Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Manipulator tracking technology based on FSRUKF

Aiming at the shortcoming that the traditional industrial manipulator using off-line programming cannot change along with the change of external environment,the key technologies such as machine vision and manipulator control are studied,and a complete manipulator vision tracking system is designed.Firstly,Denavit-Hartenberg(D-H)parameters method is used to construct the model of the manipulator and analyze the forward and inverse kinematics equations of the manipulator.At the same time,a binocular camera is used to obtain the threedimensional position of the target.Secondly,in order to make the manipulator track the target more accurately,the fuzzy adaptive square root unscented Kalman filter(FSRUKF)is proposed to estimate the target state.Finally,the manipulator tracking system is built by using the position-based visual servo.The simulation experiments show that FSRUKF converges faster and with less error than the square root unscented Kalman filter(SRUKF),which meets the application requirements of the manipulator tracking system,and basically meets the application requirements of the manipulator tracking system in the practical experiments.

Neural Dynamics for Cooperative Motion Control of Omnidirectional Mobile Manipulators in the Presence of Noises: A Distributed Approach

This paper presents a distributed scheme with limited communications, aiming to achieve cooperative motion control for multiple omnidirectional mobile manipulators(MOMMs).The proposed scheme extends the existing single-agent motion control to cater to scenarios involving the cooperative operation of MOMMs. Specifically, squeeze-free cooperative load transportation is achieved for the end-effectors of MOMMs by incorporating cooperative repetitive motion planning(CRMP), while guiding each individual to desired poses. Then, the distributed scheme is formulated as a time-varying quadratic programming(QP) and solved online utilizing a noise-tolerant zeroing neural network(NTZNN). Theoretical analysis shows that the NTZNN model converges globally to the optimal solution of QP in the presence of noise. Finally, the effectiveness of the control design is demonstrated by numerical simulations and physical platform experiments.

Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper,the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures,parameter uncertainties,and unknown time-varying boundary disturbances is addressed.The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader.Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties,the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances.Furthermore,the Lyapunov stability theory is used to demonstrate that followers’angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded.Finally,the numerical simulation results confirm the efficacy of the proposed controllers.

Recursive recurrent neural network:A novel model for manipulator control with different levels of physical constraints

Manipulators actuate joints to let end effectors to perform precise path tracking tasks.Recurrent neural network which is described by dynamic models with parallel processing capability,is a powerful tool for kinematic control of manipulators.Due to physical limitations and actuation saturation of manipulator joints,the involvement of joint constraints for kinematic control of manipulators is essential and critical.However,current existing manipulator control methods based on recurrent neural networks mainly handle with limited levels of joint angular constraints,and to the best of our knowledge,methods for kinematic control of manipulators with higher order joint constraints based on recurrent neural networks are not yet reported.In this study,for the first time,a novel recursive recurrent network model is proposed to solve the kinematic control issue for manipulators with different levels of physical constraints,and the proposed recursive recurrent neural network can be formulated as a new manifold system to ensure control solution within all of the joint constraints in different orders.The theoretical analysis shows the stability and the purposed recursive recurrent neural network and its convergence to solution.Simulation results further demonstrate the effectiveness of the proposed method in end‐effector path tracking control under different levels of joint constraints based on the Kuka manipulator system.Comparisons with other methods such as the pseudoinverse‐based method and conventional recurrent neural network method substantiate the superiority of the proposed method.

Kinematic Control of Serial Manipulators Under False Data Injection Attack

With advanced communication technologies,cyberphysical systems such as networked industrial control systems can be monitored and controlled by a remote control center via communication networks.While lots of benefits can be achieved with such a configuration,it also brings the concern of cyber attacks to the industrial control systems,such as networked manipulators that are widely adopted in industrial automation.For such systems,a false data injection attack on a control-center-to-manipulator(CC-M)communication channel is undesirable,and has negative effects on the manufacture quality.In this paper,we propose a resilient remote kinematic control method for serial manipulators undergoing a false data injection attack by leveraging the kinematic model.Theoretical analysis shows that the proposed method can guarantee asymptotic convergence of the regulation error to zero in the presence of a type of false data injection attack.The efficacy of the proposed method is validated via simulations.

Optimal Joint Space Control of a Cable-Driven Aerial Manipulator

This article proposes a novel method for maintaining the trajectory of an aerial manipulator by utilizing a fast nonsingular terminal sliding mode(FNTSM)manifold and a linear extended state observer(LESO).The developed controlmethod applies an FNTSMto ensure the tracking performance’s control accuracy,and an LESO to estimate the system’s unmodeled dynamics and external disturbances.Additionally,an improved salp swarm algorithm(ISSA)is employed to parameter tune the suggested controller by integrating the salp swarmtechnique with a cloud model.This approach also uses a model-free scheme to reduce the complexity of controller design without relying on complex and precise dynamics models.The simulation results show that the proposed controller outperforms linear active rejection disturbance control and PID controllers in terms of transient performance and resilience against lumped disturbances,and the ISSA can help the proposed controller find optimal control parameters.

Observer-Based Control for a Cable-Driven Aerial Manipulator under Lumped Disturbances

With the increasing demand for interactive aerial operations,the application of aerial manipulators is becoming more promising.However,there are a few critical problems on how to improve the energetic efficiency and pose control of the aerialmanipulator forpractical application.In this paper,a novel cable-drivenaerialmanipulatorused for remote water sampling is proposed and then its rigid-flexible coupling dynamics model is constructed which takes joint flexibility into account.To achieve high precision joint position tracking under lumped disturbances,a newly controller,which consists of three parts:linear extended state observer,adaptive super-twisting strategy,and fractional-order nonsingular terminal sliding mode control,is proposed.The linear extended state observer is adopted to approximate unmeasured states and unknown lumped disturbances and achieve model-free control structure.The adaptive super-twisting strategy and fractional-order nonsingular terminal sliding mode control are combined together to achieve good control performance and counteract chattering problem.The Lyapunovmethod is utilized to prove the overall stability and convergence of the system.Lastly,various visualization simulations and ground experiments are conducted,verifying the effectiveness of our strategy,and all outcomes demonstrate its superiorities over the existing control strategies.

A Custom Manipulator for Dental Implantation Through Model-Based Design

This paper presents a Model-Based Design(MBD)approach for the design and control of a customized manipulator intended for drilling and position-ing of dental implants accurately with minimal human intervention.While performing an intra-oral surgery for a prolonged duration within a limited oral cavity,the tremor of dentist's hand is inevitable.As a result,wielding the drilling tool and inserting the dental implants safely in accurate position and orientation is highly challenging even for experienced dentists.Therefore,we introduce a customized manipulator that is designed ergonomically by taking in to account the dental chair specifications and anthropomorphic data such that it can be readily mounted onto the existing dental chair.The manipulator can be used to drill holes for dental inserts and position them with improved accuracy and safety.Further-more,a thorough multi-body motion analysis of the manipulator was carried out by creating a virtual prototype of the manipulator and simulating its controlled movements in various scenarios.The overall design was prepared and validated in simulation using Solid works,MATLAB and Simulink through Model Based Design(MBD)approach.The motion simulation results indicate that the manipulator could be built as a prototype readily.

Fault Diagnosis in Robot Manipulators Using SVM and KNN

In this paper,Support Vector Machine(SVM)and K-Nearest Neighbor(KNN)based methods are to be applied on fault diagnosis in a robot manipulator.A comparative study between the two classifiers in terms of successfully detecting and isolating the seven classes of sensor faults is considered in this work.For both classifiers,the torque,the position and the speed of the manipulator have been employed as the input vector.However,it is to mention that a large database is needed and used for the training and testing phases.The SVM method used in this paper is based on the Gaussian kernel with the parametersγand the penalty margin parameter“C”,which were adjusted via the PSO algorithm to achieve a maximum accuracy diagnosis.Simulations were carried out on the model of a Selective Compliance Assembly Robot Arm(SCARA)robot manipulator,and the results showed that the Particle Swarm Optimization(PSO)increased the per-formance of the SVM algorithm with the 96.95%accuracy while the KNN algo-rithm achieved a correlation up to 94.62%.These results showed that the SVM algorithm with PSO was more precise than the KNN algorithm when was used in fault diagnosis on a robot manipulator.

Gravity-Based Kinetostatic Modeling of Parallel Manipulators Using Screw Theory

The pose accuracy of parallel manipulators(PMs)is a key index to measure their performance.Establishing the grav-ity-based kinetostatic model of a parallel robot provides an important basis for its error composition and accuracy improvement.In this paper,a kinetostatic modeling approach that takes real gravity distribution into consideration is proposed to analyze the influence of gravity on the infinitesimal twist and actuator forces of PMs.First,the duality of the twist screw and constraint wrenches are used to derive the gravity-attached constraint wrenches independent of the external load and the limb stiffness matrix corresponding to the kinematics-based constraint wrenches.Sec-ond,the gravity model of the mechanism is established based on the screw theory and the principle of virtual work.Finally,the analytical formulas of the infinitesimal twist and the actuator force of PMs are obtained,and the influences of the external load,platform gravity,and rod gravity on the stiffness of the mechanism are decoupled.The non-overconstrained 3RPS and overconstrained 2PRU-UPR PMs are taken as examples to verify the proposed method.This research proposes a methodology to analyze the infinitesimal deformation of the mechanism under the influence of gravity.

A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances.The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers.The proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time convergence.Since all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability.Finally,simulation results validate the effectiveness of the proposed method.

FUZZY ADAPTIVE CONTROL OF FLEXIBLE-LINK ROBOT MANIPULATOR

A fuzzy adaptive control method is proposed for a flexible robot manipulator. Due to the structure characteristics of the flexible manipulator, the vibration modes must be controlled to realize the high-precision tip position. The Lagrangian principle is utilized to model the dynamic function of the single-degree flexible manipulator incorporating the assumed modes method. Simulation results of the fuzzy adaptive control method in the location control and the trajectory tracking with different tip disturbances are presented and compared with the results of the classic PD control. It shows that the controller can obtain the stable and robust performance.

Vibration Reduction of Open-chain Flexible Manipulators by Optimizing Independent Motions of Branch Links

In order to suppress vibration in flexible manipulators, a new type of manipulator mechanism with controllable local degrees of freedom is proposed. This mechanism consists of a main chain and some branch links. The main chain is of a flexible open-chain configuration with an end-effector installed at its tip, and the rigid branch links are able to perform active movements. It is proved by kinematics and dynamic analysis that, the branch links bear no direct kinematic relation to the main chain, but their independent motions can strongly affect the dynamic behavior and performance of the flexible manipulator. Then comes a new idea of suppressing vibration, in which independent motions of the branch links are used to suppress the undesired vibration of the flexible main chain through dynamic coupling. On this basis, an optimal method for reducing vibration of flexible manipulators is proposed. Finally, the effectiveness of this method is verified by numerical simulations.

Trajectory Tracking of a Planer Parallel Manipulator by Using Computed Force Control Method

Despite small workspace, parallel manipulators have some advantages over their serial counterparts in terms of higher speed, acceleration, rigidity, accuracy, manufacturing cost and payload. Accordingly, this type of manipulators can be used in many applications such as in high-speed machine tools, tuning machine for feeding, sensitive cutting, assembly and packaging. This paper presents a special type of planar parallel manipulator with three degrees of freedom. It is constructed as a variable geometry truss generally known planar Stewart platform. The reachable and orientation workspaces are obtained for this manipulator. The inverse kinematic analysis is solved for the trajectory tracking according to the redundancy and joint limit avoidance. Then, the dynamics model of the manipulator is established by using Virtual Work method. The simulations are performed to follow the given planar trajectories by using the dynamic equations of the variable geometry truss manipulator and computed force control method. In computed force control method, the feedback gain matrices for PD control are tuned with fixed matrices by trail end error and variable ones by means of optimization with genetic algorithm.

Collision Avoidance of Cooperative Dual Redundant Manipulators

Dual redundant manipulators are extremely useful for tasks in dangerous or space environments, but efficient and real time coordinated control is hard to achieve. Collision avoidance between two cooperative manipulators is vital to the successful applications of dual redundant manipulators. Although methods based on the distance function have been demonstrated simple and efficient, different collision avoidance points can usually produce completely different results and even failure. The paper discussed the choices of collision avoidance points and proposed a novel method for the choosing of those points. The method is testified by simulation results of two redundant planar manipulators.

On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators

This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub, and mass, moment, and side of tip load. Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed. By using variational method, sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies. Based on variational formulations, a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced. With this method, the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part, as commonly used in their derivation. © 2014 Chinese Association of Automation.

Implementation and Kinematic Control of a Hyper-redundant Mobile Manipulator System

Redundant or hyper-redundant mobile manipulator can give lots of assistance to astronauts in space station. The design and implementation of a hyper-redundant mobile manipulator system are described, which is composed of an 8 DOF module robot and a 1 DOF motorized rail. Inverse kinematic resolution of the system is discussed and one simplified control method based on joint limit avoidance and configuration optimization is proposed. Simulation and experimental results are presented.