Energy dissipation rate control and parallel equations solving method for planar spined quadruped bouncing robot

This paper continues our investigation into Energy dissipation rate control (EDRC) and Parallel equations solving method (PESM). Our previous works showed how EDRC enables us to provide stable walking or running gaits for legged robots via controlling robot’s loss of energy rate during Impact phases (IP). This is while PESM facilitates the trajectory designing process of the robot’s active joints during each Single support phase (SSP) by solving the robot’s inverse kinematic and inverse dynamic equations in parallel. Even though PESM is very powerful and suitable for both quadruped robot, and despite the under actuation problem at the ankle joint, and biped robots, despite the presence of Zero momentum point criteria (ZMP) at the ankle joint, still, this method is limited to robots just with three and five DoFs. Therefore, the main purpose hereis to show how it is possible to extend the application of PESL to a spined quadruped robot with four DoFs by employment of the Central pattern generator (CPG) controller units and finding a connection among CPG’s output, PESM and the robot’s foot placement. Besides, as EDRC is employed to realize a stable bouncing gait for the robot, a whole numerical study is performed on the robot’s impact dynamic equations to evaluate the effect of spine joint on the robot’s impact dynamics.