Computer-Oriented Algorithm for Modeling Active Spatial Mechanisms for Robotics Applications

Based on a comparison of the computational complexity of different spatial mechanisms dynamics formulations it is shown that the most appropriate one is the Newton-Euler formulation using recurrence relations for velocities, accelerations, and generalized forces. This is based on numerical efficiency and intermediate results. A general algorithm which solves both the direct and inverse problem of dynamics for an open-chained spatial mechanism of an arbitrary mechanical configuration is developed and realized. It is pointed out that for control algorithms which assume knowledge of system dynamics in real time, it is necessary to compute the inertial matrix and the term taking into account the rest of the dynamical effects separately. The "accelerated" computational algorithm for real-time implementation with this property has been developed and realized. Up to now reported real-time computational schemes do not have this feature directly implementable. Depending on the control law, manipulator configuration, type of functional tasks, and given ranges of operational speed it can appear that it is sufficient to compute only the dominant dynamical influences and not the complete dynamics. The criterion for the optimal choice of the level of the approximation of the dynamical model is formulated based on nominal regimes for specific functional tasks. For this purpose the algorithm for generation of the mathematical model of variable complexity is developed and realized. The procedure is implemented on two typical manipulator mechanical configurations of six degrees of freedom (d.o.f.) and a comparison of exact and various approximate models is performed.