Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms

As for biological mechanisms, which provide a specific functional behavior, the kinematic synthesis is not so simply applicable without deep considerations on requirements, such as the ideal trajectory, fine force control along the trajectory, and possible minimization of the energy consumption. An important approach is the comparison of acknowledged mechanisms to mimic the function of interest in a simplified manner. It helps to consider why the motion trajectory is generated as an optimum, arising from a hidden biological principle on adaptive capability for environmental changes. This study investigated with systematic methods of forward and inverse kinematics known as multibody dynamics (MBD) before going to the kinematic synthesis to explore what the ideal end-effector coordinates are. In terms of walking mechanisms, there are well-known mechanisms, yet the efficacy is still unclear. The Chebyshev linkage with four links is the famous closed-loop system to mimic a simple locomotion, from the 19th century, and recently the Theo Jansen mechanism bearing 11 linkages was highlighted since it exhibited a smooth and less-energy locomotive behavior during walking demonstrations in the sand field driven by wind power. Coincidentally, Klann (1994) emphasized his closed-loop linkage with seven links to mimic a spider locomotion. We applied MBD to three walking linkages in order to compare factors arising from individual mechanisms. The MBD-based numerical computation demonstrated that the Chebyshev, Klann, and Theo Jansen mechanisms have a common property in acceleration control during separate swing and stance phases to exhibit the walking behavior, while they have different tendencies in the total energy consumption and energy-efficacy measured by the ‘specific resistance’. As a consequence, this study for the first time revealed that specific resistances of three linkages exhibit a proportional relationship to the walking speed, which is consistent with human walking and running, yet interestingly it is not consistent with older walking machines, like ARL monopod I, II. The results imply a similarity between biological evolution and robot design, in that the Chebyshev mechanism provides the simplest walking motion with fewer linkages and the Theo Jansen mechanism realizes a fine profile of force changes along the trajectory to reduce the energy consumption acceptable for a large body size by increasing the number of links.