CORDIC-based architectures for robot direct kinematics and Jacobian computations

Two efficient CORDIC-based architectures, designed to take advantage of the algorithmic characteristics of the kinematic equation, are proposed for the real-time computation of manipulator direct kinematics and Jacobian. The kinematic equation of an N-jointed manipulator involves the chain product of N homogeneous link transformation matrices and reveals the requirement for computing a large set of elementary operations: multiplications, additions, and trigonometric functions. Since these elementary operations, in general, cannot be efficiently computed in genera-purpose uniprocessor computers, the coordinate rotation digital computer (CORDIC) algorithms are used. It is found that a general homogeneous link transformation matrix can be decomposed into a product of two matrices, each of which can be computed by two CORDIC processors arranged in parallel, forming a generic two-stage cascade CORDIC computational module