This paper presents a robust-adaptive nonlinear model predictive control (MPC) technique that leverages past experiences to achieve tractability on computationally constrained systems. We propose a robust extension of the Experience-driven Predictive Control (EPC) algorithm via a Gaussian belief propagation strategy that computes an uncertainty set, bounding the evolution of the system state in the presence of time-varying state uncertainty. This uncertainty set is used to tighten the constraints in the predictive control formulation via a chance-constrained approach, thereby providing a probabilistic guarantee of constraint satisfaction. The parameterized form of the controllers produced by EPC coupled with online uncertainty estimates ensures that this robust constraint satisfaction property persists, even as the system switches controllers and experiences variations in the uncertainty model. We validate the online performance and robust constraint satisfaction of the proposed Robust EPC algorithm through a series of trials with a simulated ground robot and three experimental platforms: (1) a small quadrotor aerial robot executing aggressive maneuvers in wind with degraded state estimates, (2) a skid-steer ground robot equipped with a laser-based localization system, and (3) a hexarotor aerial robot equipped with a vision-based localization system.
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