Efficient computation of forward kinematics and Jacobian matrix of a Stewart platform-based manipulator

Abstract

The authors consider the problem of efficient computation of the forward kinematics of a six-degree-of-freedom robot manipulator built to study autonomous assembly of parts in space. The manipulator, based on the Stewart platform mechanism, consists mainly of two platforms and six linear actuators. The closed-form solution of the inverse kinematics is formulated in such a way as to optimize the computation efficiency of the iterative solution of the forward kinematics using the Newton-Raphson method. A modified Jacobian matrix which relates length velocities to Cartesian translational velocities and time rates of change of roll-pitch-yaw angles is introduced. Computer simulation is performed to evaluate the computation efficiency of the developed computation schemes.