用数学工具将机器人接触控制变线性，实现实时复杂动作
Koopman global linearization of contact dynamics for robot locomotion and manipulation enables elaborate control
- 用Koopman算子将接触切换的非线性动力学统一为全局线性模型
- 在多接触变化场景下实现机器人实时精确控制，时间跨度超1秒
- 适合需要高精度动态交互的机器人系统，如腿式行走与抓握操作
机器人在与环境发生动态接触时的控制是一个关键挑战。无论是腿式机器人与地面的交替接触，还是机械臂抓握物体，接触无处不在。然而，接触边界处动力学突变使得控制极为困难，预测控制器在涉及接触时面临非凸优化问题。本文通过应用Koopman算子，将由接触变化引起的分段动力学统一嵌入到一个全局线性模型中。我们证明，在机器人-环境相互作用中存在粘弹性接触时，无需近似即可使用Koopman算子对控制输入建模。该方法使足式机器人实现了凸型模型预测控制，且支持机械臂在动态推挤中的实时控制。本工作展示了该方法可在包含多次接触变化的时间窗口内实时发现复杂控制策略，且适用范围远超机器人领域。
原文摘要 · Abstract (English)
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.
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