Single-link Flexible-joint Manipulator Research Articles

Q-learning based model-free input-output feedback linearization control method⋆

Input-output feedback linearization is a nonlinear control method that relies on a precise dynamical model. Combining Q-learning techniques, an input-output feedback linearization correction framework is presented to accomplish model-free feedback linearization of affine nonlinear systems in order to tackle the problem caused by the unknown dynamics model. This framework formulates a model reference tracking control problem that guides the input-output relationship of the nonlinear system into a linear relationship. Due to the two Lie derivative terms present in the feedback linearized controller, the controller is designed as a dual network structure. To overcome the issue of coupling in the dual-network controller, a model-free Q-learning method is presented to solve the unknown controller network weights. The proposed method is experimentally validated on a single-link flexible joint manipulator system, and the resultant linearized system exhibits dynamics similar to the desired linear system in a new tracking task, proving the effectiveness of the proposed method.

Robust fault estimation and fault‐tolerant tracking control for uncertain Takagi–Sugeno fuzzy systems: Application to single link manipulator

SummaryThis article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO‐based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process.

A Novel Robust Control Method for Motion Control of Uncertain Single-Link Flexible-Joint Manipulator

Single-link flexible-joint manipulator (FJM) is a kind of time-varying nonlinear system with underactuated characteristics. This paper takes the uncertain single-link FJM (USLFJM) as the object, and presents a novel robust control approach based on equivalent input disturbance (EID) method for motion control (i.e., position control and trajectory tracking control) of the USLFJM. Based on the uncertain dynamic model and desired target of this system, an error system is constructed. The error system is considered as a linear system with a nonlinear virtual disturbance. The motion control objective of the USLFJM can be realized by globally asymptotically stabilizing this linear system and compensating the influence of the nonlinear virtual disturbance. Then, an EID-based control system is designed to realize this control objective. Only position measurements are utilized in this paper, and the stability of the control system is proved. The simulation results are presented to illustrate the validity and the robustness of the proposed control method.

Cluster Consensus for Nonlinear Multi-Agent Systems

A cluster consensus algorithm for nonlinear multi-agent systems under directed graph topology is proposed in this paper. Cluster consensus is the convergence of states/outputs of agents in the same cluster to consistent values which are different from those of other clusters. Cluster consensus has been obtained based on Lyapunov stability and matrix theory in terms of some sufficient conditions. A feedback control law is provided using Linear Matrix Inequality (LMI) to achieve cluster consensus for multi-agent systems. Moreover, cluster consensus for nonlinear multi-agent systems in the presence of time delay has been studied in this paper. Finally, simulation results are presented for different number of clusters to validate theoretical analysis. Examples are provided for first-order and second-order and also general high-order systems. Furthermore, first-order system with time delay is simulated for a single-link flexible joint manipulator.

Model-free active input–output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach

Traditional input–output feedback linearization requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system’s uncertainties. In this paper, a model-free active input–output feedback linearization technique based on an improved active disturbance rejection control paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with a known relative degree. The linearization control law is composed of a scaled generalized disturbance estimated by an improved nonlinear extended state observer with saturation-like behavior and the nominal control signal produced by an improved nonlinear state error feedback. The proposed active input–output feedback linearization cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, which is the only information required about the nonlinear system. Stability analysis has been conducted based on the Lyapunov functions and revealed the convergence of the improved nonlinear extended state observer and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed active input–output feedback linearization technique on the single-link flexible joint manipulator. The simulations results validated the effectiveness of the proposed active input–output feedback linearization tool based on improved active disturbance rejection control as compared to the conventional active disturbance rejection control–based active input–output feedback linearization and the traditional input–output feedback linearization techniques.

Robust cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller

In this paper robust cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics with dynamic uncertainty and external disturbances via adaptive sliding mode controller. First, robust cluster consensus for general fractional-order nonlinear multi agent systems is investigated with dynamic uncertainty and external disturbances in which multi agent systems are weakly heterogeneous because they have identical nominal dynamics with different norm-bounded parameter uncertainties. Then, robust cluster consensus for the fractional-order nonlinear multi agent systems with general form dynamics is investigated by using adaptive sliding mode controller. Robust cluster consensus for general fractional-order nonlinear multi agent systems is achieved asymptotically without disturbance. It is shown that the errors between agents can converge to a small region in the presence of disturbances based on the linear matrix inequality (LMI) and Mittag-Leffler stability theory. Finally, simulation examples are presented for general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.

Disturbance observer‐based L 1 robust tracking control for single‐link flexible‐joint manipulator systems

In this study, a novel disturbance observer-based (DOB) L 1 robust anti-disturbance tracking control problem is discussed for a kind of single-link flexible-joint manipulator with separate types of disturbances. On the one hand, a disturbance observer is imported to estimate the modelable disturbances. On the other hand, the introduction of L 1 performance index optimises the impact of unmodelled disturbances on the system. A DOB proportional-integral control input is proposed such that the stability of single-link flexible-joint manipulator can be ensured. Furthermore, the satisfactory disturbance rejection and attenuation performance with L 1 index can be obtained simultaneously. Finally, the simulation results verify this feasibility and effectiveness of the proposed control method.

Sliding Mode Fault Tolerant Tracking Control for a Single-Link Flexible Joint Manipulator System

In this paper, the fault-tolerant tracking control problem for a class of single-link flexible joint manipulator (SFJM) system with uncertainty, fault, nonlinear function, and unmatched disturbance is investigated. An observer-based sliding mode control approach is designed. Concretely, first of all, the SFJM dynamic system with uncertainty, fault, and unmatched disturbance is established. Then, by transforming the system into two subsystems, a novel composite observer is proposed to estimate the fault and disturbance, respectively. Furthermore, a robust sliding mode controller, which contains a third-order sliding mode surface, a continuous control strategy, and a visual estimated fault signal, is constructed. In the control scheme, an adaptive law is also concluded to compensate for the estimation error. Finally, the proposed method is applied to the SFJM system and the simulation results illustrate the effectiveness of the proposed method.

Adaptive consensus for high-order unknown nonlinear multi-agent systems with unknown control directions and switching topologies

In this paper, we provide a comprehensive assessment of the consensus of high-order nonlinear multi-agent systems with input saturation and time-varying disturbance under switching topologies. The control directions and model parameters of agents are supposed to be unknown. Our approach is based on transforming the problem of consensus for a network that consists of high-order nonlinear agents to that of perturbed first-order multi-agent systems. The unknown part of dynamics is cancelled using radial basis neural networks. Nussbaum gains and auxiliary systems are respectively employed to overcome the unknown input direction and the saturation. Adaptive sliding mode control is used to compensate for the time-varying disturbance and the imperfect approximation of the developed neural network as well. Through Lyapunov analysis, it is shown that the overall closed-loop system maintains asymptotic stability. Finally, our approach is applied to a group of multiple single-link flexible joint manipulators to highlight better its merit.

Neuro-adaptive observer based control of flexible joint robot

Abstract Due to high nonlinearity, strong coupling and time-varying characteristics of flexible joint robot manipulators, their control design is generally a challenging problem. There are inevitable uncertainties associated with their kinematics and dynamics, so that accurate models would not be available for control design. Furthermore, practically we may face the problem that state variables required by the controller are not measurable. In this paper, we focus on the study of control system design using a neural network observer to solve the aforementioned unmeasurable problem. First, we propose an observer based on Radial Basis Function (RBF) neural network to estimate state variables of the normal system. We then design the controller based on dynamic surface control method for a single link flexible joint manipulator whose model is unknown. The unknown model of the manipulator is constructed by RBF neural network. The stability of the observer and controller is shown by Lyapunov method. Finally, simulation studies are performed to test and verify the effectiveness of the proposed controller.

Neural Learning Control of Flexible Joint Manipulator with Predefined Tracking Performance and Application to Baxter Robot

This paper focuses on neural learning from adaptive neural control (ANC) for a class of flexible joint manipulator under the output tracking constraint. To facilitate the design, a new transformed function is introduced to convert the constrained tracking error into unconstrained error variable. Then, a novel adaptive neural dynamic surface control scheme is proposed by combining the neural universal approximation. The proposed control scheme not only decreases the dimension of neural inputs but also reduces the number of neural approximators. Moreover, it can be verified that all the closed-loop signals are uniformly ultimately bounded and the constrained tracking error converges to a small neighborhood around zero in a finite time. Particularly, the reduction of the number of neural input variables simplifies the verification of persistent excitation (PE) condition for neural networks (NNs). Subsequently, the proposed ANC scheme is verified recursively to be capable of acquiring and storing knowledge of unknown system dynamics in constant neural weights. By reusing the stored knowledge, a neural learning controller is developed for better control performance. Simulation results on a single-link flexible joint manipulator and experiment results on Baxter robot are given to illustrate the effectiveness of the proposed scheme.

Consensus Problem Over High-Order Multiagent Systems With Uncertain Nonlinearities Under Deterministic and Stochastic Topologies.

The leaderless consensus problem over a class of high-order nonlinear multiagent systems (MASs) is studied. A robust protocol is proposed which guarantees achieving consensus in the network in the presences of uncertainties in agents models. Achieving consensus in the case of stochastic links failure is studied as well. Based on the concept super-martingales, it is shown that if the probability of the network connectivity is not zero, under some conditions, achieving almost sure consensus in the network can be guaranteed. Despite existing consensus protocols for high-order stochastic networks, the proposed consensus protocol in this paper is robust to uncertain nonlinearities in the agents models, and it can be designed independent of knowledge on the set of feasible topologies (topologies with nonzero probabilities). Numerical examples for a team of single-link flexible joint manipulators with fourth-order models verify the accuracy of the proposed strategy for consensus control of high-order MASs with uncertain nonlinearities.

Simple energy-based controller for a class of underactuated mechanical systems

This paper proposes a simple energy-based controller for a class of underactuated mechanical systems. The mechanical systems considered in this study are modeled with two degrees of freedom, driven by only one actuator, and easily excited to oscillate. The proposed controller is designed by exploiting the passivity of the system. The energy storage function is constructed such that the control input is passive, with a combined output of actuated and unactuated variables. The target position of the closed-loop system is proven to be asymptotically stable using Lyapunov techniques and LaSalle’s invariance theorem. The proposed control law has a simple structure and is independent of system parameters. Numerical simulations and experiments demonstrate the superior performance of the proposed control method over a number of traditional controllers as well as its robustness against parameter uncertainties. These advantages point to the promising practical application of the proposed control method in control-underactuated systems, such as overhead cranes, single-link flexible-joint manipulators, and flexible Cartesian manipulators.

Saturated proportional derivative control of flexible-joint manipulators

In this paper, the control of flexible-joint robotic manipulators while avoiding actuator saturation is investigated. Several proportional derivative controllers are developed, all of which disallow actuator saturation by guaranteeing that the applied torque is less than a specified maximum value. In particular, a Gibbs parameterization of the joint angles is included in the control laws, which allows for an increased control torque as compared to an Euler angle parameterization. An equilibrium point of the closed-loop system is proven to be asymptotically stable using the Lyapunov stability analysis. Moreover, the proposed control laws do not require any knowledge of the [email protected]?s mass, stiffness, or dissipation properties, and as such, are robust to modelling errors. The proposed controllers are tested on a single-link flexible-joint manipulator experimentally and on a two-link flexible-joint manipulator in simulation, and are compared to the performance of controllers found in the literature.

Trajectory planning for overhead crane by trolley acceleration shaping

This paper proposes a novel off-line trolley trajectory planning method for underactuated overhead cranes. The proposed technique is feasible and efficient for overhead crane operation. Dynamic coupling between trolley motion and payload swing was successfully exploited using a staircase form of trolley acceleration. The payload swings in the constant velocity phase were efficiently suppressed and the trolley reached the desired position using this technique. The reasonable number of stairs can be determined by evaluating the residual oscillation amplitude according to the number of stairs and variation in the natural frequency of the pendulum. The proposed approach was first simulated from the kinematics viewpoint to verify the validity of the trolley trajectory and the swing angle of the payload. The proposed approach was then combined with the dynamics of the overall crane, wherein the robust sliding mode controller was applied to ensure that the trolley tracks the designed trajectory. The numerical simulation results demonstrated superior performance and robustness against parameter uncertainties of the proposed method. The proposed method exhibited potential for application in the control of underactuated systems, such as overhead cranes, single-link flexible-joint manipulators, and flexible Cartesian manipulators.

Intelligent proportional-integral (iPI) control of a single link flexible joint manipulator

This paper presents the design, stability analysis and experimental validation of a computationally non-intensive, model-free, intelligent proportional-integral (iPI) controller for flexible joint manipulators. In order to show the performance of the iPI controller, it is compared with classical proportional-integral and proportional-integral-derivative controllers. Based on this comparison, the iPI-controlled system achieved a better than 60% tracking accuracy for both kane trajectory and sine input tracking. The iPI controller also significantly reduced transient swings in the flexible joint of the manipulator, when tracking a train of pulses. Moreover, the iPI controlled system successfully eliminated both disturbances and noise effects from the dynamics of the manipulator.

Robust Self-Organizing Neural-Fuzzy Control With Uncertainty Observer for MIMO Nonlinear Systems

This paper proposes a robust self-organizing neural-fuzzy-control (RSONFC) scheme for a class of uncertain nonlinear multiple-input-multiple-output (MIMO) systems. We first develop a self-organizing neural-fuzzy network (SONFN) with concurrent structure and parameter learning. The fuzzy rules of SONFN are generated or pruned systematically. The proposed RSONFC scheme comprises an SONFN identifier, an uncertainty observer, and a supervisory controller. The SONFN identifier functions as the principal controller, and the uncertainty observer is designed to oversee uncertainties within the compound system. The supervisory controller combines sliding-mode control (SMC) and an adaptive bound-estimation scheme with various weights to achieve H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance with a desired level of attenuation. Projection-type adaptation laws of network parameters developed using the Lyapunov's synthesis approach guarantee the stability of the overall control system. Simulation studies on a single-link flexible-joint manipulator and a two-link robot demonstrate the effectiveness of the proposed control scheme.

Robust Stable Fuzzy Control via Fuzzy Modeling and Feedback Linearization with Its Applications to Controlling Uncertain Single-link Flexible Joint Manipulators

In this paper, a robust stable fuzzy control design based on feedback linearization is presented. Takagi–Sugeno fuzzy model is used as representing the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. For this structured uncertainty, the closed system can be analyzed by applying the perturbation system stability analysis to the fuzzy feedback linearization systems and a sufficient condition is derived to guarantee the stability of the closed-loop system with bounded parameter uncertainties. Based on the developed analysis method, we can design a robust fuzzy controller by choosing the control parameters satisfying the robust stability condition.

A New Approach to Parametric Identification of a Single-Link Flexible-Joint Manipulator

A new parametric observer for identifying the system parameters of a single-link flexible-joint manipulator is presented. The design achieves the desired goals provided two conditions are satisfied, i.e., the basis functions are linearly independent in terms of the steady-state trajectories and the parameter errors converge to some constants eventually. It can be incorporated with any a control scheme sustaining such steady-state trajectories. No acceleration signals are required. However, the motor inertia must be given a priori. Numerical study of the proposed scheme with a specific robust control law is undertaken to demonstrate its validity.

Robust adaptive controller design for flexible joint manipulators

In this paper the control problem for robot manipulators with flexible joints is considered. A reduced-order flexible joint model is constructed based on a singular perturbation formulation of the manipulator equations of motion. The concept of an integral manifold is utilized to construct the dynamics of a slow subsystem. A fast subsystem is constructed to represent the fast dynamics of the elastic forces at the joints. A composite control scheme is developed based on on-line identification of the manipulator parameters which takes into account the effect of certain unmodeled dynamics and parameter variations. Stability analysis of the resulting closed-loop full-order system is presented. Simulation results for a single link flexible joint manipulator are given to illustrate the applicability of the proposed algorithm.