Nonholonomic control of a planar Prismatic-Revolute under-actuated manipulator

In this paper, the point-to-point control problem of a Prismatic-Revolute (PR) under-actuated manipulator is presented. The PR under-actuated manipulator with the first prismatic actuated joint and a second revolute passive joint can only move in the horizontal plane. According to the characteristic of the dynamic equation of the system, a new equation concerned only with generalized coordinate, velocity and acceleration of passive joint is acquired by eliminating the generalized acceleration of the actuated joint. A controller is firstly proposed to control the passive joint by the new equation. Then another controller is designed to control the actuated joint with the stationary passive joint by adding a brake on the passive joint. Simulation results indicate the system can stably move from initial position to desired position by combing the two controllers.