arXiv subjects

Zeno Pavanello

Publications and source records attributed to Zeno Pavanello.

5 recordsLinked to original sources

arXiv2026

Time-Optimal Collision Avoidance Via a Greedy Polynomial Backward Sweep

Spacecraft collision avoidance for low-thrust satellites often requires determining not only how to maneuver, but also how late a maneuver can begin while still ensuring safety. This paper presents a greedy time-optimal (GTO) backward-sweep method to find the latest maneuver initiation time. The method starts from the nominal time of closest approach and iteratively propagates the maneuver backward in time, selecting at each step the thrust direction that locally minimizes the chosen danger metric. Differential algebra is used to efficiently propagate state sensitivities and update the time of closest approach online. The method is tested on a large dataset of conjunctions, using both miss distance and probability of collision as safety metrics. The approach achieves accurate results and only a small loss of optimality relative to an optimal-control benchmark, while retaining runtimes suitable for on-board implementation.

math.OC↗

arXiv2025

CAMmary: A Review of Spacecraft Collision Avoidance Manoeuvre Design Methods

Ensuring safety for spacecraft operations has become a paramount concern due to the proliferation of space debris and the saturation of valuable orbital regimes. In this regard, the Collision Avoidance Manoeuvre (CAM) has emerged as a critical requirement for spacecraft operators, aiming to efficiently navigate through potentially hazardous encounters. Currently, when a conjunction is predicted, operators dedicate a considerable amount of time and resources to designing a CAM. Given the increased frequency of conjunctions, autonomous computation of fuel-efficient CAMs is crucial to reduce costs and improve the performance of future operations. To facilitate the transition to an autonomous CAM design, it is useful to provide an overview of its state-of-the-art. In this survey article, a collection of the most relevant research contributions in the field is presented. We review and categorize existing CAM techniques based on their underlying principles, such as (i) analytic, semi-analytic, or numerical solutions; (ii) impulsive or continuous thrust; (iii) deterministic or stochastic approaches, (iv) free or fixed manoeuvring time; (v) free or fixed thrust direction. Finally, to determine the validity of the algorithms potentially implementable for autonomous use, we perform a numerical comparison on a large set of conjunctions. With this analysis, the algorithms are evaluated in terms of computational efficiency, accuracy, and optimality of the computed policy. Through this comprehensive survey, we aim to provide insights into the state-of-the-art CAM methodologies, identify gaps in current research, and outline potential directions for future developments in ensuring the safety and sustainability of spacecraft operations in increasingly congested orbital environments.

math.OC↗

arXiv2024

Collision Avoidance Maneuvers Optimization in the Presence of Multiple Encounters

The optimization of fuel-optimal low-thrust collision avoidance maneuvers (CAMs) in scenarios involving multiple encounters between spacecraft is addressed. The optimization's objective is the minimization of the total fuel consumption while respecting constraints on the total probability of collision. The solution methodology combines sequential convex programming, second-order cone programming, and differential algebra to approximate the non-convex optimal control problem progressively. A Gaussian mixture model method is used to propagate the initial covariance matrix of the secondary spacecraft, allowing us to split it into multiple mixands that can be treated as different objects. This leads to an accurate propagation of the uncertainties. No theoretical guarantee is given for the convergence of the method to the global optimum of the original optimal control problem. Nonetheless, good performance is demonstrated through case studies involving multiple short- and long-term encounters, showcasing the generation of fuel-efficient CAMs while respecting operational constraints.

math.OC↗

arXiv2024

Recursive Polynomial Method for Fast Collision Avoidance Maneuver Design

A simple and reliable algorithm for collision avoidance maneuvers (CAMs), capable of computing impulsive, multi-impulsive, and low-thrust maneuvers, is proposed. The probability of collision (PoC) is approximated by a polynomial of arbitrary order as a function of the control, transforming the CAM designinto a polynomial program. The solution procedure is initiated by computing the CAM via a first-order greedy optimization approach, wherein the control action is applied in the direction of the gradient of PoC to maximize its change. Successively, the polynomial is truncated at higher orders, and the solution of the previous order is used to linearize the constraint. This enables achieving accurate solutions even for highly nonlinear safety metrics and dynamics. Since the optimization process comprises only polynomial evaluations, the method is computationally efficient, with run times typically below 1 s. Moreover, no restrictions on the considered dynamics are necessary; therefore, results are shown for Keplerian, J2, and circular restricted three-body problem dynamics.

math.OC↗

arXiv2023

Fuel-Optimal Collision Avoidance Maneuvers in Long-Term Encounters with Station-Keeping Constraints

This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute high-thrust maneuvers by increasing the maximum available acceleration. Dealing with the long-term conjunction poses additional challenges compared to the short-term problem because the encounter is not instantaneous. Thus, under the assumption of Gaussian statistics, the probability of collision is replaced by a simpler metric, the instantaneous probability of collision (IPoC) and a keep-out zone constraint is formulated as a continuous condition to be respected throughout the time frame of interest. The robustness of the solution is improved by introducing a constraint on the sensitivity of the IPoC. Furthermore, the collision avoidance problem is coupled with the classical station-keeping requirement for geostationary Earth orbit satellites and with a return to the nominal orbit condition for low Earth orbit satellites. Even though no guarantee is given for the recovery of the global optimum solution, numerical simulations in different orbital regimes show that the proposed approach can yield a local fuel-optimal solution with a run-time suitable for autonomous applications.

eess.SY↗