Multi-Agent Passive Safe Optimal Control using Integration Constants as State Variables

This paper presents a new algorithm that provides optimal control profiles that drive a multi-agent system to a desired state at a desired time, with the guarantee of no collision, for a specified time horizon, even in case of control input application failure. The algorithm is applicable to multi-agent systems governed by nonlinear control-affine dynamics. First, the paper defines the problem of passive safe optimal control, which adds an important layer of safety to the traditional collision avoidance between agents. A multi-agent system is defined passive safe if the agents maintain safe separation even in the case any agent loses control at any time on the trajectory towards the final condition. Second, the paper shows that using the integration constants of an integrable portion of the multi-agent system dynamics as state variables is the key for including efficiently passive safety into an algorithmic framework. In particular, the number of constraints to be enforced reduces from cubic to quadratic in the number of time samples. Finally, using the integration constants, a solution algorithm based on convex programming is formalized and tested on the challenging problem of passive safe optimal control of multi-spacecraft systems in closed orbits of arbitrary eccentricity.