Convex Maneuver Planning Enables Globally Optimal Low-Thrust Spacecraft Collision Avoidance

Spacecraft collision avoidance currently relies on painstaking manual calculations and simulations, a process becoming increasingly unsustainable as the number of satellites in orbit rapidly increases. Fausto Vega, Jon Arrizabalaga, Ryan Watson, and Zachary Manchester from Carnegie Mellon University and Albedo Space now present a new approach to designing fuel-efficient maneuvers that automatically minimise the risk of collision. The team develops a method that transforms a complex, difficult problem into a more manageable one, allowing computers to quickly calculate optimal trajectories. This innovation guarantees a solution that uses the least amount of fuel while meeting strict safety standards, and crucially, offers a viable alternative even when absolute safety cannot be assured, instead prioritising the minimisation of overall risk. The researchers validate their method using realistic simulations of close satellite encounters, demonstrating its potential to significantly improve the safety and efficiency of space operations.

Optimal Collision Avoidance for Spacecraft Maneuvers

Scientists have developed a new methodology for spacecraft collision avoidance, addressing the critical need for autonomous maneuver planning in increasingly congested low-Earth orbit. The study pioneers an algorithm designed to generate low-thrust collision-avoidance maneuvers applicable to short-term conjunction events, a capability previously unmet by existing techniques. Researchers formulated the problem as a complex mathematical optimization, and then employed a technique called convex relaxation to simplify it into a solvable form. This approach guarantees finding the best possible collision avoidance maneuver, unlike methods that might get stuck in suboptimal solutions.

The core innovation lies in transforming a difficult problem into a more manageable one, allowing for efficient computation of globally optimal solutions. The method minimizes fuel or energy expenditure during the maneuver, which is important for mission efficiency, and can incorporate various constraints, such as limits on thrust or maneuver duration. The team uses linearized orbital dynamics and Gaussian uncertainty models to accurately represent spacecraft behavior. Researchers demonstrated the effectiveness of the approach through high-fidelity simulations of satellite conjunctions, confirming that the solutions obtained closely approximate the globally optimal solutions. This work has the potential to improve the safety and sustainability of space operations, enabling autonomous spacecraft operations, more effective space traffic management, and optimized constellation management.

Globally Optimal Low-Thrust Maneuver Planning for Spacecraft

Scientists developed a novel method for spacecraft collision avoidance, addressing the increasing challenges posed by satellite density in low-Earth orbit. The research team formulated the problem as a complex mathematical optimization, and then employed a technique called convex relaxation to simplify it into a solvable form. This approach guarantees finding the best possible collision avoidance maneuver, unlike methods that might get stuck in suboptimal solutions. The core achievement lies in minimizing energy expenditure while simultaneously ensuring a desired probability of collision at the point of closest approach.

The innovative approach centers on defining a mathematical representation of the problem that allows for efficient computation of globally optimal solutions. By reformulating the original problem in this manner, scientists bypassed the computational challenges associated with solving the complex optimization directly. The team implemented a minimum-energy trajectory-optimization framework, generating low-thrust maneuvers specifically designed to achieve a target probability of collision at the time of closest approach. These simulations demonstrated the accuracy of the simplified solution, confirming that the solutions obtained closely approximate the globally optimal solutions to the original complex problem. This work represents a significant advancement in autonomous spacecraft safety, offering a robust and efficient solution for mitigating risks in the increasingly crowded space environment. The method is applicable to short-term conjunction events, and can accommodate general low-thrust maneuvers.

Optimal Spacecraft Maneuvers for Collision Avoidance

Scientists have developed a new method for spacecraft collision avoidance, addressing the increasing challenges posed by satellite density in low-Earth orbit. The research team formulated the problem as a complex mathematical optimization, and then employed a technique called convex relaxation to simplify it into a solvable form. This approach guarantees finding the best possible collision avoidance maneuver, unlike methods that might get stuck in suboptimal solutions. The core achievement lies in minimizing energy expenditure while simultaneously ensuring a desired probability of collision at the point of closest approach.

The developed formulation calculates maneuvers that minimize energy expenditure while maintaining a desired level of collision probability, or alternatively, minimizes risk when a specific probability threshold cannot be met. Validation involved a high-fidelity simulation of a conjunction event in low-Earth orbit, and confirmed the effectiveness of the approach in reducing collision risk. Researchers measured the probability of collision as a critical metric for safe operations, and the method directly addresses minimizing this value. The team’s formulation accounts for uncertainties in spacecraft positioning, and the simulation demonstrated the ability to achieve a globally optimal solution. This signifies a breakthrough in autonomous spacecraft maneuvering and collision avoidance capabilities. The method adopts simplifying assumptions to improve computational efficiency, and the team verified the accuracy of the solution through mathematical analysis.

Optimal Spacecraft Maneuvers via Convex Relaxation

This research presents a new method for automatically designing collision-avoidance maneuvers for spacecraft, addressing a critical need as the number of satellites in orbit increases. The research team formulated the problem as a complex mathematical optimization, and then employed a technique called convex relaxation to simplify it into a solvable form. This approach guarantees finding the best possible collision avoidance maneuver, unlike methods that might get stuck in suboptimal solutions. The core achievement lies in minimizing energy expenditure while maintaining a desired level of collision probability.

The developed formulation calculates maneuvers that minimize energy expenditure while maintaining a desired level of collision probability, or alternatively, minimizes risk when a specific probability threshold cannot be met. Validation using a high-fidelity simulation of a satellite conjunction in low-Earth orbit confirms the effectiveness of the approach in reducing collision risk. Researchers verified the accuracy of the solution through mathematical analysis, and confirmed that the simplified solution closely approximates the globally optimal solution. This work represents a significant advance in autonomous spacecraft maneuvering and collision avoidance capabilities. Future work may focus on extending this method to handle more complex scenarios and incorporating additional constraints relevant to real-world space operations.