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34
Nonholonomic motion planning: Steering using sinusoids
 IEEE fins. Auto. Control
, 1993
"... AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vec ..."
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Cited by 251 (15 self)
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AbstractIn this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett’s result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of twoinput systems can be converted into this form. I.
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.
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.
Using Skeletons for Nonholonomic Path Planning among Obstacles
, 1992
"... This paper describes a practical path planner for nonholonomic robots in environments with obstacles. The planner is based on building a onedimensional, maximal clearance skeleton through the configuration space of the robot. However rather than using the Euclidean metric to determine clearance, a ..."
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Cited by 32 (1 self)
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This paper describes a practical path planner for nonholonomic robots in environments with obstacles. The planner is based on building a onedimensional, maximal clearance skeleton through the configuration space of the robot. However rather than using the Euclidean metric to determine clearance, a special metric which captures information about the nonholonomy of the robot is used. The robot navigates from start to goal states by loosely following the skeleton; the resulting paths taken by the robot are of low "complexity." We describe how much of the computation can be done offline once and for all for a given robot, making for an efficient planner. The focus is on path planning for mobile robots, particularly the planar twoaxle car, but the underlying ideas are quite general and may be applied to planners for other nonholonomic robots.
Steering nonholonomic systems using sinusoids
 in: Proc. 29th IEEE Conf. Decis. Contr
, 1990
"... In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields ..."
Abstract

Cited by 31 (2 self)
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In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their (first order) Lie brackets. Using Brockett's result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. Examples and simulation results are presented. 1
Nonprehensile Robotic Manipulation: Controllability and Planning
, 1997
"... the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra ..."
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Cited by 23 (5 self)
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the author and should not be interpreted as representing the o cial policies, either expressed or A good model of the mechanics of a task is a resource for a robot, just as actuators and sensors are resources. The e ective use of frictional, gravitational, and dynamic forces can substitute for extra actuators; the expectation derived from a good model can minimize sensing requirements. Despite this, most robot systems attempt to dominate or nullify task mechanics, rather than exploit them. There has been little e ort to understand the manipulation capabilities of even the simplest robots under more complete mechanics models. This thesis addresses that knowledge de cit by studying graspless or nonprehensile manipulation. Nonprehensile manipulation exploits task mechanics to achieve a goal state without grasping, allowing simple mechanisms to accomplish complex tasks. With nonprehensile manipulation, a robot can manipulate objects too large or heavy to be grasped and lifted, and a lowdegreeoffreedom robot can control more degreesoffreedom of an object by allowing relative motion between the object and the manipulator. Two key problems are determining controllability of and motion planning for
Smooth Trajectory Planning for a Car in a Structured World
, 1991
"... This paper aims at studying the trajectory planning for a car  i.e. a non holonomic vehicle whose turning radius is lower bounded  in a static and structured world. As for the structure of the world, we assume the existence of natural lanes within which the vehicle is able to move. The contribut ..."
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Cited by 20 (2 self)
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This paper aims at studying the trajectory planning for a car  i.e. a non holonomic vehicle whose turning radius is lower bounded  in a static and structured world. As for the structure of the world, we assume the existence of natural lanes within which the vehicle is able to move. The contribution of this paper is a smooth trajectory planner which, when given the polygonal line S representing the spine of a lane generates a trajectory C avoiding the obstacles of the world and which is smooth  i.e. without backing up maneuvers  and executable by the vehicle according to its own kinematic constraints. Besides C is topologically equivalent to S  i.e. C must remain in the lane defined by S. C is made up of straight segments and circular arcs.
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.