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This study reformulates Divergent Components of Motion (DCMs) as Koopman eigenfunctions, enabling their application beyond reduced models like the linear inverted pendulum. By intentionally targeting unstable eigenpairs with large eigenvalues, the authors develop data-driven DCMs that enhance balance control in legged locomotion. The approach demonstrates significant improvements in tracking reference walking patterns on a real biped robot, showcasing the practical utility of learned DCMs in conjunction with model predictive control for state-based viability constraints.
Targeting unstable eigenfunctions transforms legged locomotion control, leading to enhanced balance and tracking performance in real-world robots.
In legged locomotion, divergent components of motion (DCMs) have emerged as characteristic states for balance control. They isolate the unstable mode of the dynamics but, in existing formulations, apply only to reduced models such as the linear inverted pendulum. In this study, we show how DCMs can be more generally formulated as Koopman eigenfunctions. Whereas Koopman analysis typically targets eigenvalues near zero, which capture conserved or slowly varying quantities, our investigation leads us to deliberately search for unstable eigenpairs with large eigenvalues. The resulting Koopman DCMs are data-driven observables trained using only real-robot data. On a real biped, DCMs learned from one hour of robot data improve tracking of reference walking patterns. We further show how learned DCMs provide state-based viability constraints when combined with model predictive control.