Matrix Chain Multiplication and Equivalent Reduced-Order Parallel Calculation Method for a Robotic Arm

Abstract

Intelligence development has put forward increasing requirements of real-time planning and dynamic feedback in controlling robotic arms. It has become essential in engineering applications to complete the kinematics calculation of complex manipulators in real time. This paper proposes a matrix cascading multiplication equivalent reduced-order parallel computing method for the multiplication of homogeneous matrices in the process of forward and inverse kinematics solutions, which reduces the order of the matrix according to the distribution of zero vectors in the homogeneous matrix calculations. The method removes the unnecessary multiplication in joint homogeneous matrixes containing zero vectors. It obtains the optimal calculation order of the cascade matrix multiplication through dynamic planning searches, improving the efficiency of effective dot product calculation by parallel computation. Calculation processes and specific examples are presented in this paper. Compared with the previous algorithms, the proposed algorithm reduces the calculation cycle by 90%, effectively improving the real-time calculation efficiency in the complex control process.

Keywords

• matrix chain multiplication
• equivalent reduced order
• robotic arm
• forward and inverse kinematics solutions