Recent progress in contact-rich robotic manipulation has been striking, yet most deployed systems remain confined to simple, scripted routines. One of the key barriers is the lack of motion planning algorithms that can provide verifiable guarantees for safety, efficiency and reliability. To address this, a family of algorithms called Constant-Time Motion Planning (CTMP) was introduced, which leverages a preprocessing phase to enable collision-free motion queries in a fixed, user-specified time budget (e.g., 10 milliseconds). However, existing CTMP methods do not explicitly incorporate the manipulation behaviors essential for object handling. To bridge this gap, we introduce the \textit{Behavioral Constant-Time Motion Planner} (B-CTMP), an algorithm that extends CTMP to solve a broad class of two-step manipulation tasks: (1) a collision-free motion to a behavior initiation state, followed by (2) execution of a manipulation behavior (such as grasping or insertion) to reach the goal. By precomputing compact data structures, B-CTMP guarantees constant-time query in mere milliseconds while ensuring completeness and successful task execution over a specified set of states. We evaluate B-CTMP on two canonical manipulation tasks, shelf picking and plug insertion, in simulation and on a real robot. Our results show that B-CTMP unifies collision-free planning and object manipulation within a single constant-time framework, providing provable guarantees of speed and success for manipulation in semi-structured environments.

翻译：近年来，接触丰富的机器人操作领域取得了显著进展，但大多数已部署系统仍局限于简单的脚本化流程。其关键障碍之一在于缺乏能提供安全、高效及可靠性可验证保证的运动规划算法。为此，研究者提出了一类称为恒定时间运动规划（CTMP）的算法，该算法通过预处理阶段，能够在用户指定的固定时间预算内（例如10毫秒）实现无碰撞运动查询。然而，现有CTMP方法并未显式纳入物体操作所必需的操作行为。为弥补这一空白，我们引入了行为恒定时间运动规划器（B-CTMP），该算法扩展了CTMP，可解决一类广泛的两步操作任务：（1）无碰撞运动至行为初始状态，随后（2）执行操作行为（如抓取或插入）以达到目标。通过预计算紧凑的数据结构，B-CTMP可在数毫秒内保证恒定时间查询，同时确保在指定状态集上的完备性与任务成功执行。我们在仿真环境和真实机器人上，针对货架取物与插头插入这两个经典操作任务评估了B-CTMP。结果表明，B-CTMP将无碰撞规划与物体操作统一至单一恒定时间框架内，为半结构化环境中的操作提供了速度与成功率的可证明保证。