Transition trajectory generation with time-scaled trigonometric series control parameterization

Abstract

This paper is concerned with shaping the time behavior of controls for generating transition trajectories. Parameterizing controls with trigonometric series enables infinite differentiability with respect to time, which is very appealing in real operations. In practice, one may desire the controls to have a specific distribution over time. However, to achieve this usually relies on judicious selection of the cost function. To this end, this paper introduces a time-scaling transformation for the trigonometric series. It yields an intuitive and flexible way to design the controls tailored to the desired shape of a transition maneuver. The process does not rely on additional design effort for the cost function. The proposed method is applied to generating a transition trajectory that converges to the desired condition earlier in comparison to the unscaled formulation. Numerical results demonstrate the effectiveness of the proposed method.