This paper presents a state-of-the-art optimal controller for quadruped locomotion. The robot dynamics is represented using a single rigid body (SRB) model. A linear time-varying model predictive controller (LTV MPC) is proposed by using linearization schemes. Simulation results show that the LTV MPC can execute various gaits, such as trot and crawl, and is capable of tracking desired reference trajectories even under unknown external disturbances. The LTV MPC is implemented as a quadratic program using qpOASES through the CasADi interface at 50 Hz. The proposed MPC can reach up to 1 m/s top speed with an acceleration of 0.5 m/s2 executing a trot gait. The implementation is available at https:// github.com/AndrewZheng-1011/Quad_ConvexMPC

翻译：本文提出了一种用于四足运动的最优控制器。采用单刚体模型表示机器人动力学，通过线性化方案构建了一种线性时变模型预测控制器。仿真结果表明，该LTV MPC能够执行多种步态（如小跑步态与爬行步态），并在未知外部扰动下保持对期望参考轨迹的跟踪能力。LTV MPC通过CasADi接口调用qpOASES求解器，以50 Hz频率实现二次规划求解。所提出的MPC在执行小跑步态时，最高速度可达1 m/s，加速度为0.5 m/s²。实现代码已开源至https://github.com/AndrewZheng-1011/Quad_ConvexMPC。