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：本文提出了一种混合模型预测控制算法——共识互补控制（C3），适用于与环境发生接触及脱离接触的系统。对于需要与环境建立接触的任务（如运动与操作），许多先进控制器要么需要预先设定接触模式序列，要么计算过于复杂而无法实时运行。我们提出了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。通过共识问题表述，我们的方法实现了接触调度问题的并行化求解。我们在五个数值算例中验证了结果，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。我们进一步通过物理实验证明了本方法的有效性：使用机械臂完成了高维多接触操作任务。