Tube-Certified Trajectory Tracking for Nonlinear Systems With Robust Control Contraction Metrics

This paper presents an approach towards guaranteed trajectory tracking for nonlinear control-affine systems subject to external disturbances based on robust control contraction metrics (CCM) that aims to minimize the L infinity gain from the disturbances to the deviation of actual variables of interests from their nominal counterparts. The guarantee is in the form of invariant tubes, computed offline, around any nominal trajectories in which the actual states and inputs of the system are guaranteed to stay despite disturbances. Under mild assumptions, we prove that the proposed robust CCM (RCCM) approach yields tighter tubes than an existing approach based on CCM and input-to-state stability analysis. We show how the RCCM-based tracking controller together with tubes can be incorporated into a feedback motion planning framework to plan safe trajectories for robotic systems. Simulation results illustrate the effectiveness of the proposed method and empirically demonstrate significantly reduced conservatism compared to previous approaches

本文提出了一种基于鲁棒控制收缩度量（CCM）的方法，用于受外部干扰的非线性控制仿射系统的有保证轨迹跟踪，该方法旨在最小化从干扰到感兴趣的实际变量与其标称对应变量偏差的L∞增益。这种保证是以不变管的形式呈现的，这些不变管是离线计算得到的，围绕着任何标称轨迹，尽管存在干扰，系统的实际状态和输入都能保证处于这些不变管内。在温和的假设条件下，我们证明了所提出的鲁棒CCM（RCCM）方法比现有的基于CCM和输入到状态稳定性分析的方法能产生更紧密的管。我们展示了基于RCCM的跟踪控制器如何与管一起被纳入反馈运动规划框架，以便为机器人系统规划安全轨迹。仿真结果说明了所提方法的有效性，并通过实验证明与先前的方法相比，其保守性显著降低。