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Optimal Tire Force Allocation for Autonomous Trajectory Tracking

March, 2017

The advent of a hydraulic modulator, which is the automotive part that can control brake pressure on the wheels individually, gives a vehicle an additional authority to control its yaw motion, and this additional control authority enables active safety systems like Electronic Stability Control (ESC). ESC has been proven to be effective in avoiding a large number of car crashes, but advances that can further reduce the number are underway: recent developments in actuator technology for steering, driving, and braking dramatically improve the performance of individual actuators and expand the boundary of vehicle control authority achieved by the coordinated actions of these actuators. This expanded control authority can serve as a physical base to enable many new vehicle control systems that will further improve automobile safety and performance than ESC. This dissertation presents a method that utilizes expanded control authority for allocating tire forces optimally with a convex optimization formulation. If a vehicle has all three actuators (steering, driving, and braking) on all four wheels, each tire ideally can generate any force within the tire's maximum available friction capability through combined actions of these actuators. The basic objective of the optimal tire force allocation is to find a set of tire forces that keeps the usage of tire friction capability equal over the four wheels and minimizes that usage as much as possible. Achieving this objective has the advantage of preventing some tires from reaching saturation before other tires, thereby keeping the vehicle from sideway skidding or spinning out and enhancing automobile safety near the limits of handling. However, actually implementing all three actuators at all four wheels is technically challenging and costly. If there are any limits on actuation for a wheel, the feasible tire force region is restricted to a certain area in the entire area within the tire's maximum friction capability. To be practical, the formulation for the optimal tire force allocation has to handle the situation of limited actuation by finding a set of tire forces only within the feasible tire force regions. This dissertation shows that the boundary of the feasible tire force region can be approximated by an ellipse and circle for a wheel with steering and braking actuators. By simply taking these approximations as constraints, the formulation for the optimal tire force allocation gives a feasible set of tire forces for a given actuation layout. Actual roads are not perfectly flat and usually have some non-zero degrees of bank and grade. Even under these conditions, operating a vehicle with the basic objective of the optimal tire force allocation---keeping the same and minimal friction usage over the four wheels---has the same advantage of preventing some tires' earlier saturation. To achieve this objective, this dissertation presents a revised formulation for the optimal tire force allocation that can handle the effects of non-zero bank angles and grades of the road on the vehicle's motion. Experimental trajectory tracking demonstrates the advantages of the optimal tire force allocation, especially near the limits of handling.