An investigation of numerical computations for inverse dynamics of robotic systems

The author investigates four prominent numerical integration methods used to integrate the inverse dynamics of a manipulator system, namely, the modified Euler, Runge-Kutta, Adams-Bashforth, and Hamming methods. The study is based on the inverse dynamics computation of a two-link open-chain manipulator. The numerical results suggest that the Adams-Bashforth method is not suitable for integrating inverse dynamics of a manipulator system for step size greater than 0.01 s. For any given step size, the modified Euler method is approximately twice as efficient as the Runge-Kutta method. However, these two methods are piecewise stable for various step sizes. It is also observed that Hamming´s method should not be used in integrating the inverse dynamics of a manipulator system because it suffers from stability problems. In addition, the simulation results show that it will be better to choose smaller step size in control of a task if high precision is required