This paper presents a novel algorithm for robot task and motion planning (TAMP) problems by utilizing a reachability tree. While tree-based algorithms are known for their speed and simplicity in motion planning (MP), they are not well-suited for TAMP problems that involve both abstracted and geometrical state variables. To address this challenge, we propose a hierarchical sampling strategy, which first generates an abstracted task plan using Monte Carlo tree search (MCTS) and then fills in the details with a geometrically feasible motion trajectory. Moreover, we show that the performance of the proposed method can be significantly enhanced by selecting an appropriate reward for MCTS and by using a pre-generated goal state that is guaranteed to be geometrically feasible. A comparative study using TAMP benchmark problems demonstrates the effectiveness of the proposed approach.

翻译：本文提出一种利用可达性树解决机器人任务与运动规划（TAMP）问题的新型算法。尽管基于树的算法在运动规划（MP）中以其快速性与简洁性著称，但这类算法难以直接处理涉及抽象化状态变量与几何状态变量的TAMP问题。为克服这一挑战，我们提出分层采样策略：首先通过蒙特卡洛树搜索（MCTS）生成抽象化任务规划，继而以几何可行的运动轨迹填充细节。研究表明，通过为MCTS选择恰当的奖励函数并采用预生成的几何可行目标状态，本方法的性能可显著提升。基于TAMP基准问题的对比实验验证了所提方法的有效性。