An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning

Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Yet, few results are available that merge both bi-directional search and asymptotic optimality into existing optimal planners, such as PRM*, RRT*, and FMT*. The objective of this paper is to fill this gap. Specifically, this paper presents a bi-directional, sampling-based, asymptotically-optimal algorithm named Bi-directional FMT* (BFMT*) that extends the Fast Marching Tree (FMT*) algorithm to bi-directional search while preserving its key properties, chiefly lazy search and asymptotic optimality through convergence in probability. BFMT* performs a two-source, lazy dynamic programming recursion over a set of randomly-drawn samples, correspondingly generating two search trees: one in cost-to-come space from the initial configuration and another in cost-to-go space from the goal configuration. Numerical experiments illustrate the advantages of BFMT* over its unidirectional counterpart, as well as a number of other state-of-the-art planners.Comment: Accepted to the 2015 IEEE Intelligent Robotics and Systems Conference in Hamburg, Germany. This submission represents the long version of the conference manuscript, with additional proof details (Section IV) regarding the asymptotic optimality of the BFMT* algorith

Informed anytime fast marching tree for asymptotically-optimal motion planning

In many applications, it is necessary for motion planning planners to get high-quality solutions in high-dimensional complex problems. In this paper, we propose an anytime asymptotically-optimal sampling-based algorithm, namely Informed Anytime Fast Marching Tree (IAFMT*), designed for solving motion planning problems. Employing a hybrid incremental search and a dynamic optimal search, the IAFMT* fast finds a feasible solution, if time permits, it can efficiently improve the solution toward the optimal solution. This paper also presents the theoretical analysis of probabilistic completeness, asymptotic optimality, and computational complexity on the proposed algorithm. Its ability to converge to a high-quality solution with the efficiency, stability, and self-adaptability has been tested by challenging simulations and a humanoid mobile robot

Toward Asymptotically-Optimal Inspection Planning via Efficient Near-Optimal Graph Search

Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans that inspect the points of interest grows exponentially with the number of inspected points. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion planning roadmap using sampling-based algorithms, and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We demonstrate IRIS's efficacy on a simulated planar 5DOF manipulator inspection task and on a medical endoscopic inspection task for a continuum parallel surgical robot in anatomy segmented from patient CT data. We show that IRIS computes higher-quality inspection paths orders of magnitudes faster than a prior state-of-the-art method.Comment: RSS 201

Asymptotically Optimal Sampling-Based Motion Planning Methods

Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also optimize a cost function, such as path length. Formal path-quality guarantees for continuously valued search spaces are an active area of research interest. Recent results have proven that some sampling-based planning methods probabilistically converge toward the optimal solution as computational effort approaches infinity. This survey summarizes the assumptions behind these popular asymptotically optimal techniques and provides an introduction to the significant ongoing research on this topic.Comment: Posted with permission from the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4. Copyright 2021 by Annual Reviews, https://www.annualreviews.org/. 25 pages. 2 figure