A Homotopic Direct Collocation Approach for Operational-Compliant Trajectory Design

Abstract

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.

An Indirect Formulation of Operational Compliant Low-thrust Trajectories

“…It is usually employed in indirect methods to overcome discontinuity problems as bang-bang control in fuel optimal solutions [17,18], to impose varying maximum thrust models [19] and shutdown of the thruster due to eclipses [20]. Recently, the problem of forced coasting arcs imposition has become more and more relevant, and homotopic techniques have been employed to solve it [21,22] also in direct formulations [23].…”