Improved numerical solutions of inverse kinematics of robots

Abstract

Numerical solution of the inverse kinematics of robots using modified Newton-Raphson (MNR) and modified predictor-corrector (MPC) algorithms is discussed. These modified algorithms are highly reliable and stable. Both algorithms always find a solution if a physically realizable robot configuration exists. They are also capable of approaching singular configurations of the robot as E = C ε <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> , where E is the error between the theoretical and numerically computed singular joint values, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsiv</sup> is the convergence criteria, and C and m are appropriate constants. It is also shown that the modified predictor-corector (MPC) algorithm is 5-15 times faster than the modified Newton-Raphson (MNR) algorithm.