Shrouti Dutta, NorthStar Earth & Space, Inc.; Matteo Budoni, NorthStar Earth & Space, Inc.; Guillermo Escribano, NorthStar Earth & Space, Inc.; Priyatharsan Rajasekar, NorthStar Earth & Space, Inc.; Laura Pirovano, NorthStar Earth & Space; Manuel Sanjurjo-Rivo, NorthStar Earth & Space, Inc.; Yann Picard, NorthStar Earth & Space Inc.
Keywords: astrodynamics, collision avoidance, space debris, maneuver planning
Abstract:
Collision avoidance (CA) is one of the main pillars of the strategy to mitigate the growth of the space debris population. The current trends in space traffic have significantly increased the number of objects in LEO and, accordingly, the number of conjunctions. Satellite operators must deal with this new situation with new tools to avoid high operating costs, to design CA maneuvers in an efficient and safe manner and to help in better decision-making when carrying out CA maneuvers. Therefore, it is required to properly calculate the metrics associated with the collision risk (e.g., the probability of collision or miss-distance), to carry out a screening of the possible future conjunctions considering the maneuvering plan, to take into account the uncertainty associated with the realization of the maneuver, and to carry out safe maneuvers in case of a sudden propulsion system failure in the middle of avoidance operation.
This field has been the subject of intense research in the last years. Hernando-Ayuso and Bombardelli [1] explored several analytical and semi-analytical methods to solve the minimum energy problem to get the lowest ∆v to meet a desired distance in the encounter plane or to maximize the statistical or Euclidian distances for a given ∆v. Gonzalo et al. [2] also implemented Gauss’ Planetary equations to analytically solve for an impulsive avoidance maneuver when maximizing the statistical or Euclidian distances. Different heuristic algorithms have also been explored in literature: genetic algorithms have been implemented to solve for a single impulsive avoidance maneuver as well as to solve for avoidance of multiple threats. Gradient-based direct and indirect optimization has been used to solve several formulations which include energy-optimal, fuel-optimal, and time-optimal problems, even considering uncertainty reduction in some cases [3].
Although the works cited have addressed the problem from multiple perspectives, few of them have considered the problem as a multi-objective problem. To make informed decisions about whether and how to perform a collision avoidance maneuver, it is necessary to consider the impact of the maneuver on multiple aspects related to satellite operations. This is the rationale behind posing the problem as a multi-objective optimization problem. Thus, the first stage consists of a global search based on surrogate models for supporting decision making. Based on the operator decision, an initial guess for the trajectory and maneuver is selected, as well as the weights of the different cost functions. In a second stage, the single-objective optimization problem is solved using a sequential programming approach in which all the constraints relevant for the maneuver are considered. From this perspective, the second stage is a multidisciplinary optimization problem, in which models for the satellite subsystems, such as propulsion, power, AOCS, etc., are incorporated to constraint the search space and to produce the optimal feasible maneuver compatible with collision risk mitigation. In this line, Dutta and Misra [4] explored the effect of convex and non-convex optimization for avoidance trajectories along with return when considering linear and nonlinear evolution of uncertainties. In addition, some recent works have already explored the capabilities of sequential quadratic programming [5] with second-order cone programming, and differential algebra in the context of multiple encounters.
The method is tested on realistic scenarios involving different orbit regimes – LEO and GEO. The performance of the short-term encounter model is tested in the GEO regime when it comes to providing an initial CAM hypothesis in the global optimization problem. The method is also tested to comply with different propulsion types and accommodate several uncertainties like control actuation errors, temporal and spatial uncertainties in CDM information, etc.
References:
1. Javier Hernando Ayuso, Claudio Bombardelli. “Optimal impulsive collision avoidance in low Earth orbit.” Journal of Guidance, Control, and Dynamics 38. 2 (2015): 217-225.
2. Juan Luis Gonzalo, Camilla Colombo, and Pierluigi Di Lizia. “Analytical framework for space debris collision avoidance maneuver design.” Journal of Guidance, Control, and Dynamics 44.3 (2021): 469-487.
3. Scott Jason Zimmer. “Reducing spacecraft state uncertainty through indirect trajectory optimization.” Ph. D. thesis, Austin: Austin: The University of Texas at Austin, 2005.
4. Dutta, Shrouti, and Arun K. Misra. “Comparison between convex and non-convex optimization methods for collision avoidance maneuvers by a spacecraft.” Acta Astronautica 202 (2023): 900-908.
5. Pavanello, Zeno, Laura Pirovano, Roberto Armellin, Andrea De Vittori, and Pierluigi Di Lizia. “A Convex Optimization Method for Multiple Encounters Collision Avoidance Maneuvers.” In AIAA Scitech 2024 Forum, p. 0845. 2024.
Date of Conference: September 16-19, 2025
Track: Conjunction/RPO