Stable bipedal ramp climbing with torso

This paper presents an analytical technique to study the stability of a bipedal robot with torso in dynamic ramp climbing. Climbing is an indispensable part of locomotion on stochastically rough terrain. Kinematics of stance and swing legs have been derived from first principles. The Zero Moment Point (ZMP) criterion has been analyzed with an extension to controlling torso angle to maintain stability for different ramp angles, step sizes, stepping speeds, mass, length, and angle of torso. We found the sensitivity, upper and lower bounds of the effect of the above parameters on the stable behavior of the ZMP curve during the single support phase of bipedal walking. We also present a broad insight into the range of control strategies available for metastable bipedal walker. Moreover, analytical tools derived from first principles helped us to prove the optimality of some of the characteristic behaviors of bipedal ramp climbing.