This paper develops a new approach for robot motion planning and control in obstacle-laden environments that is inspired by fundamentals of fluid mechanics. For motion planning, we propose a novel transformation between motion space, with arbitrary obstacles of random sizes and shapes, and an obstacle-free planning space with geodesically-varying distances and constrained transitions. We then obtain robot desired trajectory by A* searching over a uniform grid distributed over the planning space. We show that implementing the A* search over the planning space can generate shorter paths when compared to the existing A* searching over the motion space. For trajectory tracking, we propose an MPC-based trajectory tracking control, with linear equality and inequality safety constraints, enforcing the safety requirements of planning and control.

翻译：本文提出了一种受流体力学基本原理启发的机器人运动规划与控制新方法，适用于存在障碍物的复杂环境。在运动规划方面，我们提出了一种新颖的变换机制，将存在任意形状与尺寸障碍物的运动空间，映射为具有测地变距和受限过渡特性的无障碍规划空间。随后，通过在规划空间均匀网格上执行A*搜索算法获取机器人期望轨迹。研究表明，相较于传统在运动空间进行的A*搜索，基于规划空间的A*搜索能够生成更短路径。针对轨迹跟踪问题，我们提出了一种基于模型预测控制（MPC）的轨迹跟踪控制器，通过引入线性等式与不等式安全约束，确保规划与控制环节的安全需求得到满足。