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：本文基于流体力学基本原理，提出了一种在障碍物密集环境中实现机器人运动规划与控制的新方法。针对运动规划问题，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约束过渡的无障碍规划空间。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，相较于传统运动空间上的A*搜索方法，本文提出的规划空间搜索策略能生成更短路径。对于轨迹跟踪控制，我们提出了基于模型预测控制（MPC）的轨迹跟踪方法，通过引入线性等式与不等式安全约束，确保了规划与控制的安全需求。