Considerations choosing the optimal equilibrium point on the rotational sphere

In order to save energy during attitude maneuvers the choice of optimal rotation is imperative, especially when considering applications where resources are inaccessible such as orbiting spacecraft. Normally the shortest rotation is considered preferable but in this paper we derive an analytical expression where the optimal rotational direction is found by performing a simple check. A passivity based PD+ controller is derived and the equilibrium points of the closed-loop system are shown uniformly asymptotically stable. We apply the control law to achieve simulation results showing the performance of the presented scheme where different initial conditions are considered, comparing power consumption for rotational maneuvers in opposite directions.