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On the Stability Properties of Perception-aware Chance-constrained MPC in Uncertain Environments

Perception-aware control systematically considers the interdependence between perception and control to optimize the overall performance of the closed-loop system subject to state and input-dependent uncertainty. That is, it accounts for the impact of control on sensing and of sensing on control. Recently, we proposed a perception-aware chance-constrained MPC (PAC-MPC) that considers the impact of control on the evolution of the environment uncertainty. In this paper, we obtain a stabilizing design for the PAC-MPC by first determining stability conditions in a general nonlinear setting and then deriving specific design rules for the linear-Gaussian case. The latter case results in a specific choice of the MPC cost function parameters, and in design conditions for that the estimation algorithm, that determine uncertainty propagation in the MPC prediction model, must satisfy.