Delta-V analysis for impulsive orbital pursuit-evasion based on reachable domain coverage

Abstract

This paper proposes a delta-V analysis method for the impulsive orbital interception of a non-cooperative maneuvering target from the perspective of reachable domain coverage. In the case of small impulse magnitude and short propagation time, the envelope of the impulsive reachable domain is approximately described by an ellipsoidal equation based on the linearized state transition matrix. Then, the minimum pursuit impulse magnitude under the reachable-domain coverage constraint is obtained by solving a two-dimensional nonlinear equation for given pursuit impulse time and given interception time. Two fuel optimization problems under the reachable-domain coverage constraint are constructed based on whether to optimize the first impulse of the chaser. For the first optimization problem, the optimization variables include the pursuit impulse time, the interception time, and the pursuit impulse magnitude; for the second optimization problem, two additional optimization variables are considered including the time and the aiming point of the first impulse. Numerical examples show that the proposed optimal delta-V approach for the chaser can cover the target's maneuvering reachable domain.