aiqbench analysis
This research advances legged robotics by redefining divergent components of motion (DCMs) as Koopman eigenfunctions, enabling data-driven balance control directly from real-robot trajectories. By targeting unstable eigenpairs rather than conserved quantities, the method improves walking pattern tracking on bipeds and integrates seamlessly with model predictive control for viability constraints. The work represents a significant theoretical step in applying linear systems theory to complex nonlinear dynamics without relying on simplified reduced-order models.
Koopman DCM: Unstable Eigenfunctions as Data-driven Representations for Legged Balancing
arXiv:2607.18760v1 Announce Type: new Abstract: 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.
Abstract: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.
Robotics (cs.RO)
arXiv:2607.18760 [cs.RO]
(or arXiv:2607.18760v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2607.18760 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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