Quaternion-based non-singular nonlinear impact angle guidance for three-dimensional engagements

Abstract

This paper proposes a three-dimensional impact angle-constrained nonlinear guidance strategy against different types of targets. To avoid the occurrence of singularities, in Euler angle-based approaches, the development of this guidance strategy is solely based on quaternion dynamics. An explicit relationship between the quaternions representing impact orientation and line-of-sight orientation at the time of collision is derived. Based on the obtained relation, a guidance law is derived using a sliding mode control technique to track the desired line-of-sight orientation for target interception. The performance of the proposed guidance strategy is evaluated for constant-speed and different time-varying-speed interceptor models accounting for the effect of varying aerodynamic parameters on interceptor speed. The numerical simulations performed show satisfactory results for all engagements, validating the efficacy and robustness of the proposed guidance law.