[Paper Review] Rapidly-exploring Random Forest: Adaptively Exploits Local Structure with Generalised Multi-Trees Motion Planning

Tin Lai|arXiv (Cornell University)|Mar 7, 2021

Robotic Path Planning Algorithms28 references4 citations

TL;DR

This paper proposes Rapidly-exploring Random Forest (rrf*), a multi-tree motion planner that adaptively deploys Bayesian local sampling in narrow passages to exploit local connectivity, while using a multi-armed bandit framework to prioritize planning on the most promising trees. rrf* achieves asymptotic optimality and superior sample efficiency, especially in high-dimensional, cluttered environments with complex narrow passages.

ABSTRACT

Sampling-based motion planners perform exceptionally well in robotic applications that operate in high-dimensional space. However, most works often constrain the planning workspace rooted at some fixed locations, do not adaptively reason on strategy in narrow passages, and ignore valuable local structure information. In this paper, we propose Rapidly-exploring Random Forest (RRF*) -- a generalised multi-trees motion planner that combines the rapid exploring property of tree-based methods and adaptively learns to deploys a Bayesian local sampling strategy in regions that are deemed to be bottlenecks. Local sampling exploits the local-connectivity of spaces via Markov Chain random sampling, which is updated sequentially with a Bayesian proposal distribution to learns the local structure from past observations. The trees selection problem is formulated as a multi-armed bandit problem, which efficiently allocates resources on the most promising tree to accelerate planning runtime. RRF* learns the region that is difficult to perform tree extensions and adaptively deploys local sampling in those regions to maximise the benefit of exploiting local structure. We provide rigorous proofs of completeness and optimal convergence guarantees, and we experimentally demonstrate that the effectiveness of RRF*'s adaptive multi-trees approach allows it to performs well in a wide range of problems.

Motivation & Objective

• Address the poor performance of sampling-based motion planners (SBPs) in narrow passages due to low sampling probability.
• Overcome the limitation of fixed sampling strategies that fail to exploit local connectivity in constrained regions.
• Develop a method that dynamically identifies bottleneck regions and deploys specialized local sampling only where needed.
• Integrate multi-tree planning with adaptive resource allocation to balance exploration and exploitation.
• Ensure theoretical guarantees of completeness and asymptotic optimality while improving sample efficiency in high-dimensional spaces.

Proposed method

• Formulates tree selection as a multi-armed bandit problem to allocate planning resources to the most promising tree at each step.
• Employs Bayesian local sampling via sequential Markov Chain Monte Carlo (MCMC) walks that update the proposal distribution based on past observations.
• Dynamically creates local trees only in regions identified as bottlenecks—areas with low visibility and high constraint complexity.
• Uses a generalized multi-tree architecture with rooted trees (from start and goal) and adaptive local trees for constrained zones.
• Applies a rewiring procedure to ensure asymptotic optimality, similar to rrt* and prm*.
• Integrates a heuristic to detect narrow passages based on tree extension failure and local connectivity metrics.

Experimental results

Research questions

• RQ1 How can sampling-based motion planners effectively exploit local connectivity in narrow passages where random sampling is inefficient?
• RQ2 Can a multi-tree approach with adaptive local sampling outperform fixed or uniformly deployed local trees in terms of sample efficiency and convergence speed?
• RQ3 How can planning resources be optimally allocated among multiple trees (rooted and local) to accelerate convergence without sacrificing completeness?
• RQ4 Can a Bayesian local sampling strategy that learns from past samples improve exploration in high-dimensional, constrained configuration spaces?
• RQ5 Does the integration of adaptive local trees and multi-armed bandit selection preserve theoretical guarantees of completeness and asymptotic optimality?

Key findings

• rrf* achieves asymptotic optimality, with the solution cost converging almost surely to the optimal cost as the number of samples increases.
• In cluttered environments like the maze and 6-DOF manipulator, rrf* finds solutions faster than rrt*, bi-rrt*, and informed rrt*, with lower cost and fewer invalid connections.
• rrf* reduces the number of invalid samples (obstacle and connection checks) significantly compared to baseline planners, especially in high-dimensional spaces.
• The algorithm demonstrates robustness in real-world testing, successfully planning trajectories for a JACO robotic arm in a cluttered environment within a five-second time budget.
• rrf* outperforms rr d t ∗ in convergence speed on complex tasks due to adaptive tree deployment, avoiding unnecessary local tree creation in open areas.
• The method achieves high sample efficiency, particularly in constrained C-spaces, by focusing computational effort only where local structure exploitation is most beneficial.