Learning Control of a Flexible Arm by B-spline Curves in Consideration of Time Scaling

A learning control method using B-spline curves is extended to be applied to the tracking of specified spatial paths at arbitrary speed. This tracking control means the tracking of time scaled trajectories with geomemc path constraints. The proposed method obtains following results : (1) By using Time Scale Factor, dynamics of controlled system is described by two separate terms, a part defining a spatial path and the other one scaling time. (2) An algorithm is proposed to estimat coefficients describing the dynamics. (3) A gain matrix for learning control is expressed as a function of Time Scale Factor. (4) The learning control method is effectively applied to the control of a one-link flexible arm to track arbitrary trajectories which are determined by specifying spatial paths and scaling time.