Safety Critical Control Using Fully Nonlinear Equations of Relative Motion for Formation Flying in Cislunar Space

With the rapid growth of missions in cislunar space, spacecraft must operate safely and autonomously in a strongly nonlinear gravitational environment where traditional linearized relative-motion models are insufficient. This paper develops a safety critical control framework that directly uses the fully nonlinear relative dynamics for both the Circular Restricted Three-Body Problem (CR3BP) and a high fidelity ephemeris model. A minimally intrusive Control Barrier Function (CBF)-based quadratic program (QP) enforces a Euclidean distance safety constraint between spacecraft, with the high relative degree of positional constraints addressed through CBF backstepping. After validating the safety filter under CR3BP dynamics, we extend it to the ephemeris model by incorporating SPICE-derived Earth–Moon states, a time varying rotating frame, and realistic angular rate and acceleration computations. For formation flying, we design a Lyapunov-based nominal controller that achieves a constant-radius orbit around the chief by steering the out-of-plane component to zero, driving the relative motion into a user-defined invariant circle set, and maintain a constant orbit. Simulations for Earth and Moon orbiting chief–deputy configurations show that the safety filter maintains the deputy on the boundary of the safe region before guiding it to the desired orbit, even under strong nonlinear coupling and near-constraint conditions. These results demonstrate that safety critical nonlinear control can be rigorously integrated with high fidelity cislunar dynamics to enable autonomous and reliable multi-spacecraft operations.