NUMERICAL INTEGRATION EFFECTIVENESS IN INVERSE DYNAMICS COMPUTATION OF MANIPULATOR SYSTEMS

Numerical integration plays a crucial role in the inverse dynamics computation of robot manipulators, which directly affect the success of real-time implementation of manipulator system control. This article investigates four prominent numerical integration methods commonly used to integrate the inverse dynamics of a manipulator system (namely, modified Euler, Runge-Kutta, Adams-Bashforth and Hamming's methods). The study is based on the inverse dynamics computation of a two-link open-chain manipulator to which the four numerical integrating methods are applied in turn. The simulation 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 piecewisely 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 to control a task if high precision is required. Moreover, it is found that smaller step size will make an unstable numerical method become stable.