This paper focuses on the motion planning for mobile robots in 3D, which are modelled by 6-DOF rigid body systems with nonholonomic kinematics 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 designed 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 issue among multiple robots. Finally, numerical simulations are conducted to verify the theoretical results.

翻译：本文研究三维空间中被建模为具有非完整运动学约束的六自由度刚体系统的移动机器人运动规划问题。我们不仅指定了目标位置，还引入了终端时刻航向方向的要求，由此生成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向量场，通过跟随该向量场，机器人能以指定航向方向导航至目的地。为避免与障碍物及其他机器人发生潜在碰撞，通过组合导航向量场与危险区域边界切向的附加向量场，设计出复合向量场。此外，我们提出了一种基于优先级的算法来处理多机器人间的运动耦合问题。最后通过数值仿真验证了理论结果。