Model Predictive Control (MPC) is a popular strategy for controlling robots but is difficult for systems with contact due to the complex nature of hybrid dynamics. To implement MPC for systems with contact, dynamic models are often simplified or contact sequences fixed in time in order to plan trajectories efficiently. In this work, we extend Hybrid iterative Linear Quadratic Regulator to work in a MPC fashion (HiLQR MPC) by 1) modifying how the cost function is computed when contact modes do not align, 2) utilizing parallelizations when simulating rigid body dynamics, and 3) using efficient analytical derivative computations of the rigid body dynamics. The result is a system that can modify the contact sequence of the reference behavior and plan whole body motions cohesively -- which is crucial when dealing with large perturbations. HiLQR MPC is tested on two systems: first, the hybrid cost modification is validated on a simple actuated bouncing ball hybrid system. Then HiLQR MPC is compared against methods that utilize centroidal dynamic assumptions on a quadruped robot (Unitree A1). HiLQR MPC outperforms the centroidal methods in both simulation and hardware tests.

翻译：模型预测控制（MPC）是控制机器人的常用策略，但由于混合动力学的复杂性质，难以应用于含接触的系统。为在含接触系统中实现MPC，动态模型常被简化或接触序列被固定时间，以实现高效轨迹规划。本研究通过以下三点将混合迭代线性二次型调节器扩展为MPC形式（HiLQR MPC）：1）修改接触模式不匹配时的代价函数计算方法，2）利用并行计算模拟刚体动力学，3）采用刚体动力学的高效解析导数计算。所得系统可修改参考行为的接触序列并协同规划全身运动——这在处理大幅扰动时至关重要。HiLQR MPC在两个系统上进行了测试：首先在简单的受驱动弹跳球混合系统上验证了混合代价修正的性能；随后与使用质心动力学假设的方法在四足机器人（Unitree A1）上进行了对比。在仿真和硬件测试中，HiLQR MPC均优于质心动力学方法。