Sampling-based motion planning algorithms are very effective at finding solutions in high-dimensional continuous state spaces as they do not require prior approximations of the problem domain compared to traditional discrete graph-based searches. The anytime version of the Rapidly-exploring Random Trees (RRT) algorithm, denoted as RRT*, often finds high-quality solutions by incrementally approximating and searching the problem domain through random sampling. However, due to its low sampling efficiency and slow convergence rate, research has proposed many variants of RRT*, incorporating different heuristics and sampling strategies to overcome the constraints in complex planning problems. Yet, these approaches address specific convergence aspects of RRT* limitations, leaving a need for a sampling-based algorithm that can quickly find better solutions in complex high-dimensional state spaces with a faster convergence rate for practical motion planning applications. This article unifies and leverages the greedy search and heuristic techniques used in various RRT* variants to develop a greedy version of the anytime Rapidly-exploring Random Trees algorithm, denoted as Greedy RRT* (G-RRT*). It improves the initial solution-finding time of RRT* by maintaining two trees rooted at both the start and goal ends, advancing toward each other using greedy connection heuristics. It also accelerates the convergence rate of RRT* by introducing a greedy version of direct informed sampling procedure, which guides the sampling towards the promising region of the problem domain based on heuristics. We validate our approach on simulated planning problems, manipulation problems on Barrett WAM Arms, and on a self-reconfigurable robot, Panthera. Results show that G-RRT* produces asymptotically optimal solution paths and outperforms state-of-the-art RRT* variants, especially in high-dimensional planning problems.

翻译：基于采样的运动规划算法在高维连续状态空间中非常有效，因为它们不需要像传统离散图搜索那样事先近似问题域。快速探索随机树（RRT）算法的任意时间版本，记为RRT*，通常通过随机采样逐步近似和搜索问题域来发现高质量解。然而，由于其采样效率低和收敛速度慢，研究提出了许多RRT*的变体，引入不同的启发式方法和采样策略来克服复杂规划问题中的限制。但这些方法仅针对RRT*的特定收敛方面，仍需要一种基于采样的算法，能在复杂高维状态空间中快速找到更优解，且收敛速度更快，以应对实际运动规划应用。本文统一并利用了多种RRT*变体中的贪心搜索和启发式技术，开发了任意时间快速探索随机树算法的贪心版本，记为贪心RRT*（G-RRT*）。它通过维护从起点和终点出发的两棵树，并使用贪心连接启发式方法相互靠近，缩短了RRT*找到初始解的时间；同时引入基于启发式的贪心直接知情采样过程，引导采样聚焦于问题域的有希望区域，从而加速收敛速度。我们在模拟规划问题、Barrett WAM机械臂的操作问题以及自重构机器人Panthera上验证了该方法。结果表明，G-RRT*能生成渐进最优解路径，并在高维规划问题中优于最先进的RRT*变体。