Direct kinematics analysis of crawl gait for a quadruped robot

The natural constraint conditions of a quadruped robot, called TITAN-VIII, are discussed. The position and velocity relationships between the independent actuation joints and the redundant ones of the robot are also derived from the constraints. Furthermore, the direct kinematic solution of the position and velocity of the body is presented in terms of the independent actuation variables. It is shown that the robot can omnidirectionally crawl on a rough ground as long as its body is parallel to the support surface of its feet on the ground. It is also found out that the kinematic solution needs to solve a sixteenth-order polynomial equation with an unknown variable. A numerical example is presented and the results are verified by an inverse kinematics analysis and an experiment.