Minimum-energy switching geometric filter on lie groups for differential-drive wheeled mobile robots

Accurate state estimation plays a critical role in various applications, such as tracking, regulation, and fault detection in robotic and mechanical systems. Typically, the Kalman-Bucy filter is used as a linear state observer for this purpose. However, real-world robots often exhibit complex behavior, characterized by a combination of dynamics, making it essential to employ hybrid filters. In this context, the Switching Kalman filter stands out as a well-established solution. In this article we aim to generalize the Brownian-Markov Stochastic Model, a hybrid dynamic model for differential-drive wheeled mobile robots, to the case of a mobile robot whose center of mass is not aligned to the wheels axle middle point, and to design a geometric hybrid state estimator by exploiting the Lie groups theory. The Brownian-Markov Stochastic Model features two modes: "grip" and "slip". These modes correspond to ideal grip and lateral slippage, with transitions governed by a state-dependent Markov chain. To validate the proposed switching filter, we conduct MATLAB (R) simulations of the robot's motion in a scenario prone to lateral grip loss, comparing the state estimates produced by the switching geometric filter with those obtained using the switching Kalman filter.