The Application of Command Shaping to the Tracking Problem

This work presents a novel technique for the solution of an optimal input for trajectory tracking. Many researchers have documented the performance advantages of command shaping, which focuses on the design of an optimal input. Nearly all research in command shaping has been centered on the point-to-point motion control problem. However, tracking problems are also an important application of control theory. The proposed optimal tracking technique extends the point-to-point motion control problem to the solution of the tracking problem. Thus, two very different problems are brought into one solution scheme. The technique uses tolerances on trajectory following to meet constraints and minimize either maneuver time or input energy. A major advantage of the technique is that hard physical constraints such as acceleration or allowable tracking error can be directly constrained. Previous methods to perform such a task involved using various weightings that lack physical meaning. The optimal tracking technique allows for fast and efficient exploration of the solution space for motion control. A solution verification technique is presented and some examples are included to demonstrate the technique.