将一阶机器人规划器扩展至二阶动力学，提升安全与收敛性。
Extending First-order Robotic Motion Planners to Second-order Robot Dynamics
- 利用标量函数负梯度设计阻尼速度，实现二阶系统稳定
- 无标量函数时，使速度误差收敛至零，保证轨迹跟踪
- 理论结合仿真，适用于需要高精度运动控制的场景
本文将一阶运动规划器扩展至由二阶动力学支配的机器人。基于一个已知标量函数（其负梯度与一阶规划器方向一致），提出两种控制方案：若该函数已知，则将一阶规划器与动态增益的阻尼速度向量结合，将原有一阶系统的安全性和收敛性保证推广至二阶系统；若该函数未知，则提出替代控制策略，确保机器人速度与一阶规划器输出之间的误差趋于零。理论分析得到仿真结果支持，验证了所提方法的有效性。
原文摘要 · Abstract (English)
This paper extends first-order motion planners to robots governed by second-order dynamics. Two control schemes are proposed based on the knowledge of a scalar function whose negative gradient aligns with a given first-order motion planner. When such a function is known, the first-order motion planner is combined with a damping velocity vector with a dynamic gain to extend the safety and convergence guarantees of the first-order motion planner to second-order systems. If no such function is available, we propose an alternative control scheme ensuring that the error between the robot's velocity and the first-order motion planner converges to zero. The theoretical developments are supported by simulation results demonstrating the effectiveness of the proposed approaches.
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