Islam I. Hussein, Trusted Space, Inc.; Thomas Kubancik, Trusted Space, Inc; Erin Griggs, Trusted Space, Inc.; Holly Borowski, Trusted Space, Inc.; Mark Bolden, Trusted Space, Inc.
Keywords: Space Traffic Management, Conjunction Assessment and Avoidance, Autonomous Maneuvering, Risk-Based Decision Making
Abstract:
Each space conjunction event is unique. This uniqueness arises not just from the situational specifics pertaining to the conjunction at hand, such as the number and the maneuvering abilities of the objects in question, but also the nature of the available relevant data. The quality and completeness of the data also contribute to the uniqueness of each event. However, current practice relies on employing a single, pre-established probability of collision threshold criteria that are applied in a one-size-fits-all framework regardless of the unique realities of each individual conjunction. In place of these current practices, in this paper we propose a formal, subjective risk/benefit analysis for conjunction assessment and decision-making that can be employed both on the ground and for onboard autonomous operations. Such an analysis replaces the use of a pre-determined probability of collision threshold with a rigorous and rational set of criteria that are optimized around the unique aspects of the situation at hand. The proposed analysis also naturally provides a prescription of how best to maneuver given the uniqueness and complexity of the conjunction event at hand.
The proposed risk-based approach can accommodate highly complex decision environments, as well as the unique aspects of the available relevant data including but not limited to: uncertain but known locations of single and multiple nearby objects; uncertainty associated with the number of nearby objects; and incomplete or altogether missing data and information, as in the case of known lost single or multiple objects. The proposed risk-based approach is amenable to an analysis where we have both aleatoric and epistemic forms of uncertainty. Aleatoric uncertainty describes truly random variability present in physical processes, such as in the case where objects locations are known but probabilistically uncertain, while epistemic uncertainty reflects the analysts lack of knowledge about some aspect of the problem at hand, such as when they know that an object exists but with no specification (certain or uncertain) about its potential location (i.e., lost objects). Specifically, in this paper we draw from various mathematical frameworks, such as multi-target, multi-hypothesis tracking and finite set statistics, and outer probability measure theory, to present the various forms that a mathematically general and rigorous definition of risk will take that enable the handling of many of the above unique situational and data quality aspects of individual collision scenarios.
The paper will be organized as follows. To introduce the framework to the uninitiated, we will first appeal to an intuitive example from finance to establish the basic definition of risk. We will then use this definition of risk to introduce a naïve definition of risk applied specifically to space conjunction assessment and decision-making. This naïve notion of risk uses the conventional mathematical definition of probability of collision and can only answer the question of whether to maneuver, but not how to maneuver. A more general definition of risk, however, not only does not require the explicit computation of the probability of collision, but also provides a prescription of how to maneuver if one is deemed necessary. This more general, formal risk definition will then be introduced in the paper. We will then extend this formal definition to handle complex environments, that include scenarios such as collision assessment in the presence of multiple targets, both of known and unknown numbers. Finally, using outer probability measure theory, we extend the analysis to include the cases when relevant data is not just uncertain, but missing altogether. This is particularly relevant to situations such as when a decision is to be made whether to maneuver or not with the knowledge that there are lost objects (i.e., objects that we know exist, but for which we have no information on their location) in the vicinity of our vehicle. We will conclude the paper with a summary of the work presented in this paper and direction for further research.
This work is especially relevant in light of the introduction of large-scale constellations, and in the diversity of the quality, completeness and trust aspects of available conjunction data. The intent of this paper is not to answer questions, per se, but to expose readers to the technical aspects, operational benefits, and feasibility of using risk as an analytical framework for tackling many collision assessment and avoidance scenarios in Space Traffic Management.
Date of Conference: September 27-20, 2022
Track: Conjunction/RPO