Control of manipulators with hyper degrees of freedom: Shape tracking based on curve parameter estimation

In this paper, a shape tracking control problem for a hyper degrees of freedom manipulator is discussed. The objective of shape tracking is to control its shape, which is characterized by all the joints and the tip positions, to follow a given time-varying curve. Crucial key to solve this problem is to introduce a 2nd-order estimator that infers the curve parameters corresponding to the target positions of the joints and the tip on the curve. The coupled dynamics of the manipulator and this estimator has the same properties as the manipulator dynamics which is useful for control design purposes. Therefore, familiar design methods for manipulator trading can be utilized to solve the shape tracking problem. Examples are shown to illustrate how to find shape tracking laws by two famous methods, that is, the ID (inverse dynamics)-based and Lyapunov-based method