An optimized real time algorithm for the inverse kinematics of general 6R robots

The existing real time algorithms for inverse kinematics of general 6R robots have the problems of complex procedures and ineffective roots, so they can not be applied in the online control systems where real time performance are strictly required. In this paper, we propose an optimized algorithm with strong real time performance and high accuracy. The six basic inverse kinematics equations are transformed and the target matrix is reduced from the order of 24 to 16 based on symbolic preprocessing, so the efficiency of the algorithm is improved while the ineffective roots eliminated. Eigen decomposition is utilized to extract roots from the target matrix and ensure the stability and accuracy of the algorithm. By invoking CLAPACK in the VC++ environment directly, all calculations are accomplished with the C/C++ language and OOP technique. Experiments on various general 6R robots show that, the proposed algorithm can solve the inverse kinematics problem in an average time of 1.37ms, and ensure that the position and orientation matrixes of the end effect corresponding to the solutions have an average accuracy of 12 digits after the decimal point. All these make it a novel algorithm for online control systems of general robots where real time performance and high accuracy are strictly required.