This paper focuses on the motion planning for mobile robots in 3D, which are modelled by 6-DOF rigid body systems with nonholonomic constraints. We not only specify the target position, but also bring in the requirement of the heading direction at the terminal time, which gives rise to a new and more challenging 3D motion planning problem. The proposed planning algorithm involves a novel velocity vector field (VF) over the workspace, and by following the VF, the robot can be navigated to the destination with the specified heading direction. In order to circumvent potential collisions with obstacles and other robots, a composite VF is presented by composing the navigation VF and an additional VF tangential to the boundary of the dangerous area. Moreover, we propose a priority-based algorithm to deal with the motion coupling among multiple robots. Finally, numerical simulations are conducted to verify the theoretical results.

翻译：本文聚焦于三维空间中移动机器人的运动规划问题，此类机器人被建模为具有非完整约束的六自由度刚体系统。我们不仅设定了目标位置，还引入了末端时刻航向方向的要求，由此催生了一个更具挑战性的新型三维运动规划问题。所提出的规划算法涉及工作空间中的新型速度矢量场，通过跟随该矢量场，机器人能够以指定航向方向导航至目的地。为规避与障碍物及其他机器人的潜在碰撞，我们通过组合导航矢量场和危险区域边界切向附加矢量场，提出了一种复合矢量场方法。此外，针对多机器人间的运动耦合问题，本文提出了基于优先级的算法。最后通过数值仿真验证了理论结果。