Continuation Method of Backstepping Tracking Control for Car-Like Mobile Robots

The trajectory tracking problem for car-like mobile robots is investigated in this paper. For the robot moving with non-sliding wheels, nonholonomic constraints naturally arise, for which the techniques associated with chained form developed before such as the backstepping controller can be adopted. However, in the transformation from the kinematic equation to chained system, singularity problem may occur which restricts the region of application. To solve this problem, two sets of complementary chained systems are used interchangeably such that the tracking path is global, i.e. every trajectory can be followed. A switching mechanism and a continuation method are proposed to generate smooth signals in the kinematic level, which are fed into the dynamic controller to steer the privileged variables. Such hierarchical scheme of the controller design is made possible by tacitly choosing the privileged coordinates in deducing the reduced Appell equations which are decoupled from the kinematic equations. To deal with the uncertainties in the system parameters, an adaptive sliding mode controller is used in the dynamical level, which subsequently drives all system variables to the desired values by natural mechanism. Simulation results demonstrate the success of the proposed systematic design of the tracking controller.