Discrete-time Closed-Loop Inverse Kinematics: A Comparison Between Euler and RK4 Methods.
2021 29TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION (MED)(2021)
摘要
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.
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关键词
Sufficient conditions,Estimation,Kinematics,Differential equations,Stability analysis,Complexity theory,Trajectory
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