Position and constraint force control of a vehicle with two or more steerable drive wheels

Since a vehicle with two or more steerable drive wheels is always traveling in a circle about an instantaneous center of rotation, the motion of the wheels is constrained. The wheel translational velocity divided by the radius to the center of rotation must be the same for all wheels. When the drive wheels are controlled independently using position control, the motion of the wheels may violate the constraints and the wheels may slip. Consequently, substantial errors can occur in the position and orientation of the vehicle. A vehicle with N steerable drive wheels has N holonomic constraints on the steering angles, (N-1) nonholonomic constraints on the wheel velocities, and one degree of freedom. The authors have developed a new approach to the control of a vehicle with N steerable drive wheels. The novel aspect of their approach is the introduction of variables to control the constraint forces. To control the vehicle, the authors have one variable to control motion and (N-1) variables that can control the constraint forces to reduce errors. Kankaanranta and Koivo (1988) developed a control architecture that allows the control variables for force and position to be decoupled. In the work of Kankaaranta and Koivo the control variables for force are an exogenous input. The authors have made the central variables for force endogenous by defining them in terms of the errors in satisfying the nonholonomic constraints. The authors have applied the control architecture to the HERMIES-III robot and have measured a dramatic reduction in error (more than a factor of 20) compared to motions without constraint force control