A unified kinematic representation and its applications to robotic control

A unified robotic kinematic representation including position and orientation is presented. Based on a special Lie algebra which collects all real 3×3 skew-symmetric matrices with its exponential mapping, a 3-D orientation vector is defined for a possible unification with 3-D position vectors. All computational formulas are developed and illustrated for the PUMA 560 robot. Utilizing the 3-D orientation vector, and integral-force matrix that transforms the conventional kinematic Jacobian to a mathematical Jacobian matrix is derived. The unified method, which has applications to robotic control systems, was simulated by computer for the PUMA 560 robot with all six joints for tracking both the positional and orientational paths, and the simulation results are given