Results 1  10
of
15
RapidlyExploring Random Trees: Progress and Prospects
 Algorithmic and Computational Robotics: New Directions
, 2000
"... this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints. ..."
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Cited by 228 (25 self)
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this paper, which presents randomized, algorithmic techniques for path planning that are particular suited for problems that involve dierential constraints.
Provably good approximation algorithms for optimal kinodynamic planning for cartesian robots and open chain manipulators
 Algorithmica
, 1995
"... shortest path, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd a minimaltime trajectory that goes from a start state to a goal state while avoiding obstacles by a speeddependent safetymargin and respecting dynamics bounds. In [1] we develop ..."
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Cited by 76 (9 self)
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shortest path, kinodynamics, polyhedral obstacles Abstract: We consider the following problem: given a robot system, nd a minimaltime trajectory that goes from a start state to a goal state while avoiding obstacles by a speeddependent safetymargin and respecting dynamics bounds. In [1] we developed a provably good approximation algorithm for the minimumtime trajectory problem for a robot system with decoupled dynamics bounds (e.g., a point robot in R 3). This algorithm di ers from previous work in three ways. It is possible (1) to bound the goodness of the approximation by an error term �(2) to polynomially bound the computational complexity of our algorithm � and (3) to express the complexity as a polynomial function of the error term. Hence, given the geometric obstacles, dynamics bounds, and the error term, the algorithm returns a solution that isclose to optimal and requires only a polynomial (in ( 1)) amount of time. We extend the results of [1] in two ways. First, we modifyittohalve the exponent inthe polynomial bounds from 6d to 3d, so that that the new algorithm is O c d N 1 3d, where N is the geometric complexity of the obstacles and c is a robotdependent constant. Second, the new algorithm nds a trajectory that matches the optimal in time with an factor sacri ced in the obstacleavoidance safety margin. Similar results hold for polyhedral Cartesian manipulators in polyhedral environments. The new results indicate that an implementation of the algorithm could be reasonable, and a preliminary implementation has been done for the planar case.
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
"... ..."
Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems
 IEEE Transactions on Robotics and Automation
, 2001
"... Abstract — We introduce the notion of kinematic controllability for secondorder underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collisionfree trajectories between zero velocity states can be decoupled into the computationally simpler problems of ..."
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Cited by 46 (12 self)
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Abstract — We introduce the notion of kinematic controllability for secondorder underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collisionfree trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by timeoptimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collisionfree trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.
Reducing metric sensitivity in randomized trajectory design
 In IEEE/RSJ Int. Conf. on Intelligent Robots & Systems
, 2001
"... ..."
Curvatureconstrained shortest paths in a convex polygon (Extended Abstract)
 SIAM JOURNAL ON COMPUTING
, 2002
"... Let B be a point robot moving in the plane, whose path is constrained to have curvature at most1, and let P be a convex polygon with n vertices. We study the collisionfree, optimal pathplanning problem for B moving between two configurations inside P( a configuration specifies both a location and ..."
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Cited by 19 (1 self)
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Let B be a point robot moving in the plane, whose path is constrained to have curvature at most1, and let P be a convex polygon with n vertices. We study the collisionfree, optimal pathplanning problem for B moving between two configurations inside P( a configuration specifies both a location and a direction of travel). We present an O(n²log n) time algorithm for determining whether a collisionfree path exists for Bbetween two given configurations. If such a path exists, the algorithm returns a shortest one. We provide a detailed classification of curvatureconstrained shortest paths inside a convex polygon and prove several properties of them, which are interesting in their own right. Some of the properties are quite general and shed some light on curvatureconstrained shortest paths amid obstacles.
SamplingBased Motion Planning with Differential Constraints

, 2005
"... Since differential constraints which restrict admissible velocities and accelerations of robotic systems are ignored in path planning, solutions for kinodynamic and nonholonomic planning problems from classical methods could be either inexecutable or inefficient. Motion planning with differential c ..."
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Cited by 18 (4 self)
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Since differential constraints which restrict admissible velocities and accelerations of robotic systems are ignored in path planning, solutions for kinodynamic and nonholonomic planning problems from classical methods could be either inexecutable or inefficient. Motion planning with differential constraints (MPD), which directly considers differential constraints, provides a promising direction to calculate reliable and efficient solutions. A large amount of recent efforts have been devoted to various samplingbased MPD algorithms, which iteratively build search graphs using sampled states and controls. This thesis addresses several issues in analysis and design of these algorithms. Firstly, resolution completeness of path planning is extended to MPD and the first quantitative conditions are provided. The analysis is based on the relationship between the reachability graph, which is an intrinsic graph representation of a given problem, and the search graph, which is built by the algorithm. Because of sampling and other complications, there exist mismatches between these two graphs. If a solution exists in the reachability graph, resolution complete algorithms must construct a solution path encoding the solution or its approximation in the search graph
Robot Motion Planning Among Moving Obstacles
, 1995
"... : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xvii 1 Introduction 2 1.1 Motivation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Previous Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2.1 Obstacles Representation : : : : ..."
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Cited by 4 (3 self)
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: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xvii 1 Introduction 2 1.1 Motivation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Previous Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 1.2.1 Obstacles Representation : : : : : : : : : : : : : : : : : : : : : 4 1.2.2 Configuration Space : : : : : : : : : : : : : : : : : : : : : : : 5 1.2.3 Dynamic Planning : : : : : : : : : : : : : : : : : : : : : : : : 6 1.2.4 Optimal Planning : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2.5 Missile Guidance : : : : : : : : : : : : : : : : : : : : : : : : : 8 1.2.6 Differential Game Theory : : : : : : : : : : : : : : : : : : : : 9 1.2.7 Conclusion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.3 Objective : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 1.4 Outline of the Approach : : : : : : : : : : : : : : : : : : : : : : : : : 12 1.5 Organization : : : : : : : : : : : : : : : : : ...
Continuous Alternation: The Complexity of Pursuit in Continuous Domains
 Algorithmica
, 1993
"... Complexity theory has used a game theoretic notion, namely alternation, to great advantage in modeling parallelism and in obtaining lower bounds. The usual definition of alternation requires that transitions be made in discrete steps. The study of differential games is a classic area of optimal cont ..."
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Cited by 4 (0 self)
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Complexity theory has used a game theoretic notion, namely alternation, to great advantage in modeling parallelism and in obtaining lower bounds. The usual definition of alternation requires that transitions be made in discrete steps. The study of differential games is a classic area of optimal control, where there is continuous interaction and alternation between the players. Differential games capture many aspects of control theory and optimal control over continuous domains. In this paper, we define a generalization of the notion of alternation which applies to differential games, and which we call "continuous alternation". This approach allows us to obtain the first known complexity theoretic results for open problems in differential games and optimal control. We concentrate our investigation on an important class of differential games, which we call polyhedral pursuit games. Pursuit games have application to many fundamental problems in autonomous robot control in the presence of ...
Convex Tours of Bounded Curvature
 In Proc. 2nd Annu. European Sympos. Algorithms
, 1999
"... We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with n vertices. We present an O(m + ..."
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Cited by 3 (2 self)
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We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with n vertices. We present an O(m + n) time algorithm finding the path, going around the obstacle, whose curvature is the smallest possible.