3,670 research outputs found
Generalizing Informed Sampling for Asymptotically Optimal Sampling-based Kinodynamic Planning via Markov Chain Monte Carlo
Asymptotically-optimal motion planners such as RRT* have been shown to
incrementally approximate the shortest path between start and goal states. Once
an initial solution is found, their performance can be dramatically improved by
restricting subsequent samples to regions of the state space that can
potentially improve the current solution. When the motion planning problem lies
in a Euclidean space, this region , called the informed set, can be
sampled directly. However, when planning with differential constraints in
non-Euclidean state spaces, no analytic solutions exists to sampling
directly.
State-of-the-art approaches to sampling in such domains such as
Hierarchical Rejection Sampling (HRS) may still be slow in high-dimensional
state space. This may cause the planning algorithm to spend most of its time
trying to produces samples in rather than explore it. In this paper,
we suggest an alternative approach to produce samples in the informed set
for a wide range of settings. Our main insight is to recast this
problem as one of sampling uniformly within the sub-level-set of an implicit
non-convex function. This recasting enables us to apply Monte Carlo sampling
methods, used very effectively in the Machine Learning and Optimization
communities, to solve our problem. We show for a wide range of scenarios that
using our sampler can accelerate the convergence rate to high-quality solutions
in high-dimensional problems
The Reach-Avoid Problem for Constant-Rate Multi-Mode Systems
A constant-rate multi-mode system is a hybrid system that can switch freely
among a finite set of modes, and whose dynamics is specified by a finite number
of real-valued variables with mode-dependent constant rates. Alur, Wojtczak,
and Trivedi have shown that reachability problems for constant-rate multi-mode
systems for open and convex safety sets can be solved in polynomial time. In
this paper, we study the reachability problem for non-convex state spaces and
show that this problem is in general undecidable. We recover decidability by
making certain assumptions about the safety set. We present a new algorithm to
solve this problem and compare its performance with the popular sampling based
algorithm rapidly-exploring random tree (RRT) as implemented in the Open Motion
Planning Library (OMPL).Comment: 26 page
Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots
Path-velocity decomposition is an intuitive yet powerful approach to address
the complexity of kinodynamic motion planning. The difficult trajectory
planning problem is solved in two separate, simpler, steps: first, find a path
in the configuration space that satisfies the geometric constraints (path
planning), and second, find a time-parameterization of that path satisfying the
kinodynamic constraints. A fundamental requirement is that the path found in
the first step should be time-parameterizable. Most existing works fulfill this
requirement by enforcing quasi-static constraints in the path planning step,
resulting in an important loss in completeness. We propose a method that
enables path-velocity decomposition to discover truly dynamic motions, i.e.
motions that are not quasi-statically executable. At the heart of the proposed
method is a new algorithm -- Admissible Velocity Propagation -- which, given a
path and an interval of reachable velocities at the beginning of that path,
computes exactly and efficiently the interval of all the velocities the system
can reach after traversing the path while respecting the system kinodynamic
constraints. Combining this algorithm with usual sampling-based planners then
gives rise to a family of new trajectory planners that can appropriately handle
kinodynamic constraints while retaining the advantages associated with
path-velocity decomposition. We demonstrate the efficiency of the proposed
method on some difficult kinodynamic planning problems, where, in particular,
quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
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