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），用于与周围环境建立和断开接触的系统。许多现有控制器在处理需要与环境建立接触的任务（如运动控制与操作）时，要么需要预设接触模式时序，要么因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，该方法能够对潜在接触事件进行高速推理。通过共识形式设计，我们的方法实现了接触调度问题的并行化。我们在五个数值案例中验证了结果，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，证明了该方法的高效性。