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14
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 260 (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.
Kinodynamic Motion Planning
, 1993
"... : Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimaltime trajectory that goes from a start position and velocity to a goal position and velocity while avoidin ..."
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Cited by 92 (6 self)
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: Kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints. In the general problem, given a robot system, we must find a minimaltime trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration. We consider the simplified case of a point mass under Newtonian mechanics, together with velocity and acceleration bounds. The point must be flown from a start to a goal, amidst polyhedral obstacles in 2D or 3D. While exact solutions to this problem are not known, we provide the first provably good approximation algorithm, and show that it runs in polynomial time. 1 An early version of this work appeared as [CDRX] 2 Computer Science Department, Cornell University, Ithaca, NY 14853 3 Computer Science Division, University of California, Berkeley, CA 94720 4 Computer Science Department, Duke Universit...
Guidelines in nonholonomic motion planning for mobile robots
 ROBOT MOTION PLANNNING AND CONTROL
, 1998
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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 65 (16 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
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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 22 (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
Lower Bounds For Geometrical And Physical Problems
 SIAM Journal on Computing
, 1996
"... . Motion planning involving arbitrarily many degrees of freedom is known to be PSPACEhard. In this paper, we examine the complexity of generalized motion planning problems for planar mechanisms consisting of independently movable objects. Our constructions constitute a general framework for reducin ..."
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Cited by 9 (0 self)
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. Motion planning involving arbitrarily many degrees of freedom is known to be PSPACEhard. In this paper, we examine the complexity of generalized motion planning problems for planar mechanisms consisting of independently movable objects. Our constructions constitute a general framework for reducing problems in information processing to motion planning, leading to easy proofs of known PSPACEhardness results and to exponential lower bounds for geometrical problems related to motion planning. Especially, we show that the problem of deciding whether a given mechanism A can always avoid a collision with another mechanism B is EXPSPACEhard. New lower bounds are also obtained for the problem of planning under given physical side conditions. We consider the case that certain motions require forces, e.g., to subdue friction, and ask for motions that stay under a given energy limit. Within our framework, we show that such shortest path problems are EXPTIMEhard if we use number representati...
Using Randomization to Find and Optimize Feasible Trajectories for Nonlinear Systems
 Proc. Annual Allerton Conference on Communications, Control, Computing
, 2000
"... Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our ..."
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Abstract We present our current progress on the design and experimentation with trajectory planning and optimization algorithms for nonlinear systems that have significant statespace constraints. An overview of our planning method based on Rapidlyexploring Random Trees (RRTs) is given. We show our current planning results for two challenging sets of nonlinear systems: 1) the determination of automobile trajectories through obstacle courses; 2) the design of reentry trajectories for a reusable launch vehicle model based on the NASA X33 prototype. We also briefly describe some early results on using randomization to optimize trajectories in the presence of state space constraints. 1