Dynamic similarity and scaling for the design of dynamical legged robots

Robots are often used to perform similar tasks on vastly different scales. When utilizing traditional design approaches, this typically requires a full redesign and optimization at each specified size, a costly and time intensive process. In this work, we propose an alternative approach based on the principle of dynamic similarity. With this method, an initial design may be conceived at any size and scaled to any other without needing to re-optimize either physical or control variables. In the following study, we derive a generalized scaling method for this application that not only preserves system performance, but also affords flexibility in the scaling process. The preservation of dynamic similarity is validated in simulation. We further explore the application for robot-to-robot scaling, flexibility afforded by an additional free parameter, and the implications of scaling on both power requirements and structural loading. With these insights, we provide an improved methodology for the efficient and cost-effective development of scaled robotic systems.