Abstract
Formulations for optimal tire force allocation find a set of tire forces over four wheels that satisfies specific allocation objectives. To actually realize this optimal set of forces on the four tires, the solution of these formulations has to exist within feasible tire force regions of the four wheels for a given actuation layout. If a wheel has steering, driving, and braking actuators, the feasible tire force region can be assumed to be the entire area within the tire's friction capability. If there are any limits on actuation, however, the feasible tire force region is restricted to a certain area. This paper presents how to describe this region mathematically as a constraint of the optimal tire force allocation formulation. With reasonable assumptions, the boundary of the feasible tire force region can be approximated by an ellipse and circle for a wheel with steering and braking actuators. If the optimal tire force allocation formulation is designed as a convex optimization problem, the boundary expressions using the ellipse and circle can be adopted as constraints without loss of the convexity of the allocation formulation. Experimental results show that the optimal tire force allocation formulation with feasible tire force region constraints results in a set of tire forces that can actually be realized by the given actuation layout.
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