Discrete-time closed-loop inverse kinematics: A comparison between Euler and RK4 methods

This paper investigates the effects of the numerical method employed to solve the system of differential equations that characterise a closed-loop inverse kinematics (CLIK) algorithm in the discrete-time domain. The paper presents a detailed comparison between a 4th order method, namely the Runge-Kutta 4 (RK4) and the explicit Euler 1-st order method, that is the one most often used in applications. In spite of a lower complexity of the mathematical model, simulations on a 7-Degree-Of-Freedom (DOF) show that using explicit Euler produces better performance in some conditions, such as when considering a constant Cartesian reference. On the other hand, significantly lower tracking error is observed for time-varying Cartesian reference when using RK4. This method also generates smoother joint trajectories when moving through a kinematic singularity. Finally, the results suggest that the stability of the closed-loop algorithm is retained for larger gain values when using RK4.