EFFICIENT PARALLEL ALGORITHMS FOR ROBOT FORWARD DYNAMICS COMPUTATION

Two efficient parallel algorithms for computing the forward dynamics for real-time simulation were developed for implementation on a single-instruction multiple-data-stream (SIMD) computer with n processors, where n is the number of degrees of freedom of the manipulator. The first parallel algorithm, based on the composite rigid-body method, generates the inertia matrix using the parallel Newton-Euler algorithm, the parallel linear recurrence algorithm, and the modified row-sweep algorithm, and then inverts the inertia matrix to obtain the joint acceleration vector at time t. The time complexity of this parallel algorithm is of the order O(n**2) with O(n) processors. Further reduction of the order of time complexity can be achieved by implementing the Cholesky's factorization procedure on very-large-scale-integrated (VLSI) array processors to invert the symmetric, positive-definite, inertia matrix. The second parallel algorithm, based on the conjugate gradient method, computes the joint acceleration with a time complexity of O(n) for multiplication operation and O(n log//2n) for addition operation. The interprocessor communication problem for the implementation of the proposed parallel algorithms on SIMD machines is also discussed and analyzed.