Dynamic Coupling Map: Acceleration Space Analysis for Underactuated Robots

Humans and animals are capable of overcoming complex terrain challenges with graceful and agile movements. One of the key ingredients for such complex behaviors is motion coordination to exploit passive dynamics. We present a direct collocation trajectory optimization to find optimal control policy and generate optimal trajectory for the swing up motion of a gymnast on high bar. Notwithstanding, the limitation of insight of trajectory optimization approach, we introduce the Dynamical Coupling Map (DCM), a novel graphical technique, to help gain insight into the output trajectory of the optimization and analyze the acceleration capability of underactuated robots.