Directed guidance for simple mechanical control systems

In this paper we describe in some generality a notion we are referring to as directed guidance and show how this approach applies to simple mechanical control systems. The basic idea is to develop a reference behavior for the mechanical system's velocity suitable for guiding it and then to use the control authority available to the system to regulate the reference. This approach breaks the guidance design process into two pieces, the design of the reference and that of the regulation. Transitioning to this hierarchical approach is important, as it transforms the intercept control problem to one of regulation, and while there exist few design techniques for general intercept problems, the controls literature provides an abundant source of regulation ideas. We use geometric control theory to show that the directed guidance approach is readily applicable to the velocity control of simple mechanical control systems that are fully actuated and to the direction control of those that have curvature controllability. The potential application areas of the results include broader classes of problems, such as motion mimicking, congruence control, and pose acquisition, yet also provide unique solutions to traditional problems, such as intercept or rendezvous guidance.