Greedy Heuristics for Sampling-based Motion Planning in High-Dimensional State Spaces (2405.03411v2)

Abstract: Informed sampling techniques improve the convergence rate of sampling-based planners by guiding the sampling toward the most promising regions of the problem domain, where states that can improve the current solution are more likely to be found. However, while this approach significantly reduces the planner's exploration space, the sampling subset may still be too large if the current solution contains redundant states with many twists and turns. This article addresses this problem by introducing a greedy version of the informed set that shrinks only based on the maximum heuristic cost of the state along the current solution path. Additionally, we present Greedy RRT* (G-RRT*), a bi-directional version of the anytime Rapidly-exploring Random Trees algorithm that uses this greedy informed set to focus sampling on the promising regions of the problem domain based on heuristics. Experimental results on simulated planning problems, manipulation problems on Barrett WAM Arms, and on a self-reconfigurable robot, Panthera, show that G-RRT* produces asymptotically optimal solution paths and outperforms state-of-the-art RRT* variants, especially in high dimensions.

• The paper introduces Greedy RRT*, a novel algorithm that integrates greedy informed sampling with bidirectional search to quickly identify near-optimal solutions.
• It leverages an L2 greedy informed set to focus sampling in critical regions, substantially improving efficiency and lowering path costs.
• Empirical results demonstrate significant speed, success rate, and cost improvements over standard RRT* methods in simulations and robotic tasks.

Overview of Greedy Heuristics for Sampling-based Motion Planning in High-Dimensional State Spaces

The paper "Greedy Heuristics for Sampling-based Motion Planning in High-Dimensional State Spaces" addresses the limitations of existing sampling-based motion planning algorithms, specifically RRT* and its variants, which often struggle with sampling efficiency and convergence speed in complex, high-dimensional planning problems. Herein, the authors present Greedy RRT* (G-RRT*), a novel algorithm that unifies existing insights gained from various RRT* adaptations by leveraging greedy search techniques and heuristics.

Main Contributions

The paper's primary contributions can be summarized as follows:

1. Greedy Informed Sampling: The authors propose a modification of the direct informed sampling technique, leading to the introduction of a $L^2$ greedy informed set. This approach strategically reduces the ellipsoidal exploration region based on heuristic cost information instead of the path cost from an initial solution, enhancing sampling efficiency in tortuous, high-dimensional paths.
2. Bidirectional Search Strategy: G-RRT* incorporates a bidirectional search perspective, maintaining two trees growing from the initial and goal states, respectively. This design choice helps identify initial solutions more rapidly compared to previous single-tree methods.
3. Empirical Validation: The paper includes empirical demonstrations across simulated environments and manipulation tasks, supplemented by validation using a self-reconfigurable robot, illustrating a superior asymptotic performance over state-of-the-art methods.

Key Results and Analyses

Through simulation experiments, G-RRT* showed substantial improvement over both the classical RRT* and more recent RRT* adaptations, particularly in high-dimensional problems. The analyses suggest G-RRT* solves problem instances faster, therefore achieving higher success rates and reduced path costs. This enhancement is largely attributed to the dual strategy of improved informed sampling and bidirectional search, allowing efficient exploitation and exploration of the problem domain.

Additionally, despite the increased complexity, G-RRT* maintains the almost-surely asymptotic optimality property. This correctness is mathematically grounded by ensuring that the sampling process continues over regions necessarily containing the optimal paths.

Implications and Future Directions

The work outlined in this paper advances the field of robotic path planning by improving the applicability of sampling-based methods to challenging high-dimensional state spaces. Practically, the improvements in computation efficiency allow for better real-time performance in autonomous systems, such as industrial robots or self-reconfigurable mobile platforms. Theoretically, this work opens avenues for further integrating heuristic information into sampling strategies, potentially extending into learning-based approaches where heuristics could be dynamically optimized based on environmental interactions.

In future work, extensions of G-RRT* could include adaptation to dynamic environments, incorporating online learning for heuristic adjustments, or hybridizing with probabilistic roadmap methods for improved multi-query performance. Integrating the insights from G-RRT* into other asymptotically optimal planners can also be explored, possibly yielding new algorithms with hybrid exploration strategies that benefit from both rapid initial solutions and efficient global convergence.

Through these contributions, the paper presents a highly effective algorithm that paves the way for robust motion planning solutions viable in high-dimensional and real-world scenarios.