A Spatial Redundant Robotic Manipulator’s Chaotic Self-motion

The model and kinematics equations of a floating redundant spatial robotic manipulator are established. The Jacobian matrices are analyzed, and the inverse kinematics is obtained. Chaotic motions which existed in the floating spatial redundant robotic manipulator's self-motions are proved by simulation. At last, a spatial 3R redundant robotic manipulator is taken as an example, and the links' self-motion has been studied when the end-effector tracking a plane path repeatedly in its workspace for PD controlling by analysis of direct observation, time history method, phase diagram method, and poincare mapping method. Results show that there exist chaotic motions in the self-motion of the floating spatial redundant robotic manipulator when solving the floating redundant robotic manipulator's inverse kinematics based on pseudo-inverse Jacobian matrix.