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149
Geometric Shortest Paths and Network Optimization
 Handbook of Computational Geometry
, 1998
"... Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of t ..."
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Cited by 147 (12 self)
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Introduction A natural and wellstudied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to be the sum of the weights of the edges that comprise it. Efficient algorithms are well known for this problem, as briefly summarized below. The shortest path problem takes on a new dimension when considered in a geometric domain. In contrast to graphs, where the encoding of edges is explicit, a geometric instance of a shortest path problem is usually specified by giving geometric objects that implicitly encode the graph and its edge weights. Our goal in devising efficient geometric algorithms is generally to avoid explicit construction of the entire underlying graph, since the full induced graph may be very large (even exponential in the input size, or infinite). Computing an optimal
Controlling Formations of Multiple Mobile Robots
 in Proceedings of the IEEE International Conference on Robotics and Automation
, 1998
"... In this paper we investigate feedback laws used to control multiple robots moving together in a formation. We propose a method for controlling formations that uses only local sensorbased information, in a leaderfollower motion. We use methods of feedback linearization to exponentially stabilize th ..."
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Cited by 94 (16 self)
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In this paper we investigate feedback laws used to control multiple robots moving together in a formation. We propose a method for controlling formations that uses only local sensorbased information, in a leaderfollower motion. We use methods of feedback linearization to exponentially stabilize the relative distance and orientation of the follower, and show that the zero dynamics of the system are also (asymptotically) stable. We demonstrate in simulation the use of these algorithms to control six robots moving around an obstacle. These types of control laws can be used to control arbitrarily large numbers of robots moving in very general types of formations. Keywords: Nonholonomic motion planning, Control theory and Formations of robots. 1 Introduction This paper addresses issues of control and coordination for many robots moving in formation using decentralized controllers. The research on control and motion planning for mobile robots is both extensive and diverse. In the area o...
Robust Hybrid Control for Autonomous Vehicle Motion Planning
, 2000
"... The operation of an autonomous vehicle in an unknown, dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities, and to react in real time to changes in the operational environment. A possible approach to reduce the computationa ..."
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Cited by 92 (7 self)
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The operation of an autonomous vehicle in an unknown, dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities, and to react in real time to changes in the operational environment. A possible approach to reduce the computational complexity of the motion planning problem for a nonlinear, high dimensional system, is based on a quantization of the system dynamics, leading to a control architecture based on a hybrid automaton, the states of which represent feasible trajectory primitives for the vehicle. This paper focuses on the feasibility of this approach: the structure of a Robust Hybrid Automaton is defined and its properties are analyzed. Algorithms are presented for timeoptimal motion planning in a free workspace, and in the presence of fixed or moving obstacles. A case study involving a small autonomous helicopter is presented: a nonlinear control law for maneuver execution is provided, and a robust hyb...
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
"... ..."
Trajectory Generation for the NTrailer Problem Using Goursat Normal Form
, 1995
"... In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the probl ..."
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Cited by 58 (9 self)
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In this paper, we develop the machinery of exterior differenllai forms, more particularly the Gourset normal form for a Ffaffian system, tor solving nonsoloMwic motion phdng probkms, &.e., motion planning for systems with lloniatcgrable velocity constraints. We use tbis technique to solve the problem of rbxing a mobile robot WMI R trailers. We present an algorithm for finding a family of ~WIS~~~OM whicb will convert the system of rolling constraints on the wheels of the robot with n traiten into the GoaFapt canonical form..nRo of these transformations are studied in detail. The Gomt normal form for exterior diffemtial systems is dual to the socalled chainedform for vector fields that bas been studied previously. Consequently, we are able to give the state feedback law aad change o € e00rdinaW tovert the Ntrai4r system id0 chained form. Tllree metbods for for chainedform systems using shrosoidg and polynomiPls aa inputs are presented. The motion prpnnhag strategy Is therefore to the Ntrailer system into Gonrsat form, use this to lind the cboinedform coordinates, plan a path for the corresponding cimkdform system, and then transform the resalting traje.ctory back into the original coordinates. Simulations and h.ames of mode animations of the Ntnder system for parallel parking and backing into a loading dock using this strategy are included.
Visibilitybased probabilistic roadmaps for motion planning
 Journal of Advanced Robotics
, 2000
"... LAASCNRS, 7 avenue du ColonelRoche, 31077 Toulouse, France Abstract This paper presents a variant of Probabilistic Roadmap Methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a freespace structuring of the configuration space into visibility domains in or ..."
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Cited by 54 (16 self)
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LAASCNRS, 7 avenue du ColonelRoche, 31077 Toulouse, France Abstract This paper presents a variant of Probabilistic Roadmap Methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a freespace structuring of the configuration space into visibility domains in order to produce small roadmaps, called visibility roadmaps. Our algorithm integrates an original termination condition related to the volume of the free space covered by the roadmap. The planner has been implemented within a software platform allowing to address a large class of mechanical systems. Experiments show the efficiency of the approach in particular for capturing narrow passages of collisionfree configuration spaces. Key words: Collisionavoidance; path planning; motion planning; global planning; probabilistic roadmaps 1.
Shortest Paths For The ReedsShepp Car: A Worked Out Example Of The Use Of Geometric Techniques In Nonlinear Optimal Control.
, 1991
"... We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion coul ..."
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Cited by 51 (5 self)
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We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion could always be achieved by means of trajectories of a special kind, namely, concatenations of at most five pieces, each of which is either a straight line or a circle, and (b) that these concatenations can be classified into 48 threeparameter families. We show how these results fit in a much more general framework, and can be discovered and proved by applying in a systematic way the techniques of Optimal Control Theory. It turns out that the "classical" optimal control tools developed in the 1960's, such as the Pontryagin Maximum Principle and theorems on the existence of optimal trajectories, are helpful to go part of the way and get some information on the shortest paths, but do not suffice ...
Towards Collaborative and Adversarial Learning: A Case Study in Robotic Soccer
 INTERNATIONAL JOURNAL OF HUMANCOMPUTER STUDIES
, 1998
"... Soccer is a rich domain for the study of multiagent learning issues. Not only must the players learn lowlevel skills, but they must also learn to work together and to adapt to the behaviors of different opponents. We are using a robotic soccer system to study these different types of multiagent ..."
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Cited by 48 (11 self)
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Soccer is a rich domain for the study of multiagent learning issues. Not only must the players learn lowlevel skills, but they must also learn to work together and to adapt to the behaviors of different opponents. We are using a robotic soccer system to study these different types of multiagent learning: lowlevel skills, collaborative, and adversarial. Here we describe in detail our experimental framework. We present a learned, robust, lowlevel behavior that is necessitated by the multiagent nature of the domain, namely shooting a moving ball. We then discuss the issues that arise as we extend the learning scenario to require collaborative and adversarial learning.
MultiLevel Path Planning for Nonholonomic Robots using SemiHolonomic Subsystems
 Int. J. Robot. Res
, 1996
"... We present a new and complete multilevel approach for solving path planning problems for nonholonomic robots. At the first level a path is found that disrespects (some of) the nonholonomic constraints. At each next level a new path is generated, by transformation of the path generated at the pre ..."
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Cited by 47 (7 self)
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We present a new and complete multilevel approach for solving path planning problems for nonholonomic robots. At the first level a path is found that disrespects (some of) the nonholonomic constraints. At each next level a new path is generated, by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the previous level. At the final level all nonholonomic constraints are respected. We present two techniques for these transformations. The first, which we call the Pick and Link technique, repeatedly picks pieces from the given path, and tries to replace these by more feasible ones. The second technique restricts the free configuration space to a "tube" around the given path, and a roadmap, capturing the free space connectivity within this tube, is constructed by the Probabilistic Path Planner. From this roadmap we retrieve a new, more feasible, path. In the intermediate levels we plan ...
Visibility Based Probabilistic Roadmaps
, 1999
"... This paper presents a variant of probabilistic roadmap algorithms that recently appeared as a promising approach to motion planning. We exploit a freespace structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a ..."
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Cited by 44 (1 self)
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This paper presents a variant of probabilistic roadmap algorithms that recently appeared as a promising approach to motion planning. We exploit a freespace structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a software platform allowing to address a large class of mechanical systems. Experiments show the efficiency of the approach in capturing narrow passages of collisionfree configuration spaces. 1 Introduction Due to the continuous increasing power of the computers, probabilistic approaches to motion planning (e.g.,[2, 6, 13, 8, 3]) allow today to solve practical problems which were not addressed few years ago. Apart some attempts aiming to provide formal models of complexity [10, 7, 4, 15], the success of such methods remains better noticed than well understood. This paper proposes a variant of the Probabilistic RoadMap (PRM) algorithm introduced in [6] (and independently in [13] as the Pro...