Chained-Form Design and Motion Planning for a Nonholonomic Manipulator

This paper provides a method for a controllable nonholonomic mechanical system. By use of the nonholonomy of the disk’s rolling constraint in the plane and the condition of chained form conversion, a multi-joint nonholonomic manipulator, which uses only two actuators and can be converted into chained form and achieves control simplicity, is presented. The Frobenius and Chow theorems prove that the nonholonomic manipulator is controllable and satisfies the condition of chained form transformation. For further verification, the manipulator prototype with two actuators and three joints is fabricate. The validity of motion planning of the manipulator prototype is demonstrated by simulation and experimental results. The conclusion indicates that the three joints nonholonomic manipulator prototype can move to terminal configuration smoothly with singularity avoidance method and it is feasible to design a controllable and nonholonomic mechanical system.