Parallel algorithms and architecture for computation of manipulator forward dynamics

Abstract

Abstract-In this paper parallel computation of manipulator forward dynamics is investigated. Considering three classes of algorithms for the solution of the problem, that is, the O(n), the O(n2), and the O(n 3) algorithms,

Fast parallel Preconditioned Conjugate Gradient algorithms for robot manipulator dynamics simulation

“…(2) The (9(n 2) Conjugate Gradient (CG) algorithms [7,8] which iteratively solve equation (1) without explicit computation and inversion of the mass matrix. (3) The (9(n 3) algorithms [7] which solve equation (1) by explicit computation and inversion of the mass matrix, leading to an (9(n 3) computational complexity.…”

“…In fact, the comparative study in [4] has shown that the C(n 3) Composite Rigid-Body algorithm is the most efficient for n less than 12. It should be pointed out that the efficiency of both the (9(n 3) and the Cg(n 2) algorithms has been recently improved [8,9]. However, despite these improvements, even the fastest serial algorithm is far from providing the efficiency required for real-time or faster-than-real-time simulation.…”

“…Although we have developed a serial CG algorithm [8] with a greater efficiency than that of [7] (and this efficiency is further improved here), it is unlikely that any serial CG algorithms can become competitive with the best serial (9(n) or (9(n 3) algorithms. But in addition to its suitability for parallel computation, there is another fact (not considered in [7,10]) that has motivated us to further investigate the CG method.…”

“…But in addition to its suitability for parallel computation, there is another fact (not considered in [7,10]) that has motivated us to further investigate the CG method. In [7,8], the Classical CG (CCG) method without preconditioning was considered, which is rarely used in practice. In fact, the development of preconditioning strategies to accelerate the convergence of iteration has made the Preconditioned CG (PCG) method a widely used fast iterative method for SPD linear systems solution.…”

“…It should be emphasized that in this comparison, n iterations is assumed for the convergence of the different CG algorithms. The greater efficiency of the CCG algorithm of [8] over that of [7] is mainly due to a better choice of coordinate frame for projection of the equations. In [7] both the computation of the bias vector and the function 52(0, (~) are performed in a link frame while in [8] they are performed (9(n 3) in [7] (~)n3 + (~)n2 (~)n3 + 8n2 2016 1546 (~2)n -49 (~2)n -64 CCG in [7] 76n 2 + 120n -21 56n + 87n -6 4543 3347 CCG in [8] 47n in a fixed frame which reduces the coefficients of the n2-dependent terms.…”