Bifurcation-Based Guidance Law for Powered Descent Landing
Neon Srinivasu, Amit Shivam, Nobin Paul
TL;DR
This work addresses onboard, computation-friendly powered descent guidance by introducing Bifurcation-Based PDG (BPDG), which models axis-wise velocity dynamics as a dynamical system undergoing a supercritical transcritical bifurcation with three design parameters $a_i$, $b_i$, and $c_i$. The parameters are chosen to produce a stable equilibrium at the landing target, with closed-form expressions linking them to the initial state and final target, and a termination time $T_s$ computed from explicit $t_{si}$ formulas. An explicit acceleration command $A_i=\ddot r_i$ is derived, enabling a deterministic, low-complexity guidance law suitable for onboard processors. Mars-descent simulations demonstrate precise targeting with small position errors, monotone velocity decay, and predictable fuel usage across multiple initial conditions, validating both the analytical design and its robustness. The approach offers a conceptually simple alternative to optimization or learning-based PDG, with future work focusing on fuel-optimality and constraint integration.
Abstract
This paper develops a new guidance law for powered descent landing of a rocket-powered vehicle. The proposed law derives the acceleration command for a point mass model of the vehicle by expressing velocity as a dynamical system undergoing supercritical transcritical bifurcation with three bifurcation parameters. The parameters are designed such that the stable equilibrium points of the velocity dynamics correspond to the guided targeting state, that is, the landing point. Numerical simulations are performed to demonstrate the working of the proposed guidance law.