Relaxed optimization for mode estimation in skid steering

Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously 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 a technique for estimating a mode sequence by optimizing a relaxation of an infinite dimensional representation of switched systems. The switching times themselves may then be estimated using switching time optimization techniques.