Joanna Hon, Turion Space Corporation.; M. Reza Emami, University of Toronto Institute for Aerospace Studies
Keywords: Active Debris Removal, Mission Planning, Rendezvous, Optimization, Metaheuristics, Space Situational Awareness
Abstract:
Numerical studies on the evolution of the space debris population in low-Earth orbit (LEO) have indicated that regardless of the frequency of future launch activities, the population is unstable, and its growth is inevitable. As the rate of naturally decaying objects is slower than that required to stabilize the LEO debris population, active debris removal (ADR) will be crucial to sustaining the space environment for ongoing and future operations. Spacecraft-based removal strategies that can visit and remove multiple debris objects in a single mission are of considerable interest due to their high impact and economic feasibility. Reduction in mission costs can be achieved by optimizing the debris sequencing and rendezvous trajectories to minimize propellant consumption. This problem, coined the multitarget rendezvous problem (MTRV), thus consists of combinatorial optimization for debris target sequencing, and continuous, nonlinear optimization for trajectory planning. Furthermore, trajectory optimization is a function of maneuver epoch, adding a time dependence that couples the embedded optimization problems. Several studies have tackled the MTRV problem through various approaches, and the applicability of each approach is dependent on the given ADR mission plan objectives, constraints, and underlying assumptions.
In this research, a framework to optimize the MTRV problem for ADR missions that remove several specific debris objects of interest is proposed. Mission window constraints, transfer strategy, and an upper bound on object-to-object transfer times are identified to bound the optimization problem. The effects due to J2 perturbation are accounted for. The debris sequence, maneuver epoch, and thrust vector are the problem variables, while the total maneuver cost (delta-V) is the design objective to minimize.
An approach to relax the coupling of the nonlinear trajectory optimization from the combinatorial optimization is devised. Sensitivity analysis of the objective function is conducted to ensure that the devised approach reliably reduces the solution space such that the optimum (and near-optima) of the simplified problem approximates those of the original MTRV problem. The trajectory optimization is conducted for long-range rendezvous. Similar ADR optimal mission planning studies employ global-search algorithms such as the branch and bound method, simulated annealing, ant colony optimization, particle swarm optimization, and evolutionary algorithms. As the solution space grows factorially with the number of debris objects, the sequence optimization for this study is achieved using a population-based metaheuristic to reduce the computational requirements and ensure the scalability of the application.
Optimization of the mixed-integer nonlinear MTRV problem is achieved by decomposing the execution into three stages. The first and second stages estimate the maneuver costs between debris object pairs as a function of maneuver epoch and employ a population-based metaheuristic to optimize debris sequencing. The method to relax the embedded nonlinear problem is informed by the sensitivity analysis of the objective function. The final stage implements a nonlinear programming algorithm to refine the trajectory optimization, provided the converged debris object sequence. The debris sequence, maneuver epoch, thrust vector time history, and total delta-V cost to remove select debris objects considering the J2 perturbation are outputs of this optimization framework. The validity of the proposed framework is demonstrated through an ADR case study. The outcome of this research is an optimal planning tool for active debris removal missions.
Date of Conference: September 27-20, 2022
Track: Space Debris