Centroidal State Estimation based on the Koopman Embedding for Dynamic Legged Locomotion

In this paper, we introduce a novel approachto centroidal state estimation, which plays a crucial role inpredictive model-based control strategies for dynamic leggedlocomotion. Our approach uses the Koopman operator theoryto transform the robot’s complex nonlinear dynamics into alinear system, by employing dynamic mode decomposition anddeep learning for model construction. We evaluate both modelson their linearization accuracy and capability to capture bothfast and slow dynamic system responses. We then select themost suitable model for estimation purposes, and integrate itwithin a moving horizon estimator. This estimator is formulatedas a convex quadratic program, to facilitate robust, real-timecentroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits,our data-driven framework outperforms conventional filteringtechniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise inhighly dynamic motions and accurately recovers the centroidalstates, demonstrating the adaptability and effectiveness of theKoopman-based linear representation for complex locomotivebehaviors. Importantly, our model based on dynamic modedecomposition, trained with two locomotion patterns (trot andjump), successfully estimates the centroidal states for a differentmotion (bound) without retraining.