Real time robot control presents a major numerical challenge. The inverse kinematics problem of determining joint motion for a specified end effector trajectory is formulated as a damped least-squares problem which balances accuracy against feasibility. This approach leads to the Singularity Robust Inverse which yields feasible joint motions even at or in the neighborhood of undesirable singular configurations. We present a new technique that optimally approximates the desired end-effector trajectory with physically realizable joint velocities at all manipulator configurations. This technique uses the Levenberg-Marquardt algorithm to compute an optimal damping factor. the Singular Value Decomposition (SVD) of the manipulator Jacobian plays a key role in this algorithm which is computationally intensive and currently limited to off-line planning. This new algorithm will be run on a parallel VLSI architecture under development at Rice. This system includes a custom CORDIC VLSI array for computing the SVD of a matrix. The array is connected to a linear array of Texas Instruments TMS320C30 DSP processors. The DSP array computes many of the matrix operations in parallel and uses the CORDIC SVD array as a co-processor.