Sensitivity-Aware Model Predictive Control for Robots With Parametric Uncertainty

This article introduces a computationally efficient robust model predictive control (MPC) scheme for controlling nonlinear systems affected by parametric uncertainties in their models. The approach leverages the recent notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">closed-loop state sensitivity</i> and the associated ellipsoidal tubes of perturbed trajectories for taking into account online time-varying restrictions on state and input constraints. This makes the MPC controller “aware” of potential additional requirements needed to cope with parametric uncertainty, thus significantly improving the tracking performance and success rates during navigation in constrained environments. One key contribution lies in the introduction of a computationally efficient robust MPC formulation with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">comparable computational complexity</i> to a standard MPC (i.e., an MPC not explicitly dealing with parametric uncertainty). An extensive simulation campaign is presented to demonstrate the effectiveness of the proposed approach in handling parametric uncertainties and enhancing task performance, safety, and overall robustness. Furthermore, we also provide an experimental validation that shows the feasibility of the approach in real-world conditions and corroborates the statistical findings of the simulation campaign. The versatility and efficiency of the proposed method make it therefore a valuable tool for real-time control of robots subject to nonnegligible uncertainty in their models.