for a number of reasons—ranging from technological to anatomical. On the contrary, the number of actively moving parts in classic prostheses or extra-limbs is often high. This paper faces this issue, by proposing and experimentally assessing a set of algorithms which are capable of proportionally and simultaneously control as many actuators as there are independent electromyographic signals available. Two sets of solutions are considered. The first uses as input electromyographic signals only, while the second adds postural measurements to the sources of information. At first, all the proposed algorithms are experimentally tested in terms of precision, efficiency, and usability on twelve able-bodied subjects, in a virtual environment. A state-of-the-art controller using twice the amount of electromyographic signals as input is adopted as benchmark. We then performed qualitative tests, where the maps are used to control a prototype of upper limb prosthesis. The device is composed of a robotic hand and a wrist implementing active prono-supination movement. Eight able-bodied subjects participated to this second round of testings. Finally, the proposed strategies were tested in exploratory experiments involving two subjects with limb loss. Results coming from the evaluations in virtual and realistic settings show encouraging results and suggest the effectiveness of the proposed approach.
... The help of γ-trajectory [13] is taken for path generation, as it is very convenient to change the path length by a parameter 'γ' which shall be discussed in section II.A.3. In literature, for creating smooth flyable paths for turn-rate constraint vehicles, a large number of work [14], [15], [16] use Dubins path [17]. The other popular approaches for generating continuous flyable paths are to use splines [18], clothoid arcs [19], [20], and Pythagorean hodograph [21]. ...
... An interceptor and target were modeled as Dubins vehicles [18] in R 2 with x representing East and y altitude, shown in Figure 1. UAV position [x y] T was determined from the integral of the velocity [ x y] T shown in Equation 1. ...
... This section develops the estimation method using an extended Kalman filter. The extended Kalman filter is a standardized algorithm [13] when the dynamics and/or measurement models are described by nonlinear relations of some states or parameters to be estimated. Once the system dynamic model and measurement model are designed, the remainder of the algorithm follows the standardized sequence. ...
... In applied works, based on the mathematical theory of control, the model of a controlled object, called the Dubins machine [12], is very popular. Such model is given by a nonlinear system of third-order differential equations. ...
The complexity of the control of the road train is due to the pronounced nonlinearities, as well as the instability of the control object during the movement in the backward motion (jackknifing). For the road trains, the location of the towing device behind the tractor's rear axle is quite typical. In this study, a synthesis of control laws for road trains with offset of coupling devices relative to the rear axle of the tractor (off-axle hitching) is proposed. The controllers have been implemented both to ensure a stable circular motion and for rectilinear motion with a given orientation angle, and the behavioral features of this model have been studied on the basis of them. Based on the analysis of the approaches to the synthesis of the laws governing the road train with the coupling out, it was decided to synthesize the required control laws using the Lyapunov function method. Synthesized controllers can be directly used to program the robotic systems of the respective models. It is also possible to use them for the development of the Dubins machine for the investigated model. They can be used to build automatic control systems that would help the driver to drive a car with a trailer while driving backward. In this research, a study was made of the state of the solution of the problem associated with the reverse movement of a road train consisting of a tractor and a semitrailer with a coupling, synthesized laws made it possible to study the features of such model, determined by its linear dimensions. For comparison of the synthesized laws, the analysis of phase portraits of trajectories, angles of folding and control, orientation angles was carried out, and also the analysis of the quality of transient processes with the change in the speed of the road train was performed.
... The Dubins path [11] is the shortest path between two states in an obstacle-free world for a car which can only drive forward at constant velocity and turn at a bounded turning rate. The shortest path consists of three segments which are either straight (S), left turn (L), or right turn (R) with the maximum turn rate. ...
Today, low-altitude fixed-wing Unmanned Aerial Vehicles (UAVs) are largely limited to primitively follow user-defined waypoints. To allow fully-autonomous remote missions in complex environments, real-time environment-aware navigation is required both with respect to terrain and strong wind drafts. This paper presents two relevant initial contributions: First, the literature's first-ever 3D wind field prediction method which can run in real time onboard a UAV is presented. The approach retrieves low-resolution global weather data, and uses potential flow theory to adjust the wind field such that terrain boundaries, mass conservation, and the atmospheric stratification are observed. A comparison with 1D LIDAR data shows an overall wind error reduction of 23% with respect to the zero-wind assumption that is mostly used for UAV path planning today. However, given that the vertical winds are not resolved accurately enough further research is required and identified. Second, a sampling-based path planner that considers the aircraft dynamics in non-uniform wind iteratively via Dubins airplane paths is presented. Performance optimizations, e.g. obstacle-aware sampling and fast 2.5D-map collision checks, render the planner 50% faster than the Open Motion Planning Library (OMPL) implementation. Test cases in Alpine terrain show that the wind-aware planning performs up to 50x less iterations than shortest-path planning and is thus slower in low winds, but that it tends to deliver lower-cost paths in stronger winds. More importantly, in contrast to the shortest-path planner, it always delivers collision-free paths. Overall, our initial research demonstrates the feasibility of 3D wind field prediction from a UAV and the advantages of wind-aware planning. This paves the way for follow-up research on fully-autonomous environment-aware navigation of UAVs in real-life missions and complex terrain.
... Some optimal control problem formulations have taken into account the effect of an external flowfield. For example, in [19], the authors addressed the problem of optimal guidance to a specified position of a Dubins vehicle [20] under the influence of an external flow. The minimum-time guidance problem for an isotropic rocket in the presence of wind has been studied in [21]. ...
In this paper, a reachability-based approach is adopted to deal with the pursuit-evasion differential game between one evader and multiple pursuers in the presence of dynamic environmental disturbances (for example, winds or sea currents). Conditions for the game to be terminated are given in terms of reachable set inclusions. Level set equations are defined and solved to generate the forward reachable sets of the pursuers and the evader. The time-optimal trajectories and the corresponding optimal strategies are subsequently retrieved from these level sets. The pursuers are divided into active pursuers, guards, and redundant pursuers according to their respective roles in the pursuit- evasion game. The proposed scheme is implemented on problems with both simple and realistic time-dependent flowfields, with and without obstacles. Copyright © 2016 by the American Institute of Aeronautics and Astronautics, Inc.
... Finally, angular velocity, ω i , is computed as ω i = k(atan2(u y i , u x i ) − θ i ) where k is a positive gain and atan2(u y i , u x i ) is the two argument variation of the arc-tangent that places the angle in the correct quadrant by considering the signs of the y and x components of u i . Because we limit (atan2(u y i , u x i ) − θ i ) to the interval [−π, π], the magnitude of ω i is bounded by kπ, matching the Dubins curve model (Dubins, 1957) often used for single and multiple UAV path planning (Chitsaz & LaValle, 2007; Ding, Rahmani, & Egerstedt, 2010). ...
The search for invariants is a fundamental aim of scientific endeavors. These invariants, such as Newton’s laws of motion, allow us to model and predict the behavior of systems across many different problems. In the nascent field of Human-Swarm Interaction (HSI), a systematic identification of fundamental invariants is still lacking. Discovering and formalizing these invariants will provide
a foundation for developing, and better understanding, effective methods for HSI. We propose two invariants underlying HSI for geometric-based swarms: (1) collective state is the fundamental percept associated with a bio-inspired swarm, and (2) a human’s ability to influence and understand the collective state of a swarm is determined by the balance between the span and persistence. We provide evidence of these invariants by synthesizing much of our previous work in the area of HSI with several new results, including a novel user study where users manage multiple swarms simultaneously. We also discuss how these invariants can be applied to enable more efficient and successful teaming between humans and bio-inspired collectives and identify several promising directions for future research into the invariants of HSI.
... Given (P i , ↵) and (P f , ), the task is to find the shortest smooth path from P i to P f such that it starts and ends with the directions of motions ↵ and , respectively, and the path curvature is limited by 1/⇢ where ⇢ is the minimum turning radius of the vehicle or the robot under consideration. The first complete solution to this problem was first reported by Dubins in 1957 [25] where he showed that the shortest feasible path consists of exactly three path segments of a sequence CCC or CSC, where C for circle is an arc of radius ⇢, and S for straight is a line segment which can then be decomposed into a set of six candidate paths. The optimum path was then found by explicitly computing all paths on the list and then comparing them which may become a problem in applications where computation time is critical, such as in real-time robot motion planning. ...
This paper proposes a path planning algorithm based on 2D Dubins' path for the construction of a curvature continuous trajectory for the autonomous guidance of line marking robots in football stadiums. The algorithm starts with four corner points representing the playable football field and generates a set of waypoints representing various parts of the field layout such as touch and goal lines, goal and penalty area, center line and mark, corner and penalty arcs, center mark and center circle, and penalty marks. A complete, continuous and smooth path is then generated by connecting these waypoints using 2D Dubins' path in a way to ensure that the generated path takes into account the dynamic constraints of the vehicle (such as maximum curvature and velocity), keep the vehicle at a safe distance from obstacles, and not harm the field grass. The efficiency of the algorithm is tested using simulation and in reality. Results showed that the algorithm is able to reliably plan a safe path in real time able to command the line marking robot with high accuracy and without the need for human guidance. The path planning algorithm developed in this paper is implemented in both Matlab and Python.
... Most of the time, a path cannot satisfy all desired properties and the designer has to compromise and select the one most fitting for a given task. For instance, Dubins (1957) showed that the shortest path for a car-like vehicle with prescribed minimum turning radius consists of straight lines and circular arcs, however this path includes curvature discontinuities. Clothoids avoid the curvature discontinuities but the computational cost is much higher (Tsourdos et al., 2011). ...
This paper investigates the feasibility of using pseudospectral (PS) optimal control in real-time path planning for marine surface vehicles in environments where both obstacles and unknown disturbances are present. In particular, the simplified kinematic equations of an underactuated marine surface vehicle exposed to unknown ocean currents are considered, and the software package DIDO is used to compute the optimal path via PS optimization, initially assuming the ocean current is zero. In that case, the resulting path is minimum-length (similar to Dubins path) but not minimum-time. The main contribution concerns the addition of a nonlinear observer, which estimates online the effects of the ocean current on the vehicle, and that of a guidance system which generates appropriate reference trajectories in order to minimize the position error and track the optimal trajectory successfully. It is shown that through occasional replanning, according to the information about the ocean current parameters coming from the observer, the updated path converges to the minimum-time path. Two different implementations of the approach are presented and illustrated through numerical simulations.
... Where sharp and angular turns on the paths are sometimes infeasible and difficult for robot control, this situation needs to be smoothed out, such that the robot can move continuously and avoid abrupt motion. Path smoothing using parametric curves was proposed as early as 1957 by L. Dublin in [17, 18]. Generally known as Dublin curves, they employ lines and circles, but suffer from the prob‐ lem of discontinuities. ...
Generating smooth and continuous paths for robots with collision avoidance, which avoid sharp turns, is an important problem in the context of autonomous robot navigation. This paper presents novel smooth hypocycloidal paths (SHP) for robot motion. It is integrated with collision-free and decoupled multi-robot path planning. An SHP diffuses (i.e., moves points along segments) the points of sharp turns in the global path of the map into nodes, which are used to generate smooth hypocycloidal curves that maintain a safe clearance in relation to the obstacles. These nodes are also used as safe points of retreat to avoid collision with other robots. The novel contributions of this work are as follows: (1) The proposed work is the first use of hypocycloid geometry to produce smooth and continuous paths for robot motion. A mathematical analysis of SHP generation in various scenarios is discussed. (2) The proposed work is also the first to consider the case of smooth and collision-free path generation for a load carrying robot. (3) Traditionally, path smoothing and collision avoidance have been addressed as separate problems. This work proposes integrated and decoupled collision-free multi-robot path planning. ‵Node caching‵ is proposed to improve efficiency. A decoupled approach with local communication enables the paths of robots to be dynamically changed. (4) A novel ‵multi-robot map update‵ in case of dynamic obstacles in the map is proposed, such that robots update other robots about the positions of dynamic obstacles in the map. A timestamp feature ensures that all the robots have the most updated map. Comparison between SHP and other path smoothing techniques and experimental results in real environments confirm that SHP can generate smooth paths for robots and avoid collision with other robots through local communication.
... The bounded-curvature path-planning problem, a central problem in robotics, involves planning a collision-free path for a nonholonomic robot moving amid obstacles, and has been widely studied (see, e.g., [2]). Dubins seminal work [3] characterizes shortest bounded-curvature paths in the absence of obstacles. He first notices that shortest boundedcurvature paths are made of arcs of minimum radius circles (C-segments) and straight line segments (S-segments). ...
This paper investigates a path planning algorithm for Dubins vehicles. Our approach is based on approximation of the trajectories of vehicles using sequence of waypoints and treating each way point as a moving particle in the space. We define interaction forces between the particles such that the resulting multi-particle system will be stable, moreover, the trajectories generated by the waypoints in the equilibria of the multi-particle system will satisfy all of the hard constraint such as bounded-curvature constraint and obstacle avoidance.
... If the vehicle has minimum turning radius, then the shortest path will consist of a sequence of arcs and straight lines [79]. Also, in [37] the authors find smooth shortest path with restriction on average curvature. Elastic bands introduced the algorithm to deform the path mobile robots in dynamic environments [78], which has been extended to mobile manipulation problem [22, 103]. ...
My thesis addresses the the problem of manipulation using multiple robots with cables. I study how robots with cables can tow objects in the plane, on the ground and on water, and how they can carry suspended payloads in the air. Specifically, I focus on planning optimal trajectories for robots.
Path planning or trajectory generation for robotic systems is an active area of research in robotics. Many algorithms have been developed to generate path or trajectory for different robotic systems. One can classify planning algorithms into two broad categories. The first one is graph-search based motion planning over discretized configuration spaces. These algorithms are complete and quite efficient for finding optimal paths in cluttered 2-D and 3-D environments and are widely used [48]. The other class of algorithms are optimal control based methods. In most cases, the optimal control problem to generate optimal trajectories can be framed as a nonlinear and non convex optimization problem which is hard to solve. Recent work has attempted to overcome these shortcomings [68]. Advances in computational power and more sophisticated optimization algorithms have allowed us to solve more complex problems faster. However, our main interest is incorporating topological constraints. Topological constraints naturally arise when cables are used to wrap around objects. They are also important when robots have to move one way around the obstacles rather than the other way around. Thus I consider the optimal trajectory generation problem under topological constraints, and pursue problems that can be solved in finite-time, guaranteeing global optimal solutions.
In my thesis, I first consider the problem of planning optimal trajectories around obstacles using optimal control methodologies. I then present the mathematical framework and algorithms for multi-robot topological exploration of unknown environments in which the main goal is to identify the different topological classes of paths. Finally, I address the manipulation and transportation of multiple objects with cables. Here I consider teams of two or three ground robots towing objects on the ground, two or three aerial robots carrying a suspended payload, and two boats towing a boom with applications to oil skimming and clean up. In all these problems, it is important to consider the topological constraints on the cable configurations as well as those on the paths of robot. I present solutions to the trajectory generation problem for all of these problems.
... The Dubins' car [16] is commonly used to model ground vehicle behavior, and describes the trajectory of a car's center of mass as a function of its velocity and steering angle. Consider an autonomous vehicle moving in a straight line (horizontally) with a constant velocity, v = 0.5 m/s. ...
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the interactions with the environment; however, one must still guarantee that the model, despite uncertainty, behaves acceptably. This paper presents a convex optimization method to efficiently compute the set of configurations of a polynomial dynamical system that are able to safely reach a user defined target set despite parametric uncertainty in the model. Since planning in the presence of uncertainty can lead to undesirable conservatives, this paper computes those trajectories of the uncertain nonlinear systems which are $\alpha$-probable of reaching the desired configuration. The presented approach uses the notion of occupation measures to describe the evolution of trajectories of a nonlinear system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation is approximated with vanishing conservatism using a hierarchy of semidefinite programs each of which is proven to compute an approximation to the set of initial conditions that are $\alpha$-probable of reaching the user defined target set safely in spite of uncertainty. The efficacy of this method is illustrated on four systems with parametric uncertainty.
... An important objective in the field of mobile robotics since the first papers of Dubins [16] is to find the optimal trajectory between two points with specified tangents vectors and velocities. Moreover, other non dynamic constraints [6, 22, 34] are considered, such as the geometric continuity of the path [33, 38], the restrictions on the maximum curvature [23, 35], the avoidance of obstacles [3, 7, 20] . ...
The basic module for the solution of the minimum time optimal control of a car-like vehicle is herein presented. The vehicle is subject to the effect of laminar (linear) and aerodynamic (quadratic) drag, taking into account the asymmetric bounded longitudinal accelerations. This module is studied and designed to be fast and robust in sight to be the fundamental building block of a more extended optimal control problem that considers a given clothoid as the trajectory and the presence of a constraint on the lateral acceleration of the vehicle. The nonlinear dynamics and the different possible boundary conditions yield different analytical solutions of the differential equations, hence they by themselves a particular attention. The study of the numeric stability of the computation for limit values of the parameters is essential as showed in the numerical tests.
... We also use the smoothness and comfort characteristics of clothoid-driving in our controller design. Early work on path planning for nonholonomic vehicles focused on the generation of Dubins' curves (i.e., paths obtained by connecting circular arcs and straight lines) [80, 81]. These type of paths do not have a continuous curvature. ...
Autonomous vehicles is a rapidly expanding field, and promise to play an important role in society. The goal of autonomous vehicles is to improve the traffic system in terms of higher efficiency, fewer accidents, lower fuel consumption, less pollution, and shorter travel times. In more isolated environments, such as mines and ports, vehicle automation can bring significant efficiency and production benefits and it eliminates repetitive jobs that can lead to inattention and accidents. The results of this thesis are developed within the iQMatic project, which is lead by Scania CV AB in collaboration with Saab AB, Autoliv, Linköping University, and KTH, with the goal of developing a fully autonomous truck for mining applications by 2018.
The thesis addresses the problem of lateral and longitudinal dynamics control of autonomous ground vehicles with the purpose of accurate and smooth path following. Clothoids are curves with linearly varying curvature, which are widely used in road design due to their smoothness properties. In the thesis, clothoids are used in the design of optimal predictive controllers aimed at minimizing the lateral forces and jerks in the vehicle.
First, a clothoid-based path sparsification algorithm is proposed to efficiently describe the reference path. This approach relies on a sparseness regularization technique such that a minimal number of clothoids is used to describe the reference path.
Second, a clothoid-based model predictive controller (MPCC) is proposed. This controller aims at producing a smooth driving by taking advantage of the clothoid properties. The motion of a vehicle traveling at low speeds is assumed to define a clothoid segment if the steering angle is chosen to vary piecewise linearly with respect to the traveled distance.
Third, an alternative formulation of a controller for smooth driving is presented. In this case, we formulate the problem as an economic model predictive controller (EMPC). In EMPC the objective function contains an economic cost (here represented by comfort or smoothness), which is described by the second and first derivatives of the curvature. This results in that the obtained curvature is approximately linear.
Fourth, the generation of feasible speed profiles, and the longitudinal vehicle control for following these, is studied. The speed profile generation is formulated as an optimization problem with two contradictory objectives: to drive as fast as possible (close to the speed limit) while accelerating as little as possible. Constraints are given by vehicle limitations and road geometry. The longitudinal controller is formulated in a similar way, but is implemented in a receding horizon fashion, and provides feasible reference speeds to a cruise controller.
Finally, experimental and simulation evaluation are performed. The EMPC is deployed on a Scania construction truck. The experimental evaluation with the EMPC demonstrates its good performance, since the deviation from the path never exceeds 30 cm and in average is 6 cm. A simulation environment is developed allowing evaluation and validation of the control design before deploying it in the experimental platform. The EMPC and the MPCC are compared with a pure-pursuit controller (PPC) and a standard MPC. The results demonstrate the effectiveness of both the MPCC and the EMPC. Furthermore, the EMPC clearly outperforms the PPC in terms of path accuracy and the standard MPC in terms of driving smoothness.
... Laumond et al. (1994) integrate grid based planning with nonholonomic constraints using Reed and Shepp's model discussed in Reeds and Shepp (1990). While these approaches Dubins (1961Dubins ( , 1957) and Reeds and Shepp (1990) give us the shortest paths joining any two configurations, the main drawback of these paths is that their curvature is not continuous. Therefore a vehicle following such a path has to stop at each discontinuity (e.g at the transition between a straight line and a circular segment), reorient it wheels, and then move forward. ...
This paper focuses on the spline based trajectory generation and motion planning in a 1:10 scale down prototype of a car. The car type vehicle can be modelled as a nonholonomic system with constraints on sideways movement. The spline based trajectory generation gives us continuous, smooth and optimized path trajectories. The motion planning algorithm is based on the nonholonomic model of a car-type robot which is differentially flat in nature. Our contribution lies in the development of spline based trajectories which overcome the parametric singularities arising from the differential flatness based approach. The spline trajectories also take care of the singularities which are otherwise observed in the optimization process if the cubic polynomial based interpolation is implemented. The hardware implementation for a prototype of a car type model is also presented. Using the concept of differential flatness, we derive control inputs which steer the vehicle along this trajectory.
... The used curves fall into two categories: those whose coordinates have a closedform expression (B-spline, quintic polynomials, polar splines, etc.) and parametric curves whose curvature is a function of their arc length (clothoids, cubic spirals, intrinsic splines, etc.) [3]. Dubins paths, which are made by joining straight lines and circular arcs of maximum curvature, were proposed to generate feasible paths for car-like robots [4]. However, as highlighted by Fraichard and Scheuer [3], the curvature of this type of path is discontinuous. ...
The process of finding an optimum, smooth and feasible global path for mobile robot navigation usually involves determining the shortest polyline path, which will be subsequently smoothed to satisfy the requirements. Within this context, this paper deals with a novel roadmap algorithm for generating an optimal path in terms of Non-Uniform Rational B-Splines (NURBS) curves. The generated path is well constrained within the curvature limit by exploiting the influence of the weight parameter of NURBS and/or the control points’ locations. The novelty of this paper lies in the fact that NURBS curves are not used only as a means of smoothing, but they are also involved in meeting the system’s constraints via a suitable parameterization of the weights and locations of control points. The accurate parameterization of weights allows for a greater benefit to be derived from the influence and geometrical effect of this factor, which has not been well investigated in previous works. The effectiveness of the proposed algorithm is demonstrated through extensive MATLAB computer simulations.
... Planners in the first category are based on geometrics. Efforts following the pioneering works by Dubins [8] and by Reeds and Shepp [9] have been devoted to plan paths that consist of straight line segments and circular arcs with minimum radius1011121314. Other kinds of smooth paths have also been pursued to ease the subsequent control execution procedure [2,15161718. ...
Autonomous parking has been a widely developed branch of intelligent transportation systems. In autonomous parking, maneuver planning is a crucial procedure that determines how intelligent the entire parking system will be. This study concerns planning time-optimal parallel parking maneuvers in a straightforward, accurate, and purely objective way. A unified dynamic optimization framework is established, which includes the vehicle kinematics, physical restrictions, collision-avoidance constraints, and an optimization objective. Interior-point method (IPM) based simultaneous dynamic optimization methodology is adopted to solve the formulated dynamic optimization problem numerically. Given that near-feasible solutions have been widely acknowledged to ease optimizing NLPs, a critical region based initialization strategy is proposed to facilitate the off-line NLP-solving process, a look-up table based strategy is proposed to guarantee the on-site planning performance, and a receding horizon optimization framework is proposed for on-line maneuver planning. A series of parallel parking cases are tested to validate our motion planner. Simulation results demonstrate that our proposal is efficient, even when the slot length is merely 10.19% larger than the car length. As a unified maneuver planner, our adopted IPM-based simultaneous dynamic optimization method can deal with any user-specified demand provided that it can be explicitly described.
... The task is to find the shortest smooth path from 0 0 ( , ; ) x y α to 1 1 ( , ; ) x y β such that the path curvature is limited by 1 / ρ , where ρ is the minimal turning radius. The problem of finding the shortest smooth path between two configurations in the plane was firstly considered by Dubins [8] . The classical 1957 result by Dubins gives a sufficient set of paths (Dubins path) which always contains the shortest path. ...
Dubins has proved in 1957 that the minimum length path between an initial and a terminal configuration can be found among the six paths {LSL, RSR, LSR, RSL, RLR, LRL}. Skel and Lumelsky have studied the length of Dubins path with the initial configuration (0, 0; α) and the terminal configuration (d, 0; β) and the minimal turning radius ρ=1 in 2001. We extended the Skel and Lumelsky’s results to the case that the initial and terminal configuration is(x 0 , y 0 , α), (x 1 , y 1 , β), respectively (where x 0 , y 0 , x 1 , y 1 ϵℝ), and the minimal turning radius is ρ>0.
... As our first example we consider a ground vehicle model based on the Dubins car [Dubins, 1957] navigating an environment of polygonal obstacles. A pictorial depiction of the model is provided in Figure 6. ...
In this paper we consider the problem of generating motion plans for a robot
that are guaranteed to succeed despite uncertainty in the environment,
parametric model uncertainty, and disturbances. Furthermore, we consider the
case where these plans must be generated in real-time, because constraints such
as obstacles in the environment may not be known until they are perceived (with
a noisy sensor) at runtime. Previous work on feedback motion planning for
nonlinear systems was limited to offline planning due to the computational cost
of safety verification. Here we augment the traditional trajectory library
approach by designing locally stabilizing controllers for each nominal
trajectory in the library and providing guarantees on the resulting closed-loop
systems. We leverage sums-of-squares (SOS) programming to design these locally
stabilizing controllers by explicitly attempting to minimize the size of the
worst case reachable set of the closed-loop system subjected to bounded
disturbances and uncertainty. The reachable sets associated with each
trajectory in the library can be thought of as "funnels" that the system is
guaranteed to remain within. The resulting funnel library is then used to
sequentially compose motion plans at runtime while ensuring the safety of the
robot. A major advantage of the work presented here is that by explicitly
taking into account the effect of uncertainty, the robot can evaluate motion
plans based on how vulnerable they are to disturbances. We demonstrate our
method using thorough simulation experiments of a ground vehicle model
navigating through cluttered environments and also present extensive hardware
experiments validating the approach on a small fixed-wing airplane avoiding
obstacles at high speed.
... Their benefit is that they can incorporate the current robot's velocity. Another work that takes Ackermann geometries into account is [12] which makes use of Dubin's paths [13]. The idea is to perform motion commands that only consist of a combination of the plain motions left, forward and right. ...
For a mobile service robot, safe navigation is essential. To do so, the robot needs to be equipped with collision avoidance and global path planning capabilities. The target platforms considered in this paper are Ackermann-driven vehicles. Hence, a planning approach which directly takes the kinematic and dynamic constraints of the vehicle into account is required. The Search-based Planning Library (SBPL) package of the Robot Operating System (ROS) provides global path planning which takes these constraints into account. However, it misses a local planner that can also make use of the Ackermann kinematic constraints for collision avoidance. A local planner is useful to take dynamic obstacles into account as early as possible. In this paper, we extend the SBPL included in ROS by a local planner, which makes use of motion primitives. We extend the ROS package and show first experimental results on Ackermann-driven vehicles.
... In this work, it is assumed is that the aircraft is able to follow any bend of the on-service path, as well as any trajectory made up by compositions of straight lines and arcs of circle tangent each other with constant turn radius R turn . This hypothesis allows to model the additional paths as Dubins curves [6], i.e. sequences of a maximum of three straight or curve primitives. ...
The aim of this paper is to implement a Game-Theorybased offline mission path planner for aerial inspectiontasks of large linear infrastructures. Like most realworldoptimisation problems, mission path planninginvolves a number of objectives which ideally should beminimised simultaneously. The goal of this work is thento develop a Multi-Objective (MO) optimisation toolable to provide a set of optimal solutions for theinspection task, given the environment data, the missionrequirements and the definition of the objectives tominimise. Results indicate the robustness and capabilityof the method to find the trade-off between the Paretooptimal solutions.
... The CCP for a nonholonomic vehicle are dealt with many previous works. Firstly, Dubins (Dubins, 1957) , Reeds-Shepp (Reeds and Shepp, 1990) (RS path) proposed the smooth path model for nonholonomic vehicle yielding to the shortest in travel length, however it lacks the curvature continuity. Fraichard-Scheuer (Fraichard and Scheuer, 2004) (FS path) presented a continuous steering planning composed by lines, circular arcs and clothoids curves. ...
This paper presents smooth trajectory generation scheme for obstacle avoidance in static and dynamic environment. The smooth trajectory has successive two steps where smooth path is generated firstly and then corresponding velocity is planned along the path. Smooth path of continuous curvature is composed by para-metrically adjusted clothoids with proposed algorithm and then the safe velocity planning is carried out in the 4D configuration framework. Two circles are used to completely surround the used nonholonomic car-like vehicle, this permit to check the probable future vehicle's collisions and to have space-time analysis. Some demonstrative simulations show the strong potential of the proposed smooth and flexible methodology for future experimentations with actual vehicles.
... The magnitude of ωi is bounded by π/2. Thus, the agent dynamics match the Dubins curve model which is often used for actual UAV path planning and applies to many constant-speed, non-holonomic ground robots [5]. Similar to the Couzin model of biological swarms [3] and the Reynold model of synthetic agents [15], agents in this model react to neighbors within three different zones: repulsion, orientation , and attraction. ...
Models of swarming and modes of controlling them are numerous; however, to date swarm researchers have mostly ignored a fundamental problem that impedes scalable human interaction with large bio-inspired robot swarms, namely, how do you know what the swarm is doing if you can't observe every agent in the collective? We examine swarm models that exhibit multiple collective motion patterns from the same parameters. These multiple emergent behaviors provide increased expressivity, but at the cost of uncertainty about the swarm's actual behavior. Because bandwidth and time constraints limit the number of agents that can be observed in a swarm, it is desirable to be able to recognize and monitor the collective behavior of a swarm through limited samples from a small subset of agents. We present a novel framework for classifying the collective behavior of a bio-inspired robot swarm using locally-based approximations of a swarm's global features. We apply this framework to two bio-inspired models of swarming that exhibit a flock and torus behavior and a swarm, torus, and flock behavior, respectively. We present both a formal metric of expressivity and a classifier that leverages local agent-level features to accurately recognize these collective swarm behaviors while sampling from only a small number of agents. Copyright © 2014, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.
Planning the path is the most important task in the mobile robot navigation. This task involves basically three aspects. First, the planned path must run from a given starting point to a given endpoint. Secondly, it should ensure robot’s collision-free movement. Thirdly, among all the possible paths that meet the first two requirements it must be, in a certain sense, optimal.
Methods of path planning can be classified according to different characteristics. In the context of using intelligent technologies, they can be divided into traditional methods and heuristic ones. By the nature of the environment, it is possible to divide planning methods into planning methods in a static environment and in a dynamic one (it should be noted, however, that a static environment is rare). Methods can also be divided according to the completeness of information about the environment, namely methods with complete information (in this case the issue is a global path planning) and methods with incomplete information (usually, this refers to the situational awareness in the immediate vicinity of the robot, in this case it is a local path planning). Note that incomplete information about the environment can be a consequence of the changing environment, i.e. in a dynamic environment, there is, usually, a local path planning.
Literature offers a great deal of methods for path planning where various heuristic techniques are used, which, as a rule, result from the denotative meaning of the problem being solved. This review discusses the main approaches to the problem solution. Here we can distinguish five classes of basic methods: graph-based methods, methods based on cell decomposition, use of potential fields, optimization methods, фтв methods based on intelligent technologies.
Many methods of path planning, as a result, give a chain of reference points (waypoints) connecting the beginning and end of the path. This should be seen as an intermediate result. The problem to route the reference points along the constructed chain arises. It is called the task of smoothing the path, and the review addresses this problem as well.
A geometric proof is given that a closed plane curve of length L and curvature bounded by K can be contained inside a circle of radius L/4 − (π − 2)/2A.
We present a safety validation approach for Sense and Avoid (SAA) algorithms aboard Unmanned Aerial Vehicles (UAVs). We build multi-agent simulations to provide a test arena for UAVs with various SAA algorithms, in order to explore potential conflict situations. The simulation is configured by a series of parameters, which define a huge input space. Evolutionary search is used to explore the input space and to guide the simulation towards challenging situations, thus accelerating the process of finding dangerous faults of SAA algorithms and supporting the safety validation process. We applied our approach to the recently published Selective Velocity Obstacles (SVO) algorithm. In our first experiment, we used both random and evolutionary search to find mid-air collisions where UAVs have perfect sensing ability. We found evolutionary search can find some faults (here, interesting problems with SVO) that random search takes a long time to find. Our second experiment added sensor noise to the model. Random search found similar problems as it did in experiment one, but the evolutionary search found some interesting new problems. The two experiments show that the proposed approach has potential for safety validation of SAA algorithms.
The paper proposes a method for determining energy optimal trajectory from source position to goal position for differential drive robots. Energy consumption depends on the velocity profile of the generated trajectory. The proposed method makes use of Dubins path of optimum turning radius to plan the trajectory between two waypoints. The results are compared with other methods in terms of energy consumption for the generated trajectories using simulation. The proposed method computes energy optimal trajectory in linear time complexity with respect to the number of waypoints.
ResearchGate has not been able to resolve any references for this publication.