Screw Theory Application: Computationally-Efficient Obstructed Constellation Access Calculation

The dimensionality of large multi-agent systems presents a challenge to simulation computational resources by multiplying the computation for each dynamic object. This paper supports performance simulation of large multi-agent systems by presenting a computationally efficient method of calculating the obstruction of the line-of-sight (LOS) between two dynamic objects due to terrain. Results are presented for an implementation calculating the time-dependent LOS from a satellite in orbit to a general user location due to the finite geometry of a central attractor such as Earth. The novelty in the approach is the utilization of screw theory to determine the point of closest approach along the LOS vector to the central attractor. The benefits of the approach are a low-operation count and the avoidance of trigonometric functions. Results from implementation in MATLAB show that the method aligns with a computationally-expensive reference trigonometric approach and that the reduced operation count translates into savings in execution time. For N > 1000, the method is an order of magnitude faster than the reference trigonometric approach. This material is intended to assist in modeling and simulation where time-dependent signal accessibility is a key metric.