Dynamic Simulation of n-Axis Serial Robotic Manipulators Using a Natural Orthogonal Complement

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Abstract
The concept of natural orthogonal complement is used to devise an algorithm that allows the systematic derivation of the n × n generalized inertia matrix of a general n-axis manipulator. To compute the joint accelerations from the governing equations of motion, two methods are presented, one based on the Cholesky decomposition of the generalized inertia matrix, and one based on a combination of mini mum-norm and least-squares approximations of underdeter mined and overdetermined linear algebraic systems, respec tively. Based on these methods, two corresponding algorithms for the dynamic simulation of general n-axis serial robotic manipulators are presented. The comparison of the two methods with those existing in the literature shows that the methods presented here are computationally more ef ficient. A simulation example of a well-known industrial manipulator is given.

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