A Burn-Coast-Burn Pointing Algorithm (BCBPA) for high-precision orbit insertion missions of solid rockets

This paper discusses a solid rocket guidance algorithm applied to orbit insertion missions. Providing continuous and smooth guidance commands to satisfy both terminal five orbit elements and propellant exhaustion constraints is the main difficulty to be solved. Dispersions in initial states and rocket engine parameters are also necessary to be addressed when high-precision is required. To simultaneously address the above issues, this paper proposes a Burn-Coast-Burn Pointing Algorithm (BCBPA) by introducing a Burn-Coast-Burn (BCB) mode in the well-established Pointing Algorithm (PA). By adding a coasting time as a new control parameter, the guidance problem is then converted to an energy management issue for a two-stage solid rocket. Subsequently, an N-BCBPA is proposed to address energy management issues for multi-stage solid rockets, thus providing converged guidance commands when the presented BCBPA fails. Based on a recursive algorithm, the N-BCBPA transforms the guidance problem of N-stage solid rockets into N-1 sub-problems under the BCB mode and solves them in order, thereby improving the robustness of the BCBPA against dispersions. Numerical simulations verify that the BCBPA is capable of guiding a two-stage solid rocket to the target orbit while satisfying propellant exhaustion constraints, and the N-BCBPA shows better robustness against dispersions than the BCBPA.