A Comparative Study of Feasible Trajectories for an Under-Actuated Two-Link Bipedal Walking Robot With Hybrid Zero Dynamics Based Motion Planning

Control of under-actuated bipedal walking robots has been an active area of research for many decades. Hybrid zero dynamics based motion planning is a technique very commonly used to plan trajectories for these robots. Exploring the solution space of optimal trajectories obtained through this method can potentially increase our understanding of bipedal walking by observing possible speeds, energy consumption etc. Very few studies are available with detailed solution space explorations of walking trajectories obtained through this method. This paper attempts to fill this gap by performing a hybrid zero dynamics based solution space exploration for an under-actuated two-link biped with a point mass at the hip as a proxy for the torso. The parameters of the biped chosen are similar to that of an average human. In addition, a comparison of the solutions obtained for different objective functions is carried out. Lastly, a non-dimensional analysis is done to identify if there are any dominant terms in the dynamics of the walking trajectories.