An Adaptive Prescribed Performance Tracking Motion Control Methodology for Robotic Manipulators with Global Finite-Time Stability

Abstract

In this paper, the problem of an APPTMC for manipulators is investigated. During the robot’s operation, the error states should be kept within an outlined range to ensure a steady-state and dynamic attitude. Firstly, we propose the modified PPFs. Afterward, a series of transformed errors is used to convert “constrained” systems into equivalent “unconstrained” ones, to facilitate control design. The modified PPFs ensure position tracking errors are managed in a pre-designed performance domain. Especially, the SSE boundaries will be symmetrical to zero, so when the transformed error is zero, the tracking error will be as well. Secondly, a modified NISMS based on the transformed errors allows for determining the highest acceptable range of the tracking errors in the steady-state, finite-time convergence index, and singularity elimination. Thirdly, a fixed-time USOSMO is proposed to directly estimate the lumped uncertainty. Fourthly, an ASTwCL is applied to deal with observer output errors and chattering. Finally, an observer-based-control solution is synthesized from the above techniques to achieve PCP in the sense of finite-time Lyapunov stability. In addition, the precision, robustness, as well as harmful chattering reduction of the proposed APPTMC are improved significantly. The Lyapunov theory is used to analyze the stability of closed-loop systems. Throughout simulations, the proposed PPTMC has been shown to perform well and be effective.

Fixed-Time RBFNN-Based Prescribed Performance Control for Robot Manipulators: Achieving Global Convergence and Control Performance Improvement

“…Other aspects generated from the proposed FNN-PPCM, such as tracking accuracy, chattering resolution, robustness to uncertainty components, and observer approximation, are also considered thoroughly through comparison with other equivalent forms, such as SMC, TSMC, and FTSMC. The 3-DOF robotic manipulator used in the simulations is based on the dynamic mathematics and kinematic design presented in previous studies [53,54], and the system parameters are selected from [43,55]. The construction of the robot is designed using both MATLAB/SIMULINK and SOLIDWORKS software, which is described in detail in [43,55].…”

“…The 3-DOF robotic manipulator used in the simulations is based on the dynamic mathematics and kinematic design presented in previous studies [53,54], and the system parameters are selected from [43,55]. The construction of the robot is designed using both MATLAB/SIMULINK and SOLIDWORKS software, which is described in detail in [43,55]. In the simulations, Euler's method is used to solve the differential equations with a sampling time of t s = 10 −3 .…”

“…PPC is a technique that is designed to ensure transient and steady-state performance in controlled systems, with limited tracking errors, convergence rate, and maximum overshoot [42][43][44][45][46]. To establish specific performance boundaries, a PPF is typically used.…”

Advanced Sensors Technologies Applied in Mobile Robot

“…An adaptive manipulator prescribed performance tracking motion control with global finite-time stability guarantees is proposed in [ 16 ]. In [ 17 ], a visual servo control approach is presented that enables an unmanned aerial vehicle to land autonomously on a fast-moving platform of another vehicle.…”