Constrained optimal collision avoidance manoeuvre allocation under uncertainty for subsequent conjunction events

With the increase of the traffic in orbit, there is the need to reconsider the optimisation of Collision Avoidance Manoeuvres (CAM) to account for the occurrence of multiple subsequent conjunction events. This paper proposes a method to compute the optimal CAM for a multiple encounter scenario accounting for operational constraints. The proposed method builds on previous works from the authors where a single CAM was optimised to achieve the required reduction in the Probability of Collision (PoC) under epistemic uncertainty in miss distance and covariance matrices, at the time of closest approach. The uncertainty in the probability of collision derived from the epistemic uncertainty in miss distance and covariance was quantified with Dempster-Shafer theory of evidence (DSt). Within the framework of DSt we defined families of uncertain ellipsoids, with associated probability assignments, that represent all possible relative positions of two objects. CAMs are then optimised to minimise the Probability of Collision for the uncertain ellipse that would yield the highest PoC. This paper extends this technique by computing the optimal strategy when more than one event with the same object is possible within a given time window. We consider both single and multi-CAM strategies. In both cases, there is a trade-off between the risk of the subsequent encounters, the complexity of the strategy (one or more manoeuvres), the cost and the inherent risk of the manoeuvre. Thus, the computation of an optimal CAM under several encounters requires the solution of a min-max optimisation problem. In addition, actual missions may present constraints on the execution of the CAM. First, we show how to derive the families of ellipsoids with their associated probability assignment. We then formulate the above-mentioned min-max optimisation to incorporate operational constraints on the multi-encounter scenario. In particular, we consider constraints on execution time or on the magnitude and direction of the manoeuvre. Finally, we incorporate the new multi-CAM optimisation in the framework of CASSANDRA (Computer Agent for Space Situational Awareness aNd Debris Remediation Actions) to automatically allocate CAM and provide operational support to operators by using Multi-Criteria Decision-Making (MCDM) methods. Some representative examples illustrate the applicability of our approach.