Cylindrical orthogonal norm-based stochastic collision risk measures in spacecraft formation flying

Abstract

The cylindrical orthogonal collision region (COCR) is introduced for the approximate satisfaction of spherical, three-dimensional avoidance constraints (S3ACs) used in spacecraft formation flying (SFF). The COCR construct affords safety sufficiency and reduced constraint satisfaction conservatism over other commonly employed regions, while it may allow for improved efficiency of collision-safe trajectory computation. The COCR is deterministically well-defined; instantaneous and joint-time stochastic measures of collision risk based on the COCR are well-defined and computable; probabilistic collision risk conservatism introduced by the COCR is characterized as consistent with volumetric conservatism. These results, which are validated computationally in pertinent relative orbital cases, demonstrate the feasibility of SFF collision risk management applications which perform COCR-based S3AC satisfaction.