In this paper, two types of trajectory control schemes are designed for the trajectory control of robotic manipulators, where the Lyapunov function method is used as a mathematical design tool.  The objective of this study is to compare the performances of PD (Proportional-Derivative) based controls to those of the usual sliding surface controls in the trajectory control of robotic manipulators.

First, a few trajectory control schemes, consisting of feed-forward compensation and PD feedback compensation, are designed for the trajectory control of a robotic manipulator. A usual parabolic Lyapunov function candidate results in a trajectory control scheme having a feedforward control and a standard PD feedback control. A V-shape Lyapunov function having a rounded tip leads to a trajectory control scheme having a feedforward control and a saturated PD feedback control, in which a new type of sigmoid function for signal saturation is derived from the Lyapunov function. The new PD-based control schemes are shown to guarantee global asymptotic stability with all internal signals bounded.     

Second, a new sliding mode trajectory control scheme is designed for the trajectory control of a robotic manipulator. In this control design, a saturated sliding surface signal, via a new sigmoid function, is low pass filtered, and then this low pass filtered saturated signal, instead of the usual sliding surface signal, is used in the feedback control of the trajectory. The signal saturation due to the sigmoid function may be actively used to limit the magnitude of the actuator inputs, especially in the beginning of the control. The new saturated sliding surface control scheme is shown to guarantee global asymptotic stability with all internal signals bounded.     

Finally, via realistic simulation studies, the control performances of the new control schemes will be analyzed in depth and will be also compared to that of a sliding mode trajectory control law designed by Slotine and Li. In the simulation of the control schemes, one sampling delay will be included in the feedback control loops as in practical real time control applications. The trapezoidal rule (via the bilinear Z transform) is used in the digitization of the analog signals for the low pass filtering of the saturated signals. For high simulation accuracy, the dynamics of the robots are solved by using the fourth-order Runge-Kutta formula with an adaptive step size. In the comparison of control schemes, the actuator inputs, as well as the asymptotic stability of tracking errors, will be considered.

 


Trajectory Control of Robotic Manipulators: A Comparison Study

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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