Control and stabilization of a third-order nonholonomic system

We study the control of a simplified model of a PPR robot manipulator subject to a third-order nonholonomic constraint. The model consists of a base body, which can translate and rotate freely in the plane, and a massless arm at the tip of which the end-effector is attached. It is assumed that two forces and a torque applied to the manipulator are available as control inputs. The objective is to control the robot end-effector movement while keeping the transverse jerk component is zero. The main result of the paper is the construction of a feedback control algorithm that transfers the manipulator from any initial equilibrium configuration to the zero equilibrium configuration in finite time. The effectiveness of the algorithm is illustrated through a simulation example.