On-Manifold Prediction Error Compensation for Model Predictive Control: Application to Quadrotors

Abstract

Model Predictive Control (MPC) has been widely employed in mobile robotics to compute optimal control inputs based on predicted future states. However, inevitable disturbances in real-world environments cause model mismatches that degrade the predictive performance of MPC. To address this issue, this letter proposes an On-Manifold Adaptive Law (OMAL) to estimate unknown disturbances and mitigate the effects of the resulting model mismatches. OMAL estimates physically consistent disturbances by explicitly respecting the compound manifold structure of the state space, thereby avoiding attitude-representation singularities through exponential and logarithmic maps. The disturbances estimated by OMAL are incorporated into the nominal model to improve prediction accuracy over the prediction horizon, while preserving the quadratic program (QP) structure of MPC and hence its feasibility under constraints. Simulations and real-world experiments with quadrotors demonstrate that the proposed OMAL reduces the effects of disturbances without prior disturbance models or additional sensors, thereby improving tracking performance during agile trajectories that involve aggressive maneuvers.