We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm.

翻译：我们提出一种混合模型预测控制算法——共识互补控制（C3），适用于与周围环境进行接触与分离的系统。许多针对需要与环境建立接触的任务（如行走运动和机械操作）的先进控制器，要么依赖先验的接触模式调度，要么计算复杂度过高而无法实现实时运行。我们提出一种基于交替方向乘子法（ADMM）的方法，能够对潜在接触事件进行高速推理。通过共识形式的建立，我们的方法实现了接触调度问题的并行化。我们通过五个数值示例验证了结果，其中包括四个高维摩擦接触问题以及一个欠驱动多接触系统的物理实验。我们进一步通过机器人手臂完成高维多接触操作任务的物理实验，展示了该方法的有效性。