  In this paper, we introduce a novel approach to centroidal state estimation,
which plays a crucial role in predictive model-based control strategies for
dynamic legged locomotion. Our approach uses the Koopman operator theory to
transform the robot's complex nonlinear dynamics into a linear system, by
employing dynamic mode decomposition and deep learning for model construction.
We evaluate both models on their linearization accuracy and capability to
capture both fast and slow dynamic system responses. We then select the most
suitable model for estimation purposes, and integrate it within a moving
horizon estimator. This estimator is formulated as a convex quadratic program,
to facilitate robust, real-time centroidal state estimation. Through extensive
simulation experiments on a quadruped robot executing various dynamic gaits,
our data-driven framework outperforms conventional filtering techniques based
on nonlinear dynamics. Our estimator addresses challenges posed by force/torque
measurement noise in highly dynamic motions and accurately recovers the
centroidal states, demonstrating the adaptability and effectiveness of the
Koopman-based linear representation for complex locomotive behaviors.
Importantly, our model based on dynamic mode decomposition, trained with two
locomotion patterns (trot and jump), successfully estimates the centroidal
states for a different motion (bound) without retraining.
