Controlling robots that dynamically engage in contact with their environment is a pressing challenge. Whether a legged robot making-and-breaking contact with a floor, or a manipulator grasping objects, contact is everywhere. Unfortunately, the switching of dynamics at contact boundaries makes control difficult. Predictive controllers face non-convex optimization problems when contact is involved. Here, we overcome this difficulty by applying Koopman operators to subsume the segmented dynamics due to contact changes into a unified, globally-linear model in an embedding space. We show that viscoelastic contact at robot-environment interactions underpins the use of Koopman operators without approximation to control inputs. This methodology enables the convex Model Predictive Control of a legged robot, and the real-time control of a manipulator engaged in dynamic pushing. In this work, we show that our method allows robots to discover elaborate control strategies in real-time over time horizons with multiple contact changes, and the method is applicable to broad fields beyond robotics.

翻译：控制机器人在动态环境中进行接触交互是一项紧迫的挑战。无论是足式机器人与地面的接触与分离，还是机械臂抓取物体，接触现象无处不在。然而，接触边界处的动力学切换使得控制问题变得复杂。涉及接触的预测控制器常面临非凸优化问题。本研究通过应用Koopman算子，将因接触变化产生的分段动力学统一嵌入到全局线性化的嵌入空间模型中，从而克服了这一难题。我们证明机器人-环境交互中的粘弹性接触特性，为无近似控制输入的Koopman算子应用提供了理论基础。该方法实现了足式机器人的凸模型预测控制，以及机械臂动态推送任务的实时控制。本研究表明，该方法使机器人能够在包含多次接触变化的时域内实时发现精细化控制策略，且该方法可拓展至机器人学之外的广泛领域。