Decoupled parallel algorithm for robot inertia matrix computation

The common characteristic of existing parallel algorithms for evaluation of the robot inertia matrix on multiprocessor architectures is strict synchronization of processors, which limit the degree of the inherent parallelism. Such algorithms can, in the best case, deliver a time complexity of O(N), even with O(N ²) processors. Consideration is given to an approximate method in which all processors are decoupled, i.e., the processor synchronization, which handles the proper values of the propagated variables, is completely abandoned. Such a scheme drops the time complexity to O(N) for O(N) processors, and to O(1) for O(N²) processors. Experimentation on the KUMARAN2 multiprocessor system based on MC68030/68882 processors, has shown surprisingly small approximation errors, which on average are below 1%. An analytical study of the approximation error is presented