Control of Nonholonomic Mobile Bases Supported by Measuring of the Slipping and Skidding Variations

This work proposes a method in order to choose suitable controllers supported by the measuring of the slipping and skidding variations, i.e., When the nonholonomic kinematic constraints are not fully satisfied. The rolling dynamics associated with the wheels are give as conditions related with variations of the slipping and the skidding. The variations are used to state formally a tool to measure the rolling performance. The dynamic of the mobile base is give with the aid of the Lagrange approach and the singular perturbations theory. Subsequently, linear models for the traction forces and a invariant manifold are used to linearize the dynamic model. The proposed controller is adjusted by selecting appropriate parameters of an auxiliary control law. Finally, the norm of rolling performance is included as an indicator of how much the controller designed satisfies the conditions related with the variations of the slipping and the skidding.