Naman Ladhad, Digantara Research and Technologies Private Limited, India; Rithwik Neelakantan, Digantara Research and Technologies Private Limited, India; Tanveer Ahmed, Digantara Research and Technologies Private Limited, India
Keywords: Multi objective optimization, Collision Avoidance, Differential Evolution, Multi perspective, Optimization
Abstract:
Humanity’s utilization of space in the last century has been marked by significant advancements, from satellite launches to crewed missions to the Moon. The proliferation of satellites for communication, navigation, and scientific research has resulted in an exponential increase in global accessibility, technological advancements and convenience. However, the increase in satellite deployment in recent times has highlighted the urgent need for robust space infrastructure. Developing a comprehensive space infrastructure is essential to ensure the safety and sustainability of future space operations, especially in the context of ever-increasing predictions of collisions in space.
Collision avoidance in practical real case scenarios involves intricate decision making processes, demanding varying fidelity of data and processes at different stages. Mission constraints, propellant constraints, reliability of collision risk estimation, nature of secondary objects and even operator’s schedules contribute to the process of decision making. Therefore, it is imperative to adopt a multi-perspective approach to the problem formulation involving many (if not all) of the above mentioned aspects. In this context, the maneuver design for collision avoidance is formulated as a heuristic multi-objective multi-perspective optimization problem in this research and the solution is obtained using Differential Evolution (DE), an evolutionary optimization technique. The aim is to obtain optimal collision avoidance maneuver(s) and return to the nominal orbit via restitution maneuver(s), minimizing the disruption of routine payload operations. The choice of the optimization technique, DE, is driven by its versatility in the scope for including multiple design variables, compatibility to formulation of multiple objective functions, the lack of need for a close initial guess in the numerical process and ease of parallelization for faster computing.
The objective functions to minimize in the problem formulation are a) mass of fuel used b) the collision probability after maneuver(s) c) the deviation of the maneuvered trajectory from the non-maneuvered nominal trajectory and d) disruption time of routine payload operations (defined as the time span for which the spacecraft deviates from its nominal orbit). The objective of this study is to obtain optimal solutions through a scalarization approach, applying weights to each objective function and obtaining a composite objective function. The effect of each individual objective function on the optimal solution is also investigated. The solution search space consists of the start time of each maneuver, the duration of the burn and the components of each maneuver. The mission related constraints are modelled as constraints to the optimization problem (for example, the altitude of the spacecraft at any point in the maneuvered trajectory cannot exceed a deviation of 10km from the nominal orbit). The generation of a member of the population in the DE-based algorithm consists of the numerical propagation from one day prior to the predicted close-approach, conducting the randomly selected maneuvers, numerical propagation till the spacecraft returns to its nominal orbit with minimized error, and evaluation of the objective function. The DE-based process is terminated when the objective function reaches a pre-defined tolerance value.
As a demonstration of the proposed algorithms, an indicative result showcasing the optimal maneuver design for avoiding the collision between two active satellites 55xxx and 39xxx is presented. A close approach between these two satellites was predicted to occur on 2024/08/07 at 08:41:00.000 (TCA) with a miss distance of 1.288 km and a collision probability of 3.0145e-4. In the optimal maneuver design process, it is ensured that there is atleast one maneuver before the TCA. The maneuver duration was restricted to be less than 30 seconds. The propulsion system in the primary satellite was assumed to provide a constant thrust of 5N. The number of members in a generation in DE was chosen as 50 and the mutation and crossover values as 0.5 and 0.7 respectively. After convergence of the numerical process, the advantage of the obtained optimal solution is quantified in comparison with a random solution (selected among one of the members of the final generation). The primary objective of avoiding the collision is accomplished, with an order of magnitude reduction in the value of collision probability (O(10^-5) to O(10^-6)) in the optimal solution. A reduction in the payload interruption time of about 6.234 hours in the two-day analysis window was achieved by the optimal solution. Further in-depth analysis will be presented in the final manuscript. The global/local nature of the obtained solution will be verified by a thorough parametric analysis.
The applications of the proposed methodology will benefit the satellite owner/operators with optimal maneuver recommendations and informed decision making contexts. The modular nature of the methodology allows for a multitude of operational constraints to be modeled, offering flexibility to the operator to tune the optimal it’s to their precise requirements. Extended mission life, confidence and reliability in collision avoidance maneuvers and overall financial gain are the broad outcomes of the proposed research.
Date of Conference: September 17-20, 2024
Track: Conjunction/RPO