This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra. Moreover, given an initial condition, the linearized tracking error dynamics and equations of motion are globally valid and evolve independently of the system trajectory. By exploiting the symmetry of the problem, the proposed approach shows faster convergence of rotation and position simultaneously than the state-of-the-art geometric variational MPC based on variational-based linearization. Numerical simulation on tracking control of a fully-actuated 3D rigid body dynamics confirms the benefits of the proposed approach compared to the baselines. Furthermore, the proposed MPC is also verified in pose control and locomotion experiments on a quadrupedal robot MIT Mini Cheetah.
翻译:本文报告了一种新的错误状态模型预测控制(MPC)方法,用于连接矩阵的机器人控制。线性跟踪错误动态和运动的线性方程式出自Lie代数。此外,在初始条件下,线性跟踪错误动态和运动方程式具有全球有效性,且独立于系统轨迹而演化。通过利用问题的对称,拟议方法显示旋转和位置与基于变式线化的最先进几何变异式的MPC同步速度更快。关于跟踪完全作用的3D硬体动态的轨迹控制的数值模拟证实了拟议方法相对于基线的好处。此外,还核实了拟议的MPC对四重机器人MIT Mini Cheetah的控制和移动实验。