AP-D: A Thickness Optimization Method of Back Protection Material for Humanoid Robot

Protective hardware is essential for mitigating damage caused by unavoidable falls in humanoid robots. Despite notable progress in fall protection hardware, the theoretical foundation for modeling and the feasibility of conducting full-scale fall experiments on robots or their surrogates remain somewhat limited. This paper proposes a method for optimizing the thickness of Expandable Polyethylene (EPE), which is used as back protection for the Chubao humanoid robot, based on small-scale impact test data to predict full-scale behavior. The optimal thickness is defined as a balance between compact design and protective effectiveness. An equivalent impact model characterized by four parameters: contact area S, mass m, fall height h, and cushioning material thickness d is introduced to describe impact conditions. The relationship between the peak impact acceleration and material thickness d, which forms the core of the method and gives rise to the name AP-D, is analyzed through their plotted curves. After introducing three characteristic parameters and two correction factors, the relationship among the aforementioned variables is derived. Subsequently, both the optimal thickness and its corresponding peak impact acceleration are predicted via nonlinear and linear regression models. Finally, the accuracy and effectiveness of the theoretically derived optimal thickness are validated on both a dummy and the actual robot. With the cushioning material applied, the peak chest acceleration is reduced to 41.57g for the dummy and 32.08g for the robot.