Serial-robot dynamics algorithms for moderately large numbers of joints

Abstract A method for solving the complete dynamic problem in robots with rigid links and ideal joints using the Gibbs–Appell equations as starting point is presented. The inverse dynamic problem is solved through a algorithm O(n), where tensor notation is used. The terms of the generalized inertia matrix are calculated by means of the Hessian of the Gibbs function with respect to generalized accelerations, and a recursive algorithm of order O(n2) is developed. Proposed algorithms are computationally efficient for serial-robots with moderately large numbers of joints. The numerical stability of the proposed algorithms is analyzed and compared with those of other methods by the use of numerical examples.

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