Kinematic singularities avoidance for the planar three-link nonholonomic manipulator

The problem of the singularities avoidance in movement control of the planar three-link nonholonomic manipulator is the main issue of this paper. Considered here nonholonomic manipulator is equipped with ball gears allowing to transmit the torque continuously from the engines to separate manipulator´s links. This mechanical structure theoretically allows to control unlimited number of joints with use of only two actuators. One of important difficulties in control of this system arises from appearance of singularities in the kinematic description of the nonholonomic manipulator. In order to avoid this problem, we propose application of the state extension of the manipulator´s kinematic model. The analytical studies are confirmed with simulations, where the closed loop feedback control was used with utilization of transverse function approach.