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:本文着重研究三维移动机器人的运动规划问题。机器人被建模为具有非完整运动学约束的6自由度刚体系统。我们不仅指定了目标位置,而且引入了在终端时间点指定航向方向的要求,这导致了一个新的更具挑战性的三维运动规划问题。所提出的规划算法涉及工作空间内的一个新型速度向量场(VF),通过遵循 VF,机器人可以被导航到具有指定航向方向的目的地。为了避免与障碍物及其他机器人的潜在碰撞,设计了一个组合VF,由导航 VF 和一个沿危险区域边界的切向VF组成。此外,我们提出了一种基于优先级的算法来处理多个机器人之间的运动耦合问题。最后,进行了数值模拟来验证理论结果。