Optimal trade-off analysis for efficiency and safety in the spacecraft rendezvous and docking problem

Abstract

We study the problem of spacecraft rendezvous and docking, specifically the tradeoff between safety and efficiency. The safety component in this problem is to stay within a line-of-sight cone and reach the target at an appropriate time in the presence of stochastic disturbance due to sensing and modeling errors. The efficiency component in this problem is our desire to minimize control effort or fuel. We pose this problem as a bi-criterion optimization problem. Using our recent convexity results for the stochastic reach-avoid problem when the control policies are restricted to open-loop policies, we show that this bi-criterion optimization problem is convex. The resulting tractability permits the exploration of the trade-off between safety and efficiency in the stochastic system. We also show that while increasing the control bounds need not always translate to an increase in the attainable safety guarantees, decreasing the control bounds typically translates to a decrease in the attainable safety guarantees.