Optimal attitude maneuvers in the presence of prohibited directions

We consider the problem of realigning a space telescope from one observation target to next in presence prohibited directions. More specifically, we want steer – modelled as gyrostat an initial attitude at rest final within fixed time interval. During motion, line sight must be kept away forbidden directions towards bright objects like sun, moon or earth due power thermal requirements. The kinematics spacecraft motion are governed by differential equation on rotation group SO(3). Treating angular velocities control variables, this takes form controlled dynamical system. To ensure reorientation maneuvers satisfying these pointing constraints, introduce cost functional penalizing proximity any Furthermore, include penalty terms which provide smooth satellite and execution rest-to-rest maneuver. chosen is minimized over all possible trajectories system between prescribed attitudes, leads optimal SO(3), solved applying version Pontryagin's Maximum Principle tailor-made for problems Lie groups. Parametrizing SO(3) Cardan angles, solution formulated boundary-value Euclidean hence can numerically conventional methods. existence two first integrals established exploited reduce computational effort. applicability approach shown concrete examples.