The Actuator Pre-Filtering Approach to Control-Coherent Koopman LQR for Robot Systems Interacting with Compliant Environment
Jasmine Terrones, Harry Asada
AI summary
Problem
Robot systems interacting with environments experience switched dynamics that complicate real-time planning and control. Traditional Koopman operator theory cannot handle non-autonomous systems with exogenous control inputs, creating a gap for practical robotic applications.
Approach
The authors introduce an actuator pre-filter that replaces physical actuator dynamics with virtual linear filters, satisfying the mathematical conditions for Control-Coherent Koopman modeling. This transforms segmented nonlinear dynamics into a unified, globally linear state-space model suitable for linear control synthesis.
Key results
- Actuator pre-filtering method formulated to satisfy Control-Coherent Koopman requirements
- Globally linear Koopman model derived for a switched cart-pole system with compliant walls
- Koopman LQR controller designed and validated for real-time wall-bouncing tasks
- Simulation analysis quantifying the impact of pre-filter time constants on control performance
Why it matters
Provides a practical pathway for real-time optimal control of contact-rich robots by bypassing the limitations of traditional Koopman theory on non-autonomous systems.
Abstract
As a robot makes and breaks contact with environment surfaces, the equations of motion are switched. Task planning and real-time control become challenging as the system traverses multiple regions and switches the governing dynamics. This paper presents a modeling and real-time control methodology for such switched dynamical systems based on Koopman operator theory. Potentially, Koopman operators allow us to subsume segmented dynamics within a unified, globally linear model amenable for control analysis and synthesis. However, the original Koopman operators are not appliable to non-autonomous systems with exogenous input. A new method for converting robot dynamics to a Koopman- compatible model using actuator pre-filtering is presented and applied to the modeling and control of robots interacting with the environment. Specifically, an underactuated cart-pole robot bouncing against multiple walls is modeled as a Control- Coherent Koopman model and a Koopman LQR controller is designed for the wall-bouncing robot. Simulation experiments demonstrate the effectiveness of the method and investigates the effect of the actuator pre-filter parameter on control performance.