Control of a differentially driven nonholonomic robot subject to a restricted wheels rotation

The paper deals with non-standard motion tasks specified for a two-wheeled nonholonomic robot. It is assumed that wheels cannot fully rotate which reduces a set of feasible movements significantly. In spite of these constraints, it is expected that position of the robot can be changed without violating nonholonomic constraints. Such a possibility comes from the small time local controllability (STLC) of the kinematics described on four-dimensional configuration manifold. In order to solve these specific tasks a feedback taking advantage of the transverse function approach is designed. Consequently, the system can be virtually released from non-holonomic constraints. The transverse function also defines a virtual geometry constraint which makes it possible to limit wheels rotation.Properties of the designed controller are illustrated by results of numerical simulations in various motion task scenarios.