1,292 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
EG-RRT: Environment-guided random trees for kinodynamic motion planning with uncertainty and obstacles
Existing sampling-based robot motion planning methods are often inefficient at finding trajectories for kinodynamic systems, especially in the presence of narrow passages between obstacles and uncertainty in control and sensing. To address this, we propose EG-RRT, an Environment-Guided variant of RRT designed for kinodynamic robot systems that combines elements from several prior approaches and may incorporate a cost model based on the LQG-MP framework to estimate the probability of collision under uncertainty in control and sensing. We compare the performance of EG-RRT with several prior approaches on challenging sample problems. Results suggest that EG-RRT offers significant improvements in performance.Postprint (author’s final draft
Completeness of Randomized Kinodynamic Planners with State-based Steering
Probabilistic completeness is an important property in motion planning.
Although it has been established with clear assumptions for geometric planners,
the panorama of completeness results for kinodynamic planners is still
incomplete, as most existing proofs rely on strong assumptions that are
difficult, if not impossible, to verify on practical systems. In this paper, we
focus on an important class of kinodynamic planners, namely those that
interpolate trajectories in the state space. We provide a proof of
probabilistic completeness for these planners under assumptions that can be
readily verified from the system's equations of motion and the user-defined
interpolation function. Our proof relies crucially on a property of
interpolated trajectories, termed second-order continuity (SOC), which we show
is tightly related to the ability of a planner to benefit from denser sampling.
We analyze the impact of this property in simulations on a low-torque pendulum.
Our results show that a simple RRT using a second-order continuous
interpolation swiftly finds solution, while it is impossible for the same
planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure
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