Nonholonomic control of 3 link planar manipulator with a free joint

This paper is concerned with point-to point control of a 3 link planar manipulator where the first two joints are actuated and the third revoluted joint is unactuated. This system is a special case of under-actuated manipulators, which have nonholonomic constraints. The main result of this paper is to show that this system is feedback equivalent to the chained form which is composed of twice differential equations. In addition, we propose a controller that stabilizes the system from any initial position to any desired position