Smooth State Feedback Control of a New Nonholonomic Manipulator Coping With Singularities

This paper presents a smooth state feedback control algorithm for set point stabilization of a three-link planar nonholonomic manipulator (NHM). Compared to known control algorithms for such a manipulator, the one presented here is able to control the NHM in its singular positions. In the control algorithm synthesis, we consider the kinematic model of the NHM. Our control algorithm solution is based on an extension of models state variables. Smooth point stabilization is achieved by implementing the transverse function approach. The control algorithm synthesis is performed with utilization of a Lie group representation. Because the Lie algebra associated with the NHM is not nilpotent, we apply a homogeneous nilpotent approximation. Analytical results have been reinforced by simulations and experiments, which were executed using a newly built three-link planar NHM. To the best of our knowledge, this manipulator is the third of its kind in the world, but due to its distinct kinematic structure, it is a unique mechanism.