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MultiModal Motion Planning in NonExpansive Spaces
"... Abstract: The motion planning problems encountered in manipulation and legged locomotion have a distinctive multimodal structure, where the space of feasible configurations consists of overlapping submanifolds of nonuniform dimensionality. These spaces do not possess expansiveness, a property that ..."
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Abstract: The motion planning problems encountered in manipulation and legged locomotion have a distinctive multimodal structure, where the space of feasible configurations consists of overlapping submanifolds of nonuniform dimensionality. These spaces do not possess expansiveness, a property that characterizes whether planning queries can be solved with traditional samplebased planners. We present a new samplebased multimodal planning algorithm and analyze its completeness properties. In particular, it converges quickly when each mode is expansive relative to the submanifold in which it is embedded. We also present a variant that has the same convergence properties, but works better for problems with a large number of modes. These algorithms are demonstrated in a legged locomotion planner. 1
Integrating task and PRM motion planning: Dealing with many infeasible motion planning queries
"... To accomplish a task an autonomous robot must break this task into “primitive ” subtasks and order them to satisfy precedence constraints. Each subtask requires performing a motion. The existence of a feasible trajectory is an additional precondition for the subtask, but a very expensive one to test ..."
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Cited by 12 (0 self)
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To accomplish a task an autonomous robot must break this task into “primitive ” subtasks and order them to satisfy precedence constraints. Each subtask requires performing a motion. The existence of a feasible trajectory is an additional precondition for the subtask, but a very expensive one to test. Probabilistic RoadMaps (PRM) are an effective approach to plan feasible trajectories when these exist. However, PRM planners are unable to detect that no solution exists. On the other hand, a task/motion planner must often consider many subtasks, a fraction of which, only, admit feasible trajectories. This paper proposes a general algorithm (I‐TMP) that specifically addresses this issue. This algorithm interweaves task and motion planning, and allows distributing computational effort where it is most useful. It is probabilistically complete in the following sense: if I‐TMP can generate a sequence of subtasks that admits a feasible trajectory, such a trajectory will eventually be found with high probability. An application of I‐TMP to multilimbed robots navigating on rough terrain is presented. I.
On the Most Likely Voronoi Diagram and Nearest Neighbor Searching?
"... Abstract. We consider the problem of nearestneighbor searching among a set of stochastic sites, where a stochastic site is a tuple (si,⇡i) consisting of a point si in a ddimensional space and a probability ⇡i determining its existence. The problem is interesting and nontrivial even in 1dimension ..."
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Abstract. We consider the problem of nearestneighbor searching among a set of stochastic sites, where a stochastic site is a tuple (si,⇡i) consisting of a point si in a ddimensional space and a probability ⇡i determining its existence. The problem is interesting and nontrivial even in 1dimension, where the Most Likely Voronoi Diagram (LVD) is shown to have worstcase complexity ⌦(n2). We then show that under more natural and less adversarial conditions, the size of the 1dimensional LVD is significantly smaller: (1) ⇥(kn) if the input has only k distinct probability values, (2) O(n log n) on average, and (3) O(n p n) under smoothed analysis. We also present an alternative approach to the most likely nearest neighbor (LNN) search using Pareto sets, which gives a linearspace data structure and sublinear query time in 1D for average and smoothed analysis models, as well as worstcase with a bounded number of distinct probabilities. Using the Paretoset approach, we can also reduce the multidimensional LNN search to a sequence of nearest neighbor and spherical range queries. 1
SUBMITTED TO International Journal of Robotics Research On the Probabilistic Foundations of Probabilistic Roadmap Planning
"... Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention so far. This paper tries to fill this gap, with the intent to identify p ..."
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Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention so far. This paper tries to fill this gap, with the intent to identify promising directions to improve future planners. It introduces the probabilistic foundations of PRM planning and examines previous work in this context. It shows that the success of PRM planning depends mainly and critically on favorable “visibility ” properties of a robot’s configuration space. A promising direction for speeding up PRM planners is to infer partial knowledge on such properties from both workspace geometry and information gathered during roadmap construction, and to use this knowledge to adapt the probability measure for sampling. This paper also shows that the choice of the sampling source— pseudorandom or deterministic—has small impact on a PRM planner’s performance, compared to that of the sampling measure. These conclusions are supported by both theoretical and empirical results. 1
Downloaded from
, 2005
"... An OWLbased extensible transcoding system for mobile multidevices ..."
Samplingbased Roadmap Planners are Probably NearOptimal after Finite Computation
, 2014
"... Samplingbased motion planners have proven to be efficient solutions to a variety of highdimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that they solve challenges efficiently by giving up formal guara ..."
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Samplingbased motion planners have proven to be efficient solutions to a variety of highdimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that they solve challenges efficiently by giving up formal guarantees and instead attain asymptotic properties in terms of completeness and optimality. Recent work has argued based on Monte Carlo experiments that these approaches also exhibit desirable probabilistic properties in terms of completeness and optimality after finite computation. The current paper formalizes these guarantees. It proves a formal bound on the probability that solutions returned by asymptotically optimal roadmapbased methods (e.g., PRM∗) are within a bound of the optimal path length I∗n with clearance n after a finite iteration n. This bound has the form P (In − I∗n  ≤ δ · I∗n) ≤ Psuccess, where δ is an error term for the length a path in the PRM ∗ graph, In. This bound is proven for general dimension Euclidean spaces and evaluated in simulation. A discussion on how this bound can be used in practice, as well as bounds for sparse roadmaps are also provided. 1
On the Probabilistic Foundations of Probabilistic
"... Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention to date. This paper tries to fill this gap and identify promising direc ..."
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Why is probabilistic roadmap (PRM) planning probabilistic? How does the probability measure used for sampling a robot’s configuration space affect the performance of a PRM planner? These questions have received little attention to date. This paper tries to fill this gap and identify promising directions to improve future planners. It introduces the probabilistic foundations of PRM planning and examines previous work in this context. It shows that the success of PRM planning depends mainly and critically on favorable “visibility ” properties of a robot’s configuration space. A promising direction for speeding up PRM planners is to infer partial knowledge of such properties from both workspace geometry and information gathered during roadmap construction, and to use this knowledge to adapt the probability measure for sampling. This paper also shows that the choice of the sampling source—pseudorandom or deterministic— has small impact on a PRM planner’s performance, compared with that of the sampling measure. These conclusions are supported by both theoretical and empirical results. KEY WORDS—robotics, motion planning, randomized algorithm, random sampling, probabilistic roadmap planning