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25
The Ariadne's clew algorithm
, 1996
"... We present a general planning strategy to plan the motions of an agent having to explore a continuous state space in order to reach one or several goals. We propose a practical method to implement this technique based on a genetic algorithm and we illustrate the approach on the problem of controllin ..."
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Cited by 82 (5 self)
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We present a general planning strategy to plan the motions of an agent having to explore a continuous state space in order to reach one or several goals. We propose a practical method to implement this technique based on a genetic algorithm and we illustrate the approach on the problem of controlling a mobile robot moving in a maze and looking for several items. Finally, we show that this planning strategy may serve as a possible control structure for an autonomous system. Problem Solving and planning 1 Introduction This study was motivated by our previous work on robot motion planning using a parallel genetic algorithm [8]. The planner we have design and implemented on a parallel machine is capable of planning collision free paths for a mobile robot placed among obstacles. The main advantage of this planner is its speed, it can plan complex paths such as the two paths represented in figure 1 in less than 0.5 second on a parallel machine with 64 Transputers. As a consequence it can b...
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize t ..."
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Cited by 65 (9 self)
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This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collisionfree segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic carlike robots is described, along with implementation results for 12 robots.
Smooth motion planning for carlike vehicles
 IEEE Transactions on Robotics and Automation
, 2001
"... Abstract—This paper presents a steering method for a carlike vehicle providing smooth paths subjected to curvature constraints. We show how to integrate this steering method in a global motion planning scheme taking obstacles into account. The main idea of the paper is to consider the car as a 4D ..."
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Cited by 41 (0 self)
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Abstract—This paper presents a steering method for a carlike vehicle providing smooth paths subjected to curvature constraints. We show how to integrate this steering method in a global motion planning scheme taking obstacles into account. The main idea of the paper is to consider the car as a 4D system from a kinematic point of view and as a 3D system from a geometric point of view of collision checking. The resulting planned motions are guaranteed to be collisionfree and between two cusp points. Index Terms—Nonholonomic carlike robot, smooth motion planning. I.
Obstacle Distance for CarLike Robots
 IEEE Transactions on Robotics and Automation
, 1999
"... This paper shows how to compute the nonholonomic distance between a pointwise carlike robot and polygonal obstacles. Geometric constructions to compute the shortest paths from a configuration (given orientation and position in the plane of the robot) to a position (i.e., a configuration with unspe ..."
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Cited by 34 (3 self)
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This paper shows how to compute the nonholonomic distance between a pointwise carlike robot and polygonal obstacles. Geometric constructions to compute the shortest paths from a configuration (given orientation and position in the plane of the robot) to a position (i.e., a configuration with unspecified final orientation) are first presented. The geometric structure of the reachable set (set of points in the plane reachable by paths of given length #) is then used to compute the shortest paths to straightline segments. Obstacle distance is defined as the length of such shortest paths. The algorithms are developed for robots that can move both forward and backward (Reeds&Shepp's car) or only forward (Dubins' car). They are based on the convexity analysis of the reachable set. Keywords Carlike robots, shortest paths, nonholonomic distance. I. Introduction Distance computation plays a crucial role in robot motion planning. Numerous motion planning algorithms rely on obstacle dis...
Generalized Velocity Obstacles
 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS
, 2009
"... We address the problem of realtime navigation in dynamic environments for carlike robots. Our approach generalizes the concept of velocity obstacles, which have been used for navigation among dynamic obstacles, to take into account the constraints of a carlike robot. We present generalized veloci ..."
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Cited by 15 (6 self)
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We address the problem of realtime navigation in dynamic environments for carlike robots. Our approach generalizes the concept of velocity obstacles, which have been used for navigation among dynamic obstacles, to take into account the constraints of a carlike robot. We present generalized velocity obstacles, which identify actions that will lead to a collision with a moving obstacle at some point in the future. We discuss using this concept to find actions that will allow collision free navigation in dynamic environments as well as the probabilistic completeness of our algorithm in finding a feasible action and in finding an action of some specified distance from a preferred action. Finally, we demonstrate the performance of our algorithm on a simulated carlike robot among moving obstacles.
Coordinating the motions of multiple robots with kinodynamic constraints
 Proceedings of the IEEE International Conference on Robotics and Automation (ICRA
, 2003
"... This paper focuses on the coordination of multiple robots with kinodynamic constraints along specified paths. The presented approach generates continuous velocity profiles that avoid collisions and minimize the completion time for the robots. The approach identifies collision segments along each rob ..."
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Cited by 7 (3 self)
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This paper focuses on the coordination of multiple robots with kinodynamic constraints along specified paths. The presented approach generates continuous velocity profiles that avoid collisions and minimize the completion time for the robots. The approach identifies collision segments along each robot’s path and then optimizes the motions of the robots along their collision and collisionfree segments. For each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. Then the collision avoidance constraints for pairs of robots can be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations that provide schedules that are lower and upper bounds on the optimum; the upper bound schedule is a continuous velocity schedule. The approach is illustrated with robots modeled as double integrators subject to velocity and acceleration constraints. An implementation that coordinates 12 nonholonomic carlike robots is described. 1
Doorway Passing of an Intelligent Wheelchair by Dynamically Generating Bézier Curve Trajectory
"... Abstract — Door passing is the basic capability of an intelligent wheelchair. This paper presents a novel strategy to address the door passing issue by dynamically generating the Bézier curve based trajectory. It consists of door finding, optimization based trajectory generation and tracking control ..."
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Cited by 3 (3 self)
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Abstract — Door passing is the basic capability of an intelligent wheelchair. This paper presents a novel strategy to address the door passing issue by dynamically generating the Bézier curve based trajectory. It consists of door finding, optimization based trajectory generation and tracking control, which are executed repeatedly to increase the ability of passing the door and improve the performance. Whenever the door is detected, the optimization method produces a new smooth reference trajectory in real time for the wheelchair to follow. The proposed approach is tested in reality to verify its feasibility and efficiency, and the experimental results show its good performance in terms of the accuracy of finding the door and passing the doorway. I.
1 Path Planning and State Estimation for Unmanned Aerial Vehicles in Hostile Environments
"... Unmanned Aerial Vehicles (UAVs) are now widely used in antiterrorism activities and intelligence gathering to enhance mission performance and maximize safety. The susceptibility of these UAVs in hostile environments raises requirements for flight path planning. Path planning strategies in hostile e ..."
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Cited by 2 (0 self)
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Unmanned Aerial Vehicles (UAVs) are now widely used in antiterrorism activities and intelligence gathering to enhance mission performance and maximize safety. The susceptibility of these UAVs in hostile environments raises requirements for flight path planning. Path planning strategies in hostile environments normally are comprised of two phases [1], [2]. The first phase is a Voronoi graph search, which will generate polygonal graphs and will
SMOOTH LOCAL PATH PLANNING FOR A MOBILE MANIPULATOR
"... This paper presents a path planning technique for a mobile manipulator whose endeffector path is imposed by a given task. The planning is done decoupling the kinematics of the mobile platform and the manipulator, and planning for the former as a normal mobile robot. Two criteria for planning the pa ..."
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Cited by 1 (0 self)
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This paper presents a path planning technique for a mobile manipulator whose endeffector path is imposed by a given task. The planning is done decoupling the kinematics of the mobile platform and the manipulator, and planning for the former as a normal mobile robot. Two criteria for planning the path were implemented, one minimizing the need to turn the mobile robot and the other minimizing the gravity induced torque components of the manipulator. The linear velocity for following the path is also calculated, as a function of the given endeffector speed. Several results are presented in some typical applications of this planning.
Fast and accurate G1 fitting of clothoid curves
"... A new effective solution to the problem of Hermite G1 interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is a system of three nonlinear equations with multiple solutions ..."
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A new effective solution to the problem of Hermite G1 interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is a system of three nonlinear equations with multiple solutions which is difficult to solve also numerically. Here the solution of this system is reduced to the computation of the zeros of one single function in one variable. The location of the zero associated to the relevant solution is studied analytically: the interval containing the zero where the solution is proved to exists and to be unique is provided. A simple guess function allows to find that zero with very few iterations in all possible configurations. The computation of the clothoid curves and the solution algorithm call for the evaluation of Fresnel related integrals. Such integrals need asymptotic expansions near critical values to avoid loss of precision. This is necessary when, for example, the solution of the interpolation problem is close to a straight line or an arc of circle. A simple algorithm is presented for efficient computation of the asymptotic expansion. The reduction of the problem to a single nonlinear function in one variable and the use of asymptotic expansions make the present solution algorithm fast and robust. In particular a comparison with algorithms present in literature shows that the present algorithm requires less iterations. Moreover accuracy is maintained in all possible configurations while other algorithms have a loss of accuracy near the transition zones.