Parallelism in Manipulator Dynamics

This paper addresses the problem of efficiently computing the motor torques required to drive a manipulator arm in free motion, given the desired trajectory—that is the inverse dynamics problem. It analyzes the high degree of parallelism inherent in the computations and presents two "mathemati cally exact "formulations especially suited to high-speed, highly parallel implementations using VLSI devices. The first method presented is a parallel version of the recent linear Newton-Euler recursive algorithm. The time cost is linear in the number of joints, but the real-time coefficients are re duced by almost two orders of magnitude. The second formu lation reports a new parallel algorithm that shows that it is possible to improve on the linear time dependency. The real time required to perform the calculations increases only as the log 2 of the number of joints. Either formulation is sus ceptible to a systolic pipelined architecture in which complete sets of joint torques emerge at successive intervals of four floating-point operations. Hardware requirements necessary to support the algorithm are not excessive, and a VLSI im plementation architecture is possible.