Efficient Recursive Algorithm for Inverse Dynamics

An efficient recursive computational scheme for the robot manipulator inverse dynamics is outlined. The algorithm is a new computational approach and is based on the application of the Gibbs-function. The solution of the inverse dynamic problem is formulated as a problem in quadratic programming, and the recursive equations for the computation of the driving torques are derived from the necessary conditions of minimum usage of the Lagrange method of undetermined multipliers. The algorithm involves the recursive computations of links' angular velocities, angular accelerations and linear accelerations expressed in moving coordinate systems. Further simplification can be performed by writing the vector equations as equations of coordinates. The reduced computational scheme is presented by a Pascal program detail. The computational complexity of the algorithm is analyzed.