Kinematic control of nonholonomic mobile manipulators in the presence of steering wheels

Abstract

We consider the kinematic control problem for nonholonomic mobile manipulators (NMMs) whose base contains steering wheels. For all typical tasks, the steering velocity inputs of such systems do not appear in the differential relationship between the first-order time derivative of the task output and the available NMM inputs. As a consequence, these inputs are not used by velocity-level control laws based on simple (pseudo)inversion of the task Jacobian, leading in general to the impossibility of completing the task. We propose two control solutions to this open problem based on the framework of input-output feedback linearization. First, a static feedback law is presented that defines the unspecified steering velocities via an optimization action in the null space of the task Jacobian. A dynamic feedback law is then proposed based on the input-output differential map obtained by considering the task acceleration. In this case, the velocity of the steering wheels becomes an active input for task execution, together with the manipulator joint accelerations and the driving accelerations of the base. The feasibility and performance of the two kinematic controllers are compared in simulation for a car-like base carrying a planar manipulator.