Flexible Joint Manipulator Research Articles

Enhanced precision in robot arm positioning: A nonlinear damping approach for flexible joint manipulators

AbstractThis article introduces an advanced nonlinear controller designed for optimizing the performance of a single‐link robot arm featuring a flexible joint. The proposed nonlinear control strategy incorporates a Proportional‐Integral (PI) controller in conjunction with a nonlinear velocity feedback component, aimed at providing effective nonlinear damping and suppressing vibrations. To validate the controller's performance, extensive simulations are conducted utilizing machine learning techniques within the Python environment. The performance of the proposed nonlinear damping controller is benchmarked against a conventional linear cascaded P‐PI control structure, with both controllers fine‐tuned using the Nelder‐Mead algorithm. Simulation results demonstrate that the nonlinear damping controller yields substantial improvements in the dynamic behavior of the robot axis arm, showcasing superior step and sinusoidal position tracking performance, along with active vibration damping capabilities. This research contributes valuable insights into the enhanced nonlinear control strategies for flexible‐joint robot arms, offering promising advancements in their overall dynamic performance.

Vibration Suppression and Trajectory Tracking Control of Flexible Joint Manipulator Based on PSO Algorithm and Fixed-Time Control

Vibration Suppression and Trajectory Tracking Control of Flexible Joint Manipulator Based on PSO Algorithm and Fixed-Time Control

An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators.

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.

Observer-based Fixed-time Output Feedback Control for Flexible-joint Manipulators via Improved Command-filtered Backstepping

Observer-based Fixed-time Output Feedback Control for Flexible-joint Manipulators via Improved Command-filtered Backstepping

Observer-Based Neural Control of N-Link Flexible-Joint Robots.

This article concentrates on the adaptive neural control approach of n -link flexible-joint electrically driven robots. The presented control method only needs to know the position and armature current information of the flexible-joint manipulator. An adaptive observer is designed to estimate the velocities of links and motors, and radial basis function neural networks are applied to approximate the unknown nonlinearities. Based on the backstepping technique and the Lyapunov stability theory, the observer-based neural control issue is addressed by relying on uplink-event-triggered states only. It is demonstrated that all signals are semi-globally ultimately uniformly bounded and the tracking errors can converge to a small neighborhood of zero. Finally, simulation results are shown to validate the designed event-triggered control strategy.

Fixed-time adaptive fuzzy control with prescribed tracking performances for flexible-joint manipulators

In this paper, we study the tracking control problem of flexible-joint manipulators with uncertain unstructured dynamics, and develop a prescribed fixed-time solution scheme by combining direct adaptive fuzzy control design with a class of smooth functions. With our scheme, only one adaptive law needs to be calculated online, and also there are no complicated terms, e.g., the partial derivatives of some multivariable functions, involved in virtual controllers and the actual control input, which show that the raised scheme is computationally attractive. Moreover, the boundedness of all closed-loop signals, and the fixed-time convergence of tracking error to a prescribed interval can be established through a rigorous proof, and the obtained results are further confirmed by simulation tests.

Energy shaping-based consensus control in networked underactuated Euler–Lagrange systems with communication and input delays

This paper aims to solve the problems of energy shaping-based consensus control in networked underactuated Euler–Lagrange systems (NUELSs) in the presence of communication and input delays. By appropriately introducing the auxiliary sliding mode variable describing local communication interaction among agents and the corresponding adaptive velocity observer in energy-shaping framework, two decentralized time-varying consensus tracking schemes are proposed for NUELSs. The developed schemes systematically integrate the energy of three parts: the system model energy of actuated and underactuated components, the energy of the controller dynamics and the energy of the adaptive update law, as the total energy. Then this total energy formulates the resultant Lyapunov function that can fully guarantee the distributed time-varying consensus tracking of NUELSs having time-varying communication and input delays. Furthermore, simulation examples of multiple flexible-joint manipulator systems characterized by NUELSs demonstrate the potential advantages of the proposed consensus schemes in stability, adaptability, and robustness. The effects of communication and input delays on cooperative tracking performance are also numerically investigated for NUELSs.

Robust adaptive dynamic surface control of high-order strict feedback systems based on fully actuated system approach

In this study, the authors propose a robust adaptive dynamic surface control method by using the fully actuated system approach for high-order strict-feedback systems (SFSs) with parameter uncertainty and disturbance. Each subsystem of the SFSs is a high-order system with a full actuation structure. In contrast to the traditional first-order state space method, the proposed control method directly treats each high-order subsystem as a whole without transforming it into a first-order system, which is a concise and efficient treatment. By introducing a series of first-order low-pass filters in each step of the design, the high-order derivatives of the virtual control law are obtained, and the complex and multiple derivation operations are transformed into simple algebraic operations. Adaptive control and robust control are combined to address parameter uncertainty and external disturbances in the system. The Lyapunov stability theory is utilised to demonstrate that all signals in the closed-loop system are uniformly ultimately bounded. The system output can effectively track the desired reference signal under specific constraints, and the tracking error can be adjusted by tweaking the parameters to converge to a sufficiently small neighbourhood around zero. Ultimately, the efficiency of the proposed control method is validated through simulations on a flexible joint manipulator system.

Double-loop frame-based adaptive neural sliding-mode control of single-input 3-DOF flexible-joint manipulator

Flexible-joint manipulators (FJMs) have been attracting much attention in recent decades. However, position control and vibration suppression of single-input (SI) multi-degrees-of-freedom (multi( ⩾ 3 )-DOF) FJM is still a high mountain to climb due to the characteristic that some states of such FJMs cannot be directly controlled by the SI. This paper aims to carry out this challenging research. We present a double-loop frame-based adaptive neural sliding-mode control method for an uncertain horizontal SI 3-DOF FJM, i.e. a two-link FJM with only one actuator at the first joint. Since only the actuator angle can be directly controlled, in the inner loop, we design a torque controller so that the actuator angle tracks a time-varying reference actuator angle, designed in real-time by the outer loop. In the outer loop, we consider the reference actuator angle as a virtual control signal and design it based on the dynamic coupling relationships, aiming to indirectly control the first link to its target position and suppress the vibration of both links. Furthermore, to enhance the transient system performance, we plan the input signal of the outer loop (i.e. the target angle) as a smooth reference-trajectory signal. The validity and superiority of this method are demonstrated in simulations.

Whole Body Control of an Autonomous Mobile Manipulator Using Series Elastic Actuators

The flexible joint robot has superior attractive features because of its high mobility, high load ratiohigh torque fidelity, robustness for external disturbance, task adaptability, and safety. In this paper, an autonomous mobile manipulator driven by the designed series elastic actuators (SEAs) is developed. A complete dynamic model of nonholonomic mobile manipulator including a mobile platform and manipulator with joint flexibility operating simultaneously is proposed. An integrated whole body trajectory control framework is proposed for such robot to perform mobile manipulation tasks. Considering the nonholonomic and holonomic constraints in the mobile manipulation, the whole-body dynamics is formulated and reduced. To address the highly nonlinear of the dynamics and model uncertainty, a novel integral Lyapunov function (ILF)-based adaptive neural network control for task tracking under uncertainties of the flexible joint robot model is proposed. Compared with existing methods, the proposed method provides an alternative for controlling flexible joint robots. The feasibility of the proposed method is verified by the extensive trajectory tracking experiment results in our developed flexible joint manipulator.

Adaptive Fuzzy Finite-Time Singular Perturbation Control for Flexible Joint Manipulators With State Constraints

Adaptive Fuzzy Finite-Time Singular Perturbation Control for Flexible Joint Manipulators With State Constraints

Dynamic Event-Triggered Adaptive Fuzzy Leader–Follower Consensus Control of State-Constrained Flexible-Joint Manipulators

Dynamic Event-Triggered Adaptive Fuzzy Leader–Follower Consensus Control of State-Constrained Flexible-Joint Manipulators

Adaptive fuzzy extended state observer for a class of nonlinear systems with output constraint

Abstract In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.

A suboptimal control scheme based on integrated real-time nonlinear estimation-identification approach for developed flexible joint manipulators structure

As the safety of human-robot interaction is of great interest in various applications, the flexibility of machine joints becomes increasingly important. In this paper, a general model is developed for electrically driven flexible-joint robots (ED-FJR), in which the coupled phenomena of stiffness-damping and friction in the joints are modeled as nonlinear and time-varying parameters. Because the output torque of the actuator mounted on the link cannot be measured, its state variables are estimated by the suboptimal estimator. Furthermore, the unknown parameters of joint flexibility are identified by the identification algorithm based on time-varying nonlinear least-squares error (TV-NLS), which are then used in the proposed control algorithm to compensate for negative effects and errors. The state-dependent Riccati equation (SDRE) method is developed in this paper using the combined estimator-identifier approach. The novel proposed method for a 3-degree-of-freedom (3-DOF) mechanical arm with electrically driven flexible joints is implemented and validated. The obtained results show that the system's performance has improved by 83% in terms of modeling accuracy. Furthermore, when compared to other methods, the proposed algorithm reduces tracking error by 59%, making it easier to reach the target point.

Event-triggered adaptive prescribed performance control of flexible-joint manipulators with output constraint

PurposeThis paper aims to design an event-triggered adaptive prescribed performance controller for flexible manipulators, with the primary objectives of achieving output performance constraints and addressing communication resource limitations.Design/methodology/approachThe authors propose a novel prescribed performance barrier Lyapunov function (PP-BLF) that considers both output and tracking performance constraints. The PP-BLF ensures that the system's output, transient behavior and steady-state performance, adhere to prescribed constraints. The boundary of the PP-BLF is established by an exponential function that decays over time. Notably, the PP-BLF can be applied seamlessly in unconstrained cases without necessitating controller redesign. Moreover, the controller design incorporates an event-triggered mechanism, effectively reducing the frequency of controller updates and optimizing the utilization of communication resources. Additionally, the authors employ adaptive techniques to estimate the system's unknown parameters and approximate unknown nonlinear functions using radial basis function neural networks (RBFNN). To address the challenge of “complexity explosion”, dynamic surface technology is employed.FindingsNumerical simulations are conducted under five different cases to verify the effectiveness of the proposed controller. The results demonstrate that the controller successfully constrains the output tracking error within the prescribed performance boundary. Moreover, compared with the traditional time-triggered mechanism, the event-triggered mechanism significantly reduces the controller's update frequency, resolving the problem of limited communication resources.Originality/valueThe paper reduces the update frequency of control signals and improves resource utilization through an event-triggered mechanism in the form of relative thresholds. The authors recognize that the event-triggered mechanism may impact the output performance of the system. To address this challenge, the authors propose a prescribed performance Barrier Lyapunov Function (PP-BLF). The PP-BLF is designed to effectively constrain the output performance of the system, ensuring satisfactory control even when the control signal updates are reduced.

Enhancing robustness and noise rejection in flexible joint manipulators: an optimized sliding mode controller with enhanced gray wolf optimization for trajectory tracking

The objective of this study is to enhance the performance of a nonlinear three-rigid-link manipulator (RLM) with a focus on trajectory tracking, robustness against disturbances and noises, and adaptability to joint flexibility. To achieve this, we have employed an optimized sliding mode controller with a proportional integral derivative (PID) sliding manifold. The tuning process involves selecting the critical gains of the controller that minimizes the integral time absolute error (ITAE), serving as the objective function (OBJF) to optimize the performance of the robot manipulator. To identify the optimal gains of the controller, we have utilized a new optimization algorithm known as memory enhanced linear population size reduction gray wolf optimization (MELGWO). The efficacy of this algorithm is compared to other existing optimization methods in the literature. Moreover, this research has delved into the impact of joint flexibility on the robot system’s performance. Encouragingly, the results demonstrate that the optimized SMC–PID with MELGWO adaptation can effectively address joint flexibility while maintaining acceptable performance levels.

Distributed robust‐multivariate‐observer‐based FDI attacks estimation for nonlinear multi‐agent systems with directed graphs

AbstractThis article investigates the distributed robust estimation problem for false data injection (FDI) attacks in nonlinear multi‐agent systems with directed graphs. To approximate the realistic attack scenario, the case where both the actuator network channel and sensor network channel suffering from FDIs are considered, and the attack signals contain time‐varying circumstances. A novel distributed robust‐multivariate‐observer (DRMO) strategy is developed such that the online estimation of FDI attack dynamics can be realized with the partially unknown nonlinear dynamics, attack transient increments, and disturbances impact being eliminated. The designed DRMO scheme only depends on the received compromised/uncompromised measurement output information on the account that whole state information cannot be measured directly. Finally, two simulation examples, including a network of four one‐link flexible joint manipulator systems with comparisons to existing methods, are given to show the effectiveness of the proposed scheme.

Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

This paper presents a practical study on how to improve the ℋ∞ performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon ℋ∞ controller is designed to improve the system ℋ∞ performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of ℋ∞ control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments.

Control Law Synthesis for Flexible Joint Manipulator Based on Synergetic Control Theory

In this paper, the authors present the synthesis of control laws for the flexible joint manipulator to stabilize the oscillation and track the desired trajectory. To solve this problem, the article applies synergetic control theory. In synergetic control theory the desired values are impressed as invariants. So the invariants act as the control objectives of the system and our task is to find the control laws for them. Using this theory, the control law is designed to ensure the movement of the closed-loop system from an arbitrary initial state into the vicinity of the desired invariant manifold, i.e. the objective attracting manifold. Thereby, not only reach the necessary invariant but also ensure the asymptotic stability of the entire system. The quality of the proposed control law is shown through simulation results on Matlab and its efficiency is shown by comparison with backsteping control law.

Visual Servoing of Rigid-Link Flexible-Joint Manipulators in the Presence of Unknown Camera Parameters and Boundary Output

Exact position control of the flexible-joint manipulator (FJM) is a challenging task due to the manipulator’s nonlinearity and underactuated characteristic. For the three-dimensional (3-D) rigid-link FJM, the image-based visual servoing (IBVS) approach with link-position output constraint and unknown camera parameters is investigated in this article. The controller is designed to deal with three problems. First, the visual servoing control law is divided into two domains based on the singular perturbation method, where the control input for the fast subsystem is developed to damp out the flexible joint’s vibration. Second, the adaptive updating law for estimating the unknown camera parameters is presented in the slow subsystem. Third, to guarantee that the rigid-link position keep in set constraints, the controller for the slow subsystem is designed by introducing a barrier Lyapunov function. According to the Lyapunov theorem of stability, the proposed controller for the FJM is theoretically proved to be asymptotically stable. Several numerical simulation experiments are provided to illustrate that the presented control scheme is effective.