Structure preserving koopman models improve prediction for nonlinear robots
Port-Hamiltonian Koopman Operator Synthesis for Mechanical Systems
Robotics
Summary
Predicting how robots move can be tricky because their movements follow complex physical rules. The authors developed a new way to make simplified models that still respect the natural energy and mechanics of robots. Their approach helps these models avoid unrealistic energy changes and stay accurate longer when making predictions. They tested their method on simulations and real robots, showing better accuracy and control compared to previous models.
What this means in practice
- •For robotics engineers: Improve model-based control of nonlinear robotic arms by preserving physical energy properties in predictions.
- •For automation system designers: Enhance accurate forecasting and control in complex mechanical systems like automated vehicles or industrial robots using structure-aware Koopman models.
Authors
Rajpal Singh, Aditya Singh, Jishnu Keshavan
Abstract
Finite-dimensional Koopman models enable efficient linear prediction and control of nonlinear robotic systems. However, models learned purely from trajectory data may violate the energetic structure of the underlying mechanics, producing predictions that exhibit artificial energy growth and diverge under recursive propagation. This work presents a structure-preserving Koopman framework for Euler-Lagrange systems built on generalized-momentum coordinates. The momentum transformation exposes the mechanical actuation as a known, state-independent port, which is preserved explicitly in the lifted dynamics. A structure-constrained neural architecture is developed to jointly learn the lifting functions and a port-Hamiltonian Koopman generator, rendering the learned dynamics passive by construction rather than through penalty terms or post-hoc projection. A Cayley-midpoint discretization further preserves the corresponding storage-dissipation balance exactly in discrete time. These properties are established analytically by deriving the discrete storage balance and associated stability guarantees of the learned predictor. Simulation and experimental studies demonstrate improved prediction accuracy, data efficiency, and closed-loop tracking over Koopman baselines, with increasing gains for higher-dimensional systems.