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21
Control of Mechanical Systems with Rolling Constraints: Application to the Dynamic Control of Mobile Robots”, Int
 Journal of Robotics Research
, 1994
"... There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holo ..."
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Cited by 69 (6 self)
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There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then discuss the inputoutput linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic inputoutput stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performance of trajectorytracking and pathfollowing algorithms. 1.
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...
Approximation Algorithms for CurvatureConstrained Shortest Paths
, 1996
"... Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time a ..."
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Cited by 24 (4 self)
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Let B be a point robot in the plane, whose path is constrained to have curvature of at most 1, and let\Omega be a set of polygonal obstacles with n vertices. We study the collisionfree, optimal pathplanning problem for B. Given a parameter ", we present an O((n 2 =" 2 ) log n)time algorithm for computing a collisionfree, curvatureconstrained path between two given positions, whose length is at most (1 + ") times the length of an optimal robust path (a path is robust if it remains collisionfree even if certain positions on the path are perturbed). Our algorithm thus runs significantly faster than the previously best known algorithm by Jacobs and Canny whose running time is O(( n+L " ) 2 + n 2 ( n+L " ) log n), where L is the total edge length of the obstacles. More importantly, the running time of our algorithm does not depend on the size of obstacles. The path returned by this algorithm is not necessarily robust. We present an O((n=") 2:5 log n) time algorithm that...
The AngularMetric Traveling Salesman Problem
 In Proceedings of the Eighth Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
"... Motivated by applications in robotics, we formulate the problem of minimizing the total angle cost of a TSP tour for a set of points in Euclidean space, where the angle cost of a tour is the sum of the direction changes at the points. We establish the NPhardness of both this problem and its relaxat ..."
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Cited by 21 (0 self)
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Motivated by applications in robotics, we formulate the problem of minimizing the total angle cost of a TSP tour for a set of points in Euclidean space, where the angle cost of a tour is the sum of the direction changes at the points. We establish the NPhardness of both this problem and its relaxation to the cycle cover problem. We then consider the issue of designing approximation algorithms for these problems and show that both problems can be approximated to within a ratio of O(log n) in polynomial time. We also consider the problem of simultaneously approximating both the angle and the length measure for a TSP tour. In studying the resulting tradeoff, we choose to focus on the sum of the two performance ratios and provide tight bounds on the sum. Finally, we consider the extremal value of the angle measure and obtain essentially tight bounds for it. In this extended abstract we restrict our attention to the planar setting, but all our results are easily extended to higher dimensio...
Pathvelocity decomposition revisited and applied to dynamic trajectory planning
 In IEEE International Conference of Automation and Robotics
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Dynamic Trajectory Planning, PathVelocity Decomposition and Adjacent Paths
, 1993
"... This paper addresses Dynamic Trajectory Planning, which is defined as Motion Planning for a robot A moving in a dynamic workspace W, i.e. with moving obstacles. Besides A is subject both to kinematic constraints and dynamic constraints. We consider the case of a carlike robot A with bounded velocit ..."
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Cited by 10 (5 self)
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This paper addresses Dynamic Trajectory Planning, which is defined as Motion Planning for a robot A moving in a dynamic workspace W, i.e. with moving obstacles. Besides A is subject both to kinematic constraints and dynamic constraints. We consider the case of a carlike robot A with bounded velocity and acceleration, moving in a dynamic workspace W = IR 2 . Our approach is an extension to the PathVelocity Decomposition [Kant and Zucker, 1986]. We introduce the concept of adjacent paths and we use it within a novel planning schema which operates in two complementary stages: (a) Paths Planning and (b) Trajectory Planning. In Paths Planning, a set of adjacent paths, one of which leading A to its goal, are computed. These paths are collisionfree with the stationary obstacles and respect A's kinematic constraints. In Trajectory Planning, knowing that A is able to shift from one path to an adjacent one freely, we determine the motion of A along and between these paths so as to avoid the...
Kinodynamic planning in a structured and timevarying 2d workspace
 In IEEE Int. Conf. Robot. & Autom
, 1500
"... Abstract This paper deals with a trajectory planning problem that we call the 'highway problem'. It consists in planning a timeoptimal trajectory for a mobile which is travelling in a structured workspace amidst moving obstacles and is subject to constraints on its velocity and accelerat ..."
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Cited by 9 (3 self)
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Abstract This paper deals with a trajectory planning problem that we call the 'highway problem'. It consists in planning a timeoptimal trajectory for a mobile which is travelling in a structured workspace amidst moving obstacles and is subject to constraints on its velocity and acceleration. By structured workspace, we mean that there exists lanes characterized by onedimensional curves along which the mobile is able to move. The mobile has to follow a lane but it may also shift from its lane to an adjacent one. This paper presents an efficient method which determines an approximate timeoptimal solution to the highway problem. The approach consists in discretizing time and selecting the accelerations applied to the mobile among a discrete set. These hypotheses make it possible to define a grid in the mobile's timestate space, i.e. the mobile's state (or phase) space augmented of the time dimension. This grid is then searched in order to find a soh tion.
Nonuniform Discretization For Kinodynamic Motion Planning And Its Applications
 SIAM J. COMPUT
, 2000
"... The first main result of this paper is a novel nonuniform discretization approximation method for the kinodynamic motionplanning problem. The kinodynamic motionplanning problem is to compute a collisionfree, timeoptimal trajectory for a robot whose accelerations and velocities are bounded. Previ ..."
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Cited by 8 (0 self)
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The first main result of this paper is a novel nonuniform discretization approximation method for the kinodynamic motionplanning problem. The kinodynamic motionplanning problem is to compute a collisionfree, timeoptimal trajectory for a robot whose accelerations and velocities are bounded. Previous approximation methods are all based on a uniform discretization in the time space. On the contrary, our method employs a nonuniform discretization in the configuration space (thus also a nonuniform one in the time space). Compared to the previously best algorithm of Donald and Xavier, the running time of our algorithm reduces in terms of 1/#, roughly from O((1/#) 6d1 ) to O((1/#) 4d2 ), in computing a trajectory in a ddimensional configuration space, such that the time length of the trajectory is within a factor of (1 + #) of the optimal. More importantly, our algorithm is able to take advantage of the obstacle distribution and is expected to perform much better than the analyt...
Reactive Motion Planning for an Intelligent Vehicle
 In Proc. of the IEEE Symposium on Intelligent Vehicles
, 1992
"... This paper is concerned with the problem of controlling the motion of a carlike vehicle moving in a dynamic environment. We propose a dynamic approach which enables the vehicle to autonomously avoid stationary and moving obstacles while executing a nominal motion plan. The framework of this researc ..."
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Cited by 8 (6 self)
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This paper is concerned with the problem of controlling the motion of a carlike vehicle moving in a dynamic environment. We propose a dynamic approach which enables the vehicle to autonomously avoid stationary and moving obstacles while executing a nominal motion plan. The framework of this research program is the European Prometheus Eureka project whose purpose is to design autonomous cars in order to increase the safety in traffic situations. 1 Introduction To solve the problem of motion control of a carlike vehicle, we have developed an approach which enables the vehicle to avoid static and dynamic obstacles in realtime [6]. This approach is based on a classical two layered system composed of a "trajectory planner" and a "motion controller". The purpose of the trajectory planner is to generate a nominal motion plan made up of a geometric path and a velocity profile along this path. The reactive motion controller enables the autonomous vehicle to execute this nominal plan in a rea...
Motion Control for a CarLike Robot: Potential Field and MultiAgent Approaches
 Proc. of the Int. Workshop on Intelligent Robots and Systems. IEEE
, 1992
"... This paper is concerned with the problem of controlling the motion of a mobile robot moving in a timevarying environment. The study considers a carlike vehicle moving in a roadwaylike environment. We present two approaches which enable the vehicle to execute a given nominal motion plan and to adj ..."
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Cited by 7 (3 self)
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This paper is concerned with the problem of controlling the motion of a mobile robot moving in a timevarying environment. The study considers a carlike vehicle moving in a roadwaylike environment. We present two approaches which enable the vehicle to execute a given nominal motion plan and to adjust it in order to avoid static and dynamic obstacles. The first approach is based on classical potential field techniques. The second one relies upon a multiagent approach. I Introduction We are intersted in the problem of motion control of a carlike vehicle. To deal with this problem, we use a classical two layered system composed of a "trajectory planner" and a "motion controller". The purpose of the trajectory planner is to generate a nominal plan made up of a geometric path and a velocity profile along this path. The motion controller enables the autonomous vehicle to execute this nominal plan in a reactive way and to optimize its behaviour, i.e. to avoid moving obstacles while respec...