Observer-Based State Feedback Model Predictive Control Framework for Legged Robots

Legged robots must contend with challenges like load fluctuations, external forces, and modeling errors in their working environment, all of which can lead to inaccuracies in the model predictive control (MPC) state mapping equation. Neglecting these issues can result in deviation from the predefined trajectory, and even instability. In this article, we propose a novel MPC strategy for legged robots that enables dynamic correction of the system model and enhancing computational robustness. First, a state feedback MPC controller is proposed. Unlike prior works, we reconstruct the original nonlinear model with uncertainties as a linear model with time-varying disturbances. Subsequently, we design a closed-loop state observer to approximate the reconstructed model and employ it as the benchmark for prediction in MPC. We utilized the Lyapunov function to demonstrate that this method can ensure the ultimate uniform boundedness of state estimation errors. Second, we cascaded a whole-body controller with computational robustness as a compensatory controller for the MPC. Finally, extensive experiments on the biped robot BRAVER validated the proposed framework in both simulation and physical prototype.