The role of rotation representations in computational robot kinematics

Various methods of implementing forward and inverse kinematics of six-axis industrial robots are analyzed from the viewpoint of numerical conditioning and convergence speed both close to a solution and away from it. Computational complexities are derived in terms of the number of arithmetic operations and comparisons are made by observing the actual CPU time consumption. The formulations presented make use of different sets of invariants describing the orientation of the gripper. It is shown that, in inverse kinematics, there is a tradeoff between numerical stability and computational speed