New paper on the Energy-optimal trajectory problems in relative motion - Acta Astronautica
Energy-optimal trajectory problems in relative motion solved via Theory of Functional Connections
We are glad to share that the last paper on the Journal "Acta Astronautica" is finally out!
In this paper, we present a new approach for solving a broad class of energy-optimal trajectory problems in relative motion using the recently developed Theory of Functional Connections (TFC). A total of four problem cases are considered and solved, i.e. rendezvous and intercept with fixed and free final time. Each problem is formulated using an indirect approach which casts the optimal trajectory problem as a system of linear or nonlinear two-point boundary value problems for the fixed and free final time cases, respectively. Using TFC, we convert each two-point boundary value problem into an unconstrained problem by analytically embedding the boundary constraints into a “constrained expression.” To validate the proposed approach, the TFC solutions are compared with solutions obtained via an analytical-based method as well as direct and indirect numerical methods. In general, the proposed technique produces solutions to machine-level accuracy. Additionally, for the cases tested, it is reported that computational run-time within the MATLAB implementation is lower than 28 and 300 ms for the fixed and free final time problems respectively. Consequently, the proposed methodology is potentially suitable for on-board generation of optimal trajectories in real-time.
A special thank goes to our SSEL's members, Kristofer Drozd, Roberto Furfaro, Enrico Schiassi, Hunter Johnston, and Daniele Mortari.
You can read it on ScienceDirect:
10.1016/j.actaastro.2021.01.031
and ResearchGate: