Design and Stability Analysis of a Robust-Adaptive Sliding Mode Control Applied on a Robot Arm with Flexible Links

Modelling errors and robust stabilization/tracking problems under parameter and model uncertainties complicate the control of the flexible underactuated systems. Chattering-free sliding-mode-based input-output control law realizes robustness against the structured and unstructured uncertainties in the system dynamics and avoids the excitation of unmodeled dynamics. The main purpose of this paper was to propose a robust adaptive solution for stabilizing and tracking direct-drive (DD) flexible robot arms under parameter and model uncertainties, as well as external disturbances. A lightweight robot arm subject to external and internal dynamic effects was taken into consideration. The challenges were compensating actuator dynamics with the inverter switching effects and torque ripples, stabilizing the zero dynamics under parameter/model uncertainties and disturbances while precisely tracking the predefined reference position. The precise control of this kind of system demands an accurate system model and knowledge of all sources that excite unmodeled dynamics. For this purpose, equations of motion for a flexible robot arm were derived and formulated for the large motion via Lagrange’s method. The goals were determined to achieve high-speed, precise position control, and satisfied accuracy by compensating the unwanted torque ripple and friction that degrades performance through an adaptive robust control approach. The actuator dynamics and their effect on the torque output were investigated due to the transmitted torque to the load side. The high-performance goals, precision and robustness issues, and stability concerns were satisfied by using robust-adaptive input-output linearization-based control law combining chattering-free sliding mode control (SMC) while avoiding the excitation of unmodeled dynamics. The following highlights are covered: A 2-DOF flexible robot arm considering actuator dynamics was modelled; the theoretical implication of the chattering-free sliding mode-adaptive linearizing algorithm, which ensures robust stabilization and precise tracking control, was designed based on the full system model including actuator dynamics with computer simulations. Stability analysis of the zero dynamics originated from the Lyapunov theorem was performed. The conceptual design necessity of nonlinear observers for the estimation of immeasurable variables and parameters required for the control algorithms was emphasized.

Compound robust tracking control of disturbed quadrotor unmanned aerial vehicles: A data-driven cascade control approach

In this paper, the robust trajectory tracking control problem of disturbed quadrotor unmanned aerial vehicles (UAVs) with disturbances, uncertainties and unmodeled dynamics is addressed, by devising a novel compound robust tracking control (CRTC) approach via data-driven cascade control technique. By deploying the data-driven philosophy, a data-based sliding-mode surface is proposed, and thereby contributing to strong adaptability to nonlinearity and model-unknown properties of the UAVs. By utilizing the backstepping technique, virtual control strategy and a novel cascaded compound robust PD control structure, the attitude and position subsystems are efficiently cohered such that a data-driven cascaded compound robust controller containing both PD control and sliding-mode control can be developed to conquer the lumped disturbances induced by uncertainties, disturbances and unmodeled dynamics. Eventually, the asymptotic convergence of the tracking errors with respect to both attitude and position subsystems can be guaranteed rigorously. Simulation studies on a prototype quadrotor UAV are performed to evaluate the efficacy and superiority of the devised CRTC method.

FAT-based robust adaptive control of cooperative multiple manipulators without velocity measurement

This article addresses the problem of pose and force control in a cooperative system comprised of multiple n-degree-of-freedom (n-DOF) electrically driven robotic arms that move a payload. The proposed controller should be capable of maintaining the position and orientation of the payload in the desired path. In addition, the force exerted by robot end effectors on the object must remain limited. The system has unmodeled dynamics, and measuring the robot joint velocities is impossible. Therefore, a FAT-based observer–controller is designed to estimate the uncertainty and velocities based on universal approximation property of Fourier series expansion. The stability of the system is confirmed based on Lyapunov’s stability theorem. Finally, the proposed adaptive controller–observer is applied on two 3-DOF cooperative robotic arms carrying a payload, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation method.

Practical Design Considerations for Performance and Robustness in the Face of Uncertain Flexible Dynamics in Space Manipulators

Low frequency dynamics introduced by structural flexibility can result in considerable performance degradation and even instability in on-orbit, robotic manipulators. Although there is a wealth of literature that addresses this problem, the author has found that many advanced solutions are often precluded by practical considerations. On the other hand, classical, robust control methods are tractable for these systems if the design problem is properly constrained. This paper investigates a pragmatic engineering approach that evaluates the system’s stability margins in the face of uncertain, flexible perturbation dynamics with frequencies that lie close to or within the bandwidth of the nominal closed-loop system. The robustness of classical control strategies is studied in the context of both collocated (joint rate) and non-collocated (force/torque and vision-based) feedback. It is shown that robust stability and performance depend on the open-loop control bandwidth of the nominal control law (as designed for a simplified, rigid plant). Namely, the designed bandwidth must be constrained to be lower than the minimum flexible mode frequency of the unmodeled dynamics by a given factor. This strategy gives credence to popular heuristic methods commonly used to reduce the effect of unmodeled dynamics in complex manipulator systems.