Study on effects of spinal joint for running quadruped robots

Most legged animals use their flexible body and supporting muscles to produce power for their locomotion, resulting in superior mobility and fast motions. In reality, an animal body consists of multiple bones and joints as well as legs having two or three segments with mass and inertia. In this paper, we study the bounding locomotion of a quadruped robot with a model closer to a real animal, i.e., a model that has one spinal joint, multiple two-segmented prismatic legs with masses and series elastic actuators, to obtain an insight into the robot’s dynamic behaviors. The models with passive mechanical properties are optimized with open-loop control to achieve the periodic bounding gait. The effects of spine flexibility in a segmented body are investigated on quadrupedal bounding gait by changing dynamic properties and hardware parameters. Comparisons of models reveal that body flexibility affects energy consumption and increases leg recirculation and stride length. The cost of transport of the articulated spine models is smaller than that of the rigid body one at low speed (<0.45gl0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$< 0.45\sqrt{gl_0}$$\end{document}) and bigger at high speed (>0.45gl0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$>0.45\sqrt{gl_0}$$\end{document}). The stride length increases 25%. Furthermore, the study on location of spinal joint reveals that the asymmetric segmented body possesses bigger spine oscillation; up to 370% higher actuator force/torque in the rear leg but 36.1% smaller in the front leg; shorter stride period; and smaller cost of transport which helps the robot to run more efficiently. The study also shows that the asymmetric mass distribution of the body caused the torque/force increase at the rear leg, especially at hip joint, and the decrease at the front leg.