Optimal Trajectory Generation for Linear Systems Based on Double Generating Functions

Abstract

Recently, the generating function method for the optimal control problems was proposed. It provides a family of optimal trajectories for different boundary conditions. This paper proposes a method to compute a family of optimal trajectories by using a pair of generating functions. The proposed method reduces the on-line computational effort in calculating the numerical integration required in the conventional generating function method. It is useful for on-line trajectory generation problems.