Koopman Dynamic Modeling and Control for Robotic Systems Making and Breaking Contact

Abstract

Controlling robots that dynamically engage in contact with their environment is a pressing challenge. Whether a legged robot making-and-breaking contact during locomotion, or a manipulator grasping objects, contact is everywhere. Unfortunately, the switching of dynamics at contact boundaries makes practical control difficult. Applying predictive control techniques to systems with contact results in non-convex optimization problems, which are notoriously difficult to solve online. In this work, I show how the use of a compliant contact model can enable the application of Koopman linearization techniques to systems with contact. This enables the construction of fast and reactive controllers for online decision making.

This approach is first demonstrated on the planar pushing task, which captures the key challenges of switching contact modes and non-prehensile manipulation. I show that a Koopman-based controller can discover dynamic control policies without any sequence of contacts being defined in advance, while still allowing for operation at real-time rates. I highlight the importance of compliance in enabling Koopman theory for contact dynamics, and also explore how mechanical compliance can be co-designed with the controller for optimal performance. Varying the compliance of a robotic manipulator results in a trade-off between the responsiveness of the system and the accuracy of the linearized model being used for control. I study the robustness of this controller to modeling errors in friction, and present a friction-aware extension that enables adaptation to online friction estimates.

A novel framework for constructing Koopman approximations is also developed for systems with contact dynamics, and compared to existing approaches for a range of autonomous systems. By combining radial basis functions (RBFs) and Deep Koopman Networks (DKNs), we observe improved prediction accuracy for complex systems, while also highlighting the impressive capabilities of completely learning-based DKN approaches.

Finally, we look at segmented dynamics more generally. A simple problem - inspired by a hot air balloon that must navigate alternating wind currents - is used to probe how Koopman models enable predictive control in the proximity of mode boundaries. We show that linear approximations of the global dynamics, as afforded by Koopman, can allow for Koopman MPC to outperform nonlinear (and non-convex) alternatives that explicitly represent the true segmented dynamics with a mixed-integer formulation.