A spatial distribution measure and collision analysis technique for distributed space systems

Abstract A distributed space system (DSS) is an architecture with more than one spacecraft to achieve a common objective. A number of questions arise with respect to the characteristics and dynamics of distributed system in space. How fast is the system spreading? How are the elements within the system distributed? Is it tightly or loosely packed? What is the effect of perturbations on its absolute and relative dynamics? What are the chances of a collision within the system? There has not been much research in these areas concerning a DSS. In this paper, quantitative metrics are established that allow characterizing DSS and assisting in answering above questions. Key performance indicators for a DSS are identified as size or envelope of the cluster, a distribution measure, and a measure for collision. Determining the geometric system size is straightforward through numerical or analytical propagation methods. The focus of this paper will be on the other two metrics: a cluster distribution index (CDI) and a measure for collision probability within the system. The distribution index can be used to assess the effectiveness of DSS in meeting system requirements such as coverage and resolution. An n-dimensional grid-based numerical approach is used to evaluate CDI. The collisions analysis using line-integral method (CALM) is proposed as an effective and efficient approach to analyzing collision probability within DSS. Results show that the CDI is an effective indicator to assess the influence of perturbations, such as differential drag, on spatial distribution of the system. The CALM approach is three orders of magnitude faster than existing approaches that evaluate collision probability for non-linear motion.