Optimal Bounded Thrust Directional Orbital Rendezvous

This paper proposes optimal analytical guidance laws for the three-dimensional directional orbital rendezvous problem, for both unbounded and bounded controllers. The guidance laws strictly constrain the chaser’s motion to be in a predetermined approach direction (glideslope), assuming its initial position and velocity are in that direction. The guidance laws are derived from a linear-quadratic optimal control problem, and the Clohessy-Wiltshire equations are used as the dynamic model. The bounded guidance law explicitly accounts for the thrust acceleration limitation, yielding predictions of the entering and exiting times from the saturated regions. This prediction enables the guidance law to accelerate more when needed to compensate for the expected saturation, reshaping the acceleration profile, and utilizing more of the engine’s capabilities. Simulations demonstrate the performance of both guidance laws, showing excellent results for the unbounded guidance law in the absence of acceleration saturation. When saturation was encountered, the unbounded guidance law missed the target, whereas the bounded guidance law rendezvoused with it perfectly.