Exponential control law for a multi-degree of freedom mobile robot

In this paper, we describe the development of a nonlinear exponential control law for a multi-degree of freedom (MDOF) wheeled mobile robot. These vehicles have many advantages over the more classical 2-DOF mobile robots. Indeed, the MDOF vehicles can negotiate tight turns easily and are able to travel sideways. Nevertheless, the MDOF robots are over constrained systems, which are difficult to control. By this reason, MDOF robots are limited to simple applications, like following a guide-wire. In order to obtain an autonomous behavior, we propose the use of a nonlinear control law, which exponentially leads the robot to a desired position with a given orientation. A new set of error variables is defined in order to propose the control vector. This control vector makes the final configuration globally exponentially stable. Results of simulation, which illustrate the effectiveness of the control, are also included.