Nonlinear feedback control of flexible joint manipulators: a single link case study

For the control of 2-link flexible joint manipulators, a control method based on the singular perturbation theory and the Udwadia-Kalaba (U-K) method was proposed. The control design was implemented by 2 steps. First, the system order was reduced based on the singular perturbation method and the system was divided into fast and slow sub-systems, to simplify the solution process and overcome the system flexibility. Second, the state feedback constraint following control law for the fast and slow sub-systems was designed with the U-K method, to make the constraint following errors of the fast and slow sub-systems converge to zero, even if the system can't initially satisfy the constraints. The proposed method can deal with holonomic and nonholonomic servo constraints at the same time without the auxiliary variables of the Lagrange multiplier and the pseudo generalized velocity. The method was applied to 2-link flexible joint manipulator systems to solve the flexible oscillation and constraint following problems. Through simulations on MATLAB, and was compared with the traditional PID control, to verify the effectiveness and superiority.

In this paper, the vibration suppression and trajectory tracking control of a flexible joint manipulator (FJM) based on particle swarm optimization (PSO) and fixed-time nonsingular terminal sliding mode control (NTSMC) are studied. Firstly, in order to suppress the residual vibration of the FJM, an optimal trajectory planning method based on higher-order trajectory planning (HOTP) and the PSO algorithm is proposed. Then, to ensure that the FJM can track the optimized trajectory without being affected by the initial value of the trajectory, a novel fixed-time NTSMC scheme is proposed. Compared with the cubic spline trajectory, the proposed HOTP is smoother and can more accurately suppress the residual vibration of the FJM. By combining the HOTP with the PSO algorithm, the vibration amplitude of FJM can be suppressed to around 0.002 mm. Unlike finite-time NTSMC, the rate of convergence of the proposed fixed-time NTSMC does not depend on the initial value of FJM’s joint trajectory. Especially when the initial value of the trajectory is large, the FJM can still quickly track the optimal trajectory within 0 to 1 s. Finally, the effectiveness of this method is verified through simulation and comparison.

In this paper, a robust fuzzy-tuned PID controller is proposed for the trajectory tracking and vibration control of a flexible joint manipulator system (FJMS) with parametric uncertainties. Flexible joint manipulators are widely used in industry due to their flexibility, light in weight and fast response, low cost, and low energy consumption. The dynamic modeling via Euler-Lagrange equation for a single link flexible joint manipulator system (FJMS) is presented first. By analyzing the characteristics of the high order linear system, the Fuzzy-Tuned PID control strategy is utilized. The parameters of classical PID controller are updated by the intelligent method of fuzzy logic. With the adaptivity to the parametric uncertainties from the system stiffness and moment of inertia, the contrived approach provides more efficient results compared to existing techniques in terms of vibration suppressions, time response, and overshoot. Finally, the effectiveness of the controller is corroborated through multiple experiments on the QUANSER's flexible joint manipulator system (FJMS).

We focus on the experimental comparison of feedback controllers for flexible joint manipulators. It completes a previous set of experimental results presented by Brogliato et al. (1998), on a 2 degree-of-freedom (DOF) manipulator with a stiff second joint (50 Nm/rad). The process considered is quite different since it consists of a 1-DOF flexible joint manipulator (i.e. a 4th order linear system) with a high flexibility (3.4 Nm/rad). The main goal of the present work is to apply a systematic way of tuning the gains of backstepping- and energy shaping-like controllers, using a method developed for LQ controllers by De Larminat. It is shown that although other linear controllers could be applied to the process tested in this paper, we restrict ourselves to those control laws that extend to the nonlinear general case of flexible joint manipulators, and yield global stability results.

The control of flexible joint manipulators is studied in detail. The model of N-axis flexible joint manipulators is derived and reformulated in the form of singular perturbations, and the integral manifold is used to separate fast dynamics from slow dynamics. A composite control algorithm is proposed for the flexible joint robots, which consists of two main parts. Fast control, u/sub f/, which guarantees that the fast dynamics remains asymptotically stable, and the corresponding integral manifold remains invariant. Slow control, u/sub s/, itself consists of a robust PID design based on the rigid model, and a corrective term designed based on the reduced flexible model. The stability of the overall closed loop system is proved to be UUB stable, by Lyapunov stability analysis. Finally, the effectiveness of the proposed control law is verified through simulations. It is shown that the proposed control law ensures robust stability and performance, despite the modeling uncertainties.

This paper proposes a finite-time adaptive backstepping control for an n-link flexible joint manipulator based on neural network approximation. In each recursive step, an adaptive virtual controller or practical controller is designed to guarantee that all the state errors can converge into a small region within a finite time. Besides, two simple neural networks are employed to approximate and compensate for the lumped uncertainties, and the finite time stability analysis is provided based on Lyapunov synthesis. Finally, simulation results show the effectiveness of the proposed method.

Flexible link manipulators are widely used in many areas such the space technology, medical, defense and automation industries. They are more realistic than their rigid counterparts in many practical conditions. Most of the investigations have been confined to manipulators with only rotational joint. Combining such systems with translational joints enables these manipulators more flexibility and more applications. In this paper, a nonlinear dynamic modeling and control of flexible link manipulator with rigid translational and rotational joints is presented. This model TR (Translational-Rotational) is developed based on single flexible link manipulator with only rotational joint. Finite element method and Lagrange approach are used to model and build equations of the motion. PID controller is designed with parameters (Kp, Ki, Kd) which are optimized by using Particle Swarm Optimization algorithm (PSO). Errors of joints variables and elastic displacements at the end-effector point are reduced to warrant initial request. The results of this study play an important role in modeling generalized planar flexible two-link robot and in selecting the suitable structure robot with the same request.

We consider the problem of output feedback tracking of flexible joint manipulators where the link angle is the output to be controlled and the motor angle is the measured output. We allow the use of any globally stabilizing full state feedback control. We show recovery of the stability and trajectory performance of the state feedback by using a high gain observer-based output feedback control. Finally, we demonstrate the effectiveness of the proposed scheme in the single link case, where the zero dynamics are not asymptotically stable.

The singular perturbation approach has been shown to be successful in controlling both flexible link manipulators and flexible joint manipulators. In this paper, the technique is extended to control both link and joint flexibility of a multilink manipulator simultaneously while a desired trajectory is being tracked. A comprehensive, closed-form, Euler-Lagrange, assumed-mode model of a multilink manipulator has been formulated in which the effects of the link and joint flexibility are incorporated. This is then converted into a two-time-scale, state-space, singular perturbation model where the slow subsystem involves the link angles and the fast subsystem consists of the joint deflection and the link deflection variables. A composite controller is designed based on the two-time-scale model of the flexible link and joint manipulator. Numerical simulation results confirm that the proposed controller satisfactorily suppresses the tip deflection and joint flexibility of the manipulator while very good trajectory tracking is achieved.

In this paper, the H∞ tracking control problem is studied for a class of single-link flexible-joint manipulators with external disturbances. Aiming at a state space model of the flexible-joint manipulator system with strict feedback form, the H∞ tracking controller of the system is designed based on backstepping method, robust H∞ control theory and Lyapunov stability theory. The obtained controller can ensure that the closed-loop manipulator system can track precisely the given reference input signal, the tracking error can convergence to origin, and the system has robustness to external disturbances. The simulation results show the effectiveness of the proposed method.

In this paper, a comparison between PI and sliding mode control is proposed for the control for flexible joint manipulator driving by Brushless DC motor (BDCM)to improve the performance in the presence of errors in the parameters identification. First, the model of flexible joint manipulator was presented. Then, a PI control is studied and designed for tracking problem of the single flexible joint manipulator. Besides, sliding mode control is studied and designed also for the same problem. Finally, those strategies of control are implemented in the Matlab-Simulink environment to show the high performances and a comparative study of the different strategies of PI and sliding mode controllers was achieved. Although the presence of flexibility in the joint, the simulation results show the high performances of sliding mode controller by converging the error to zero and guaranteeing stability of the robot.

In robot manipulators, the joint flexibility may be or not introduced intentionally. Thus, flexible joint robots (FJRs) are useful in aerospace applications and human rehabilitation, for example. Besides, FJRs appear in industrial manipulators. The feedback linearization control has been applied to many mechatronics systems, including FJRs. However, if spring damping between the links and rotors is present, the state feedback linearization design is no longer feasible. In order to overcome this situation, in this paper, an input-output feedback linearization approach is developed to achieve trajectory tracking control of FJRs. The study is complemented with simulation results, which validates the proposed theory. By assuming the presence of spring damping, a comparison between the known state feedback linearization technique and the proposed input-output feedback linearization is given, showing better results for the introduced approach.

This paper introduces a novel control strategy for managing the uncertainties in flexible joint manipulators, incorporating a Radial Basis Function Neural Network (RBFNN) with Adaptive Dynamic Surface Control (ADSC). This strategy innovatively utilizes RBFNN to precisely approximate uncertain system dynamics and integrates a nonlinear damping term to effectively counteract external disturbances, enhancing the overall control accuracy. We have also developed an adaptive law that updates neural network weights and system parameters in real-time, ensuring the system's adaptability to dynamic changes. The application of the Lyapunov method ensures that all signals within the closed-loop system remain semi-globally uniformly bounded, significantly reducing tracking errors. Moreover, we introduce the use of Long Short-Term Memory (LSTM) networks for predictive analysis of state data, which further confirms the robustness and effectiveness of our control method through extensive simulations. The distinctive integration of these technologies and their practical validation through comparative simulations underscore the innovative aspects of our approach in addressing real-world challenges in flexible manipulators.

A Passivity/Lyapunov Approach for the Control of Flexible Joint Manipulators

This paper is focused on the adaptive control design for flexible joint robots with parameter uncertainties. Based on the singular perturbation theory, the flexible joint robot is transformed into a fast subsystem and a slow subsystem. For the fast subsystem, the PD control strategy is used to suppress elastic oscillations by the feedback of the motor angular displacement error. For the slow subsystem, an adaptive control scheme is proposed to guarantee the parameter estimation error convergence. The closed-loop system is testified to be globally exponentially stable via the designed Lyapunov function. The comprehensive simulation results demonstrate great tracking precision and high robustness of the proposed control scheme.