Control-Based Planning over Probability Mass Function Measurements via Robust Linear Programming

We propose an approach to synthesize linear feedback controllers for linear systems in polygonal environments. Our method focuses on designing a robust controller that can account for uncertainty in measurements. Its inputs are provided by a perception module that generates probability mass functions (PMFs) for predefined landmarks in the environment, such as distinguishable geometric features. We formulate an optimization problem with Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints to derive a stable and safe controller. Using the strong duality of linear programs (LPs) and robust optimization, we convert the optimization problem to a linear program that can be efficiently solved offline. At a high level, our approach partially combines perception, planning, and real-time control into a single design problem. An additional advantage of our method is the ability to produce controllers capable of exhibiting nonlinear behavior while relying solely on an offline LP for control synthesis.