Passive Quadrupedal Gait Synchronization for Extra Robotic Legs Using a Dynamically Coupled Double Rimless Wheel Model

The Extra Robotic Legs (XRL) system is a robotic augmentation worn by a human operator consisting of two articulated robot legs that walk with the operator and help bear a heavy backpack payload. It is desirable for the Human-XRL quadruped system to walk with the rear legs lead the front by 25% of the gait period, minimizing the energy lost from foot impacts while maximizing balance stability. Unlike quadrupedal robots, the XRL cannot command the human's limbs to coordinate quadrupedal locomotion. Using a pair of Rimless Wheel models, it is shown that the systems coupled with a spring and damper converge to the desired 25% phase difference. A Poincar\'e return map was generated using numerical simulation to examine the convergence properties to different coupler design parameters, and initial conditions. The Dynamically Coupled Double Rimless Wheel system was physically realized with a spring and dashpot chosen from the theoretical results, and initial experiments indicate that the desired synchronization properties may be achieved within several steps using this set of passive components alone.