A simple and efficient computational approach for the forward dynamics of elastic robots

A simple and efficient Lagrangian formulation is presented for the forward dynamic analysis of elastic robots. The proposed method formulates the equations of motion with respect to a floating frame that follows the rigid motion of the links. By virtue of the proposed formulation the constraint conditions are inserted in the Hamilton's principle by means of a penalty formulation rather than by the classical Lagrange's multiplier technique. As a consequence, the number of equations that define the behavior of the robot does not increase. The numerical implementation of the new method is very simple and always leads to the solution of positive definite matrices. A series of elastic robots are analyzed and the results demonstrate the capabilities of the new formulation for the forward dynamics.

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