Dynamic model for industrial robots based on a compact Lagrangian formulation

A compact Lagrangian formulation has been developed and discussed to deal with the highly coupled non-linear dynamic equations of robotic manipulators. It bridges the dynamic and kinematic problems of robotics closely together by means of Jacobian and subjacobian matrices. Its numeric computational complexity has been reduced to O(n2) time. When n<6, the number of operations required for computing all joint torques is almost close to that of Newton-Euler approach. Due to its significant insight of the robot behavior, it is concluded that the compact Lagrangian formulation offers a convenient approach to building up a feasible real-time adaptive control strategy for computer-based manipulators. Finally, it has been found that all information required for solving the dynamic equation and the adaptive control problems is concentrated in Hessian matrix of the kinetic energy for a given robotic manipulator.