Holonomy-Based Control of a Three-Joint Underactuated Manipulator

In the author's previous work, a motion planning algorithm for nonholonomic systems in the second-order chained form has been proposed. A basic idea of the algorithm is that the use of sinusoidal inputs extracts holonomy, which is essential motion of nonholonomic systems. This paper addresses a control problem of rest-to-rest motion for a three-joint underactuated manipulator that moves in a horizontal plane. The dynamics of this manipulator can be transformed to the second-order chained form via appropriate coordinate and input transformation. This correspondence between two system description helpes us to construct a control method based on the proposed algorithm. The effectiveness of the control method is numerically demonstrated by some examples.