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On the Relationship Between Classical Grid Search and Probabilistic Roadmaps
"... We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that use ..."
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Cited by 125 (11 self)
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We present, implement, and analyze a spectrum of closelyrelated planners, designed to gain insight into the relationship between classical grid search and probabilistic roadmaps (PRMs). Building on quasiMonte Carlo sampling literature, we have developed deterministic variants of the PRM that use lowdiscrepancy and lowdispersion samples, including lattices. Classical grid search is extended using subsampling for collision detection and also the optimaldispersion Sukharev grid, which can be considered as a kind of latticebased roadmap to complete the spectrum. Our experimental results show that the deterministic variants of the PRM offer performance advantages in comparison to the original PRM and the recent Lazy PRM. This even includes searching using a grid with subsampled collision checking. Our theoretical analysis shows that all of our deterministic PRM variants are resolution complete and achieve the best possible asymptotic convergence rate, which is shown superior to that obtained by random sampling. Thus, in surprising contrast to recent trends, there is both experimental and theoretical evidence that some forms of grid search are superior to the original PRM.
A kinematicsbased probabilistic roadmap method for closed chain systems
 In Robotics:New Directions
, 2000
"... In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical anim ..."
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Cited by 110 (16 self)
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In this paper we consider the motion planning problem for arbitrary articulated structures with one or more closed kinematic chains in a workspace with obstacles. This is an important class of problems and there are applications in many areas such as robotics, closed molecular chains, graphical animation, reconfigurable robots. We use the kinematicsbased probabilistic roadmap (kbprm) strategy proposed in [7] that conceptually partitions the linkage into a set of open chains and applies random generation methods to some of the chains and traditional inverse kinematics methods to the others. The efficiency of the method depends critically on how the linkage is partitioned into open chains, and the original method assumed the partition was provided as input to the problem. In this paper, we propose a fully automated method for partitioning an arbitrary linkage into open chains and for determining which should be positioned using the inverse kinematic solver. Even so, the size (number of links) of the closed loops that can be handled by this method is limited because the inverse solver can only be applied to small chains. To handle high dof closed loops, we show how we can use the Iterative Relaxation of Constraints (IRC) strategy [3] to efficiently handle large loops while still only using inverse kinematics for small chains. Our results in 3dimensional workspace both for planar and spatial linkages show that our framework performs well for general linkage. We also use our planner to simulate an adjustable lamp called Luxo. Using IRC, our planner can handle a single loop of up to 44 links.
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 77 (20 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.
DynamicDomain RRTs: Efficient Exploration by Controlling the Sampling Domain
 IN PROCEEDINGS IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 2005
"... Samplingbased planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidlyexploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have w ..."
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Cited by 66 (10 self)
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Samplingbased planners have solved difficult problems in many applications of motion planning in recent years. In particular, techniques based on the Rapidlyexploring Random Trees (RRTs) have generated highly successful singlequery planners. Even though RRTs work well on many problems, they have weaknesses which cause them to explore slowly when the sampling domain is not well adapted to the problem. In this paper we characterize these issues and propose a general framework for minimizing their effect. We develop and implement a simple new planner which shows significant improvement over existing RRTbased planners. In the worst cases, the performance appears to be only slightly worse in comparison to the original RRT, and for many problems it performs orders of magnitude better.
Dynamicallystable Motion Planning for Humanoid Robots
, 2000
"... We present an algorithm for computing stable collisionfree motions for humanoid robots given fullbody posture goals. The motion planner is part of a simulation environment under development for providing highlevel software control for humanoid robots. Given a robot's internal model of the e ..."
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Cited by 65 (5 self)
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We present an algorithm for computing stable collisionfree motions for humanoid robots given fullbody posture goals. The motion planner is part of a simulation environment under development for providing highlevel software control for humanoid robots. Given a robot's internal model of the environment and a staticallystable desired posture, we use a randomized path planner to search the configuration space of the robot for a collisionfree path. Balance constraints are imposed on incremental search motions in order to maintain the overall dynamic stability of the computed trajectories. The algorithm is presented along with preliminary results using an experimental implementation on a dynamic model of the H5 humanoid robot.
Planning Paths for Elastic Objects Under Manipulation Constraints
 International Journal of Robotics Research
, 2001
"... This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to ..."
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Cited by 53 (10 self)
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This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to deform in order to achieve a collisionfree path from the initial to the final configuration. Any required deformations are automatically computed by our planner according to the principles of elasticity theory from mechanics. The problem considered in this paper differs significantly from that of planning for a rigid or an articulated object. In the first part of the paper we point out these differences and highlight the reasons that make planning for elastic objects an extremely difficult task. We then present a randomized algorithm for computing collisionfree paths for elastic objects under the abovementioned restrictions of manipulation.
LQRTrees: Feedback motion planning via sums of squares verification
 International Journal of Robotics Research
, 2010
"... Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree ..."
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Cited by 50 (16 self)
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Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQRstabilized trajectories. The region of attraction of this nonlinear feedback policy “probabilistically covers ” the entire controllable subset of the state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm. 1
LQRTrees: Feedback motion planning on sparse randomized trees
 in In Proceedings of Robotics: Science and Systems (RSS
"... Abstract — Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of stability for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses these results to efficiently combine locall ..."
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Cited by 48 (8 self)
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Abstract — Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of stability for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses these results to efficiently combine locally valid linear quadratic regulator (LQR) controllers into a nonlinear feedback policy which probabilistically covers the reachable area of a (bounded) state space with a region of stability, certifying that all initial conditions that are capable of reaching the goal will stabilize to the goal. We investigate the properties of this systematic nonlinear feedback control design algorithm on simple underactuated systems and discuss the potential for control of more complicated control problems like bipedal walking. I.
SamplingBased Motion Planning under Kinematic LoopClosure Constraints
 In 6th International Workshop on Algorithmic Foundations of Robotics
, 2004
"... Kinematic loopclosure constraints significantly increase the di#culty of motion planning for articulated mechanisms. Configurations of closedchain mechanisms do not form a single manifold, easy to parameterize, as the configurations of open kinematic chains. In general, they are grouped into sever ..."
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Cited by 48 (8 self)
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Kinematic loopclosure constraints significantly increase the di#culty of motion planning for articulated mechanisms. Configurations of closedchain mechanisms do not form a single manifold, easy to parameterize, as the configurations of open kinematic chains. In general, they are grouped into several subsets with complex and a priori unknown topology. Samplingbased motion planning algorithms cannot be directly applied to such closedchain systems. This paper describes our recent work [7] on the extension of samplingbased planners to treat this kind of mechanisms.
Resolution complete rapidlyexploring random trees
 In Proc. IEEE Int’l Conf. on Robotics and Automation
, 2002
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