Fast symbolic computation of the inverse kinematics of robots

Abstract

It is known that the solution of the inverse kinematics problem for robot arms is mathematically very elaborate. A technique is proposed for automatically generating the closed-form inverse kinematics solution for most industrial robots very efficiently. This is achieved by a careful structural analysis of equations resulting from systems like A/sub i-1//sup -1/ A/sub i-2//sup -1/. . . A/sub 1//sup -1R/T/sub H/=A/sub i/A/sub i+1/. . . A/sub n/ with (i=1, . . ., n), where A/sub i/ and /sup R/T/sub H/ denote the homogeneous transformation matrices between the adjacent robot links and the homogeneous robot hand-base transformation, respectively. Features derived from these equations are described, and it is shown how they can be used advantageously to solve the inverse kinematics problem symbolically. The system is implemented in Prolog and needs a few seconds on a PC for a complete inversion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>