Switching mode generation and optimal estimation with application to skid-steering

Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skid-steered vehicle. In order to treat the skid-steered vehicle as a switched system, the vehicle’s ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents second-order optimization algorithms for estimating these switching times. We emphasize the importance of the second-order algorithm because it exhibits quadratic convergence and because even for relatively simple examples, first-order methods fail to converge on time scales compatible with real-time operation. Furthermore, the paper presents a technique for estimating the mode sequence by optimizing a relaxation of the switched system.