Lunar Lander Landing Dynamic Model and App Development in Simscape

With the recent renewed interest in manned Lunar exploration, it is critical to revisit the Apollo Moon landings with new analysis tools. Modeling the Moon landings of the past can help guide the development of new landing vehicles for the present and the future. One of the critical subsystems to model is the vehicle’s landing gear. During a landing event, structural loading, energy absorption, and toppling stability are important factors that drive the design of landing gear subsystems. These aspects can be studied using models and simulations in addition to physical testing. This study explores one recent modeling tool for modeling the landing gear and uses the Apollo 11 Moon landing as a use case.

A generic model was built using MATLAB®, Simulink®, and Simscape® Multibody to model the dynamics of a landing event. The landing gear structure comprising the primary strut, secondary struts, footpads, and joints were modeled in Simscape® Multibody. Various energy absorption mechanisms in the struts were modeled based on the relative motions of the inner and outer cylinders of the leg. Touchdown contact forces, when the footpads strike the lunar surface, were modeled considering the soil mechanical properties. Slosh dynamics were modeled using a mechanical pendulum module and tip-over controllers were developed using Simulink®. However, neither were applied in the presented analysis relating to the Apollo lunar module.

After developing the generic landing dynamic model, the Apollo 11 landing was simulated for validation purposes with results closely matching the historical measured data. A MATLAB® Graphical User Interface application (app) also was developed based on this model for usability and better accessibility of the landing simulation by non-experts on landing dynamics. It offered the opportunity for landing stability study with and without control, i.e., the max slope a lander can land without tipping over in 3D realistic landing situations.