Residue arithmetic VLSI array architecture for manipulator pseudo-inverse Jacobian computation

The use of residue arithmetic for the exact computation of the manipulator pseudoinverse Jacobian, to obviate the roundoff errors normally associated with the computations, is considered. A two-level macropipelined residue arithmetic array architecture implementing Decell´s pseudoinverse algorithm has been developed to overcome the ill-conditioned problem of the pseudoinverse computation. The Decell algorithm is suitable for VLSI array implementation to achieve the real-time computation requirement. The first-level arrays are data-driven, wavefront-like arrays and perform the matrix multiplications, matrix diagonal additions, and trace computations. A pool of the first-level arrays are configured into a second-level macro-pipeline with outputs of one array acting as inputs to another array in the pipe. The proposed architecture can calculate the pseudoinverse Jacobian with a pipelined time in the same computational complexity order as evaluating a matrix product in a wavefront array