A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander

Many sophisticated mathematical approaches have been developed to calculate and optimized trajectory solutions for lunar landing systems, including but not limited to Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and convex optimization techniques among others. Many of these approaches require expensive computational resources in order to achieve convergence to a solution, which may be problematic due to the well known limitations in computational power and memory capacity of space hardened computers when compared to modern computers. In an effort to reduce complexity and the computational load required to generate the real-time guidance commands that are necessary during manual piloting, a simple physics-based work-energy approach is formulated. This approach is based on the dissipation of mechanical energy of the vehicle in reference to the final energy state required to achieve a safe landing. The rocket engine(s) used during landing and other maneuvers dissipate mechanical energy both by doing work against the velocity vector of the vehicle and by jettisoning mass. Therefore, by analytically solving the energy dissipation problem during every step of the maneuver, a much simpler algebraic solution that naturally and quickly attains convergence is obtained. This concept is not limited to approach and landing, but it may also be applied to de-orbiting, braking-burn, and divert maneuvers. The principle also applies for other type of maneuvers such as ascent and orbital insertion, where instead of energy dissipation, the engine injects the necessary energy into the system to attain the desired final state.