A Homotopic Direct Collocation Approach for Operational-Compliant Trajectory Design.

Stand-alone deep-space CubeSats are the future of the space sector. For limited budget reasons, these spacecraft need to follow operational-compliant (OC) trajectories: transfers with thrusting and coasting periods imposed at pre-defined time instants. Traditional trajectory optimisation algorithms exhibit convergence problems when handling discontinuous constraints. In this work, a homotopic direct collocation approach is presented. It employs a continuation algorithm that maps the classical bang-bang trajectory of a fuel-optimal low-thrust problem into an OC solution. M-ARGO CubeSat mission is considered as case study for validation, including a realistic thruster model with variable specific impulse and maximum thrust. The trajectories computed with the developed algorithm are compared with non-operational-compliant solutions. Our algorithm produces transfers similar to the optimal solutions with no operational constraint, both in terms of thrusting profile and propellant mass.