[Paper Review] RRT+ : Fast Planning for High-Dimensional Configuration Spaces

Marios Xanthidis, Ioannis Rekleitis+1 more|arXiv (Cornell University)|Dec 21, 2016

Robotic Path Planning Algorithms3 citations

TL;DR

This paper introduces RRT+, a novel family of RRT-based motion planning algorithms that accelerate pathfinding in high-dimensional configuration spaces by incrementally exploring lower-dimensional subspaces. By prioritizing subspaces likely to contain solutions and adapting sampling strategies, RRT+ variants—especially PrioritizedRRT+-Connect—achieve significantly faster convergence than standard RRT and state-of-the-art planners like RRT-Connect and KPIECE, particularly in highly redundant systems.

ABSTRACT

In this paper we propose a new family of RRT based algorithms, named RRT+ , that are able to find faster solutions in high-dimensional configuration spaces compared to other existing RRT variants by finding paths in lower dimensional subspaces of the configuration space. The method can be easily applied to complex hyper-redundant systems and can be adapted by other RRT based planners. We introduce RRT+ and develop some variants, called PrioritizedRRT+ , PrioritizedRRT+-Connect, and PrioritizedBidirectionalT-RRT+ , that use the new sampling technique and we show that our method provides faster results than the corresponding original algorithms. Experiments using the state-of-the-art planners available in OMPL show superior performance of RRT+ for high-dimensional motion planning problems.

Motivation & Objective

• To address the computational inefficiency of standard RRT algorithms in high-dimensional configuration spaces common in hyper-redundant and mobile manipulators.
• To reduce planning time in high-DOF systems by focusing search on lower-dimensional subspaces where solutions are more likely to exist.
• To develop a generalizable framework that can be easily integrated into existing RRT-based planners to boost performance without sacrificing theoretical guarantees.
• To evaluate the performance of RRT+ variants against state-of-the-art planners in diverse, high-dimensional environments.
• To explore the impact of prioritization and dynamic subspace selection on planning speed and solution quality.

Proposed method

• RRT+ decomposes the full configuration space into a sequence of increasing-dimensional subspaces, enabling incremental tree expansion within each subspace.
• The algorithm uses a prioritized sampling strategy that favors subspaces with higher likelihood of containing feasible paths, based on geometric and kinematic constraints.
• Each RRT+ variant (e.g., PrioritizedRRT+-Connect) modifies the original planner’s sampling and expansion logic to operate within subspaces, maintaining RRT’s theoretical completeness.
• The method dynamically adjusts the search depth by identifying when a subspace has been sufficiently explored, reducing redundant computation.
• The approach is designed to be modular, allowing integration into existing RRT-based planners with minimal code changes—often in under five minutes.
• A parameter $ Q_{\text{max}} $ controls the maximum time per subsearch, with performance sensitive to its value, though the method remains robust across diverse environments.

Experimental results

Research questions

• RQ1 Can focusing search on lower-dimensional subspaces significantly reduce planning time in high-dimensional configuration spaces?
• RQ2 How does prioritized sampling across subspaces compare to uniform or biased sampling in terms of convergence speed and solution quality?
• RQ3 To what extent can RRT+ outperform state-of-the-art planners like RRT-Connect, KPIECE, and STRIDE in highly redundant robotic systems?
• RQ4 Can the RRT+ framework be generalized and easily adapted to other RRT-based planners with minimal implementation effort?
• RQ5 What role does prior knowledge about the system’s kinematic structure play in accelerating the planning process?

Key findings

• PrioritizedRRT+-Connect achieved the fastest solution time in every trial across all test environments, with the single fastest solution in each case.
• In the Horn environment (30-DOF), PrioritizedRRT+-Connect reduced mean planning time to 4.77 seconds, compared to 66.71 seconds for RRT-Connect, a 13.6x speedup.
• For the 17-DOF kinematic chain, RRT+ variants reduced mean planning time by up to 70% compared to standard RRT-Connect in cluttered and horn environments.
• In low-redundancy environments, KPIECE and STRIDE outperformed RRT+ variants, but RRT+ remained competitive and faster in high-redundancy scenarios.
• The method maintained theoretical completeness and probabilistic completeness while achieving substantial speedups, demonstrating its robustness and scalability.
• The performance of RRT+ was highly sensitive to the $ Q_{\text{max}} $ parameter, indicating a need for adaptive tuning or metric-based termination criteria in future work.