Safe, smooth, and optimal motion planning for nonholonomically constrained mobile robots and autonomous vehicles is essential for achieving reliable, seamless, and efficient autonomy in logistics, mobility, and service industries. In many such application settings, nonholonomic robots, like unicycles with restricted motion, require precise planning and control of both translational and orientational motion to approach specific locations in a designated orientation, such as for approaching changing, parking, and loading areas. In this paper, we introduce a new dual-headway unicycle pose control method by leveraging an adaptively placed headway point in front of the unicycle pose and a tailway point behind the goal pose. In summary, the unicycle robot continuously follows its headway point, which chases the tailway point of the goal pose and the asymptotic motion of the tailway point towards the goal position guides the unicycle robot to approach the goal location with the correct orientation. The simple and intuitive geometric construction of dual-headway unicycle pose control enables an explicit convex feedback motion prediction bound on the closed-loop unicycle motion trajectory for fast and accurate safety verification. We present an application of dual-headway unicycle control for optimal sampling-based motion planning around obstacles. In numerical simulations, we show that optimal unicycle motion planning using dual-headway translation and orientation distances significantly outperforms Euclidean translation and cosine orientation distances in generating smooth motion with minimal travel and turning effort.

翻译：对于非完整约束移动机器人和自动驾驶车辆而言，安全、平滑且最优的运动规划对于在物流、交通和服务行业中实现可靠、无缝且高效的自主性至关重要。在许多此类应用场景中，非完整机器人（如运动受限的单轮机器人）需要对平移和转向运动进行精确规划与控制，以特定朝向接近目标位置，例如驶入充电站、停车区和装载区等。本文提出一种新的双前视距单轮机器人位姿控制方法，该方法利用自适应放置在单轮机器人位姿前方的视距点与目标位姿后方的尾随点。简而言之，单轮机器人持续跟踪其视距点，该视距点追逐目标位姿的尾随点，而尾随点渐近趋近目标位置的运动引导单轮机器人以正确朝向接近目标地点。双前视距单轮位姿控制简洁直观的几何构造，能够为闭环单轮运动轨迹提供显式的凸反馈运动预测边界，从而实现快速准确的安全性验证。我们展示了双前视距单轮控制在障碍物环境下进行最优基于采样运动规划的应用。数值仿真表明，采用双前视距平移与转向距离的最优单轮运动规划，在生成平滑运动轨迹并最小化行进与转向代价方面，显著优于采用欧几里得平移距离与余弦转向距离的方法。