Indirect Trajectory Optimization with Path Constraints for Multi-Agent Proximity Operations

The growing emphasis on spacecraft sustainability through in-space servicing, assembly, and manufacturing highlights the need for ongoing technological advancement in this complex and multi-disciplinary area. Small multi-agent spacecraft teams will likely play a key role in autonomous and routine in-space servicing and assembly missions. The team, as a whole, must operate with fuel efficiency while adhering to various constraints such as maintaining a minimum inter-agent separation distance to prevent collisions during the servicing or assembly operation. In this paper, we present a novel approach for multi-agent path-constrained trajectory optimization using indirect methods, without increasing the problem size. Using a hyperbolic tangent function and smoothing, we successfully formulate the constrained multi-agent trajectory planning problem as a single indirect optimal control problem, guaranteeing that the converged solution is at least locally optimal and that the path constraints are always satisfied while retaining the trajectories as single arcs. The hyperbolic tangent function is employed to smooth the transition from an inactive to an active path constraint, with the final solution exhibiting the true constrained motion. Multi-agent trajectory optimization simulations are performed using a unique relative dynamical model, based on circular restricted three-body problem dynamics, with a frame-center shift as well as a smaller distance unit to better condition the problem for numerical convergence. We demonstrate the performance of the algorithm by simulating different configurations of agents (i.e., 2, 3 and 4 agents) simultaneously transporting modular components between a service vehicle (100 m away) and a space telescope undergoing servicing or assembly, in a Halo orbit at Sun–Earth L2, while satisfying the specified inter-agent anti-collision constraint. An independent validation of the method is also provided by solving the well-known Brachistochrone problem while satisfying a prescribed linear path constraint.