Cover schemes and coupled radial basis functions applied to solving optimal control problems in in-space servicing, assembly, and manufacturing applications

Abstract In-space servicing is a major capability of in-space servicing, assembly, and manufacturing (ISAM), and often requires a spacecraft to conduct proximity, rendezvous, and docking operations. These operations allow the servicing spacecraft to perform activities such as refueling, repairs, and inspections on the target spacecraft, thus increasing its overall performance and allowing longer missions. Minimizing time or fuel in the design of proximity, rendezvous, and docking maneuvers requires optimization of the trajectory or maneuver. In this original paper (v1), a cover scheme method and coupled radial basis functions (CRBFs) are used to compute the optimal thrust and trajectory for a servicing satellite meeting a target spacecraft for in-space servicing. Local collocation is used, and the problem domain is divided into elements with overlapping sections called “covers” to reinforce continuity. CRBFs are utilized as the basis functions for approximation. They offer flexibility in being insensitive to the shape parameter, not requiring a certain nodal distribution, and collocating at nodes where the solution is needed. The linearized equations of orbital relative motion, the Hill–Clohessy–Wiltshire (HCW) equations, are solved to demonstrate the method. Next, an optimal attitude control problem is considered for in-space servicing and spacecraft maneuvering during proximity operations. A path constraint is implemented to demonstrate the CRBF-cover scheme method on a more complex scenario. All results are compared to optimal control software tool results to validate the method, and display the method’s advantages of being agnostic to nodal distribution and not requiring a priori information nor a good initial guess.