Inverse kinematic control of robots by applying the C-B notation

In this paper, a generalized approach for solving inverse kinematics problems is presented. This method is applicable to the nonredundancy control of most industrial robots and to the redundancy control of manipulators such as the LDUA (light duty utility arm). The joint control variables embedded in the multivariable, nonlinear direct kinematic equations are separated and restructured into a system of linear Jacobian equations. The simultaneous equations are then further rewritten and solved in matrix form. A 12×n (n is the degree-of-freedom of the robot) augmented manipulator Jacobian is defined to calculate the differential changes of each joint. To accelerate and ensure the convergence of the iterative process, the ordinary Jacobian equation is modified by the “dynamic convergent factor” which regulates the convergent direction to prevent divergence. Numerical examples for the CINCINNATI 6R, Bendix AA/CNC (RRP/RRR), and Unimate Spherical (SP/RRR) robots are analyzed and simulated