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.

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.

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.

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.

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.

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.

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.

A Decentralized Autonomous Control on Highly Redundant Robot Manipulators

The control method of highly redundant robot manipulators is introduced. A decentralized autonomous control scheme is used to guide the movement of robot manipulators so that the work done by manipulators is minimized. The method of computing pseudoinverse which needs too many complicated calculation can be avoided. Then the calculation and control of robots are simplified. At the same time system robustness/fault tolerance is achieved.

ON HYBRID POSITION/FORCE COORDINATED LEARNING CONTROL OF MULTIPLE MANIPULATORS

In this paper, coordinated control of multiple robot manipulators holding a rigid object is discussed. In consideration of inaccuracy of the dynamic model of a multiple manipulator system, the error equations on object position and internal force are derived. Then a hybrid position/force coordinated learning control scheme is presented and its convergence is proved. The scheme can improve the system performance by modifying the control input of the system after each iterative learning. Simulation results of two planar robot manipulators holding an object show the effectiveness of this control scheme.

Impedance force control for position controlled robotic manipulators under the constraint of unknown environments

A force control strategy for position controlled robotic manipulators is presented. On line force feedback data are employed to estimate the local shape of the unknown constraint. The estimated vectors are used to generate the virtual reference trajectory for the target impedance model that is driven by the force error to produce command position. By following the command position trajectory the robotic manipulator can follow the unknown constraint surface while keeping an acceptable force error in a manner depicted by the target impedance model. Computer simulation on a 3 linked planar manipulator and experimental studies on an Adept 3, an SCARA type robotic manipulator, are conducted to verify the force tracking capability of the proposed control strategy.

Motion planning for redundant prismatic-jointed manipulators in the free-floating mode

This paper investigates the motion planning of redundant free-floating manipulators with seven prismatic joints. On the earth, prismatic-jointed manipulators could only position their end-effectors in a desired way. However, in space, the end-effectors of free-floating manipulators can achieve both the desired orientation and desired position due to the dynamical coupling between manipulator and satellite movement, which is formally expressed by linear and angular momentum conservation laws. In this study, a tractable algorithm particle swarm optimization combined with differential evolution （PSODE） is provided to deal with the motion planning of redundant free-floating prismatic-jointed manipulators, which could avoid the pseudo inverse of the Jacobian matrix. The polynomial functions, as argument in sine functions are used to specify the joint paths. The co- efficients of the polynomials are optimized to achieve the desired end-effector orientation and position, and simulta- neously minimize the unit-mass-kinetic energy using the redundancy. Relevant simulations prove that this method pro- vides satisfactory smooth paths for redundant free-floating prismatic-jointed manipulators. This study could help to recognize the advantages of redundant prismatic-jointed space manipulators.

SELF-RECONFIGURATION OF UNDERACTUATED REDUNDANT MANIPULATORS WITH OPTIMIZING THE FLEXIBILITY ELLIPSOID

The multi-modes feature, the measure of the manipulating flexibility, andself-reconfiguration control method of the underactuated redundant manipulators are investigatedbased on the optimizing technology. The relationship between the configuration of the joint spaceand the manipulating flexibility of the underactuated redundant manipulator is analyzed, a newmeasure of manipulating flexibility ellipsoid for the underactuated redundant manipulator withpassive joints in locked mode is proposed, which can be used to get the optimal configuration forthe realization of the self-reconfiguration control. Furthermore, a time-varying nonlinear controlmethod based on harmonic inputs is suggested for fulfilling the self-reconfiguration. A simulationexample of a three-DOFs underactuated manipulator with one passive joint features some aspects ofthe investigations.

Motion Planning Algorithms of Redundant Manipulators Based on Self-motion Manifolds

The current motion planning approaches for redundant manipulators mainly includes two categories： improved gradient-projection method and some other efficiency numerical methods. The former is excessively sensitive to parameters, which makes adjustment difficult; and the latter treats the motion planning as general task by ignoring the particularity, which has good universal property but reduces the solving speed for on-line real-time planning. In this paper, a novel stepwise solution based on self-motion manifold is proposed for motion planning of redundant manipulators, namely, the chief tasks and secondary tasks are implemented step by step. Firstly, the posture tracking of end-effector is achieved accurately by employing the non-redundant joint. Secondly, the end-effector is set to keep stationary. Finally, self-motion of manipulator is realized via additional work on the gradient of redundant joint displacement. To verify this solution, experiments of round obstacle avoiding are carried out via the planar 3 degree-of-~eedom manipulator. And the experimental results indicate that this motion planning algorithm can effectively achieve obstacle avoiding and posture tracking of the end-effector. Compared with traditional gradient projection method, this approach can accelerate the problem-solving process, and is more applicable to obstacle avoiding and other additional work in displacement level.

Type Design for Heavy-payload Forging Manipulators

Heavy-payload forging manipulators are mainly characterized by large load output and large capacitive-load input.The relationship between outputs and inputs,which will greatly influence the control and the reliability,is the key issue in type design for heavy-payload forging manipulators.In this paper,a type design method by considering the incidence relationship between output characteristics and actuator inputs is presented and used to design the mechanism for forging manipulators.The concept of modeling method based on the outputs tasks is defined and investigated.The principle of type design from the viewpoints of the relationship between output characteristics and actuator inputs is discussed.An idea of establishing the incidence relationship between output characteristics and actuator inputs is proposed.The incidence relationship matrix between outputs and inputs is also given.The design flow is obtained,and the incidence relationship between outputs and inputs for heavy-payload forging manipulators is divided into three parts after detailed understanding of the functional properties.Four types of mechanisms for heavy-payload forging manipulators are given,and the corresponding spatial mechanical sketches are also drawn,some new designed mechanisms have been adopted by company or used as prototype.These novel forging manipulators which satisfy certain functional requirements provide an effective help for the design of forging manipulators and patent application.

Topology Search of 3-DOF Translational Parallel Manipulators with Three Identical Limbs for Leg Mechanisms

Three-degree of freedom（3-DOF） translational parallel manipulators（TPMs） have been widely studied both in industry and academia in the past decades. However, most architectures of 3-DOF TPMs are created mainly on designers＇ intuition, empirical knowledge, or associative reasoning and the topology synthesis researches of 3-DOF TPMs are still limited. In order to find out the atlas of designs for 3-DOF TPMs, a topology search is presented for enumeration of 3-DOF TPMs whose limbs can be modeled as 5-DOF serial chains. The proposed topology search of 3-DOF TPMs is aimed to overcome the sensitivities of the design solution of a 3-DOF TPM for a LARM leg mechanism in a biped robot. The topology search, which is based on the concept of generation and specialization in graph theory, is reported as a step-by-step procedure with desired specifications, principle and rules of generalization, design requirements and constraints, and algorithm of number synthesis. In order to obtain new feasible designs for a chosen example and to limit the search domain under general considerations, one topological generalized kinematic chain is chosen to be specialized. An atlas of new feasible designs is obtained and analyzed for a specific solution as leg mechanisms. The proposed methodology provides a topology search for 3-DOF TPMs for leg mechanisms, but it can be also expanded for other applications and tasks.

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.

Optimum Selection of Mechanism Type for Heavy Manipulators Based on Particle Swarm Optimization Method

The mechanism type plays a decisive role in the mechanical performance of robotic manipulators. Feasible mechanism types can be obtained by applying appropriate type synthesis theory, but there is still a lack of effective and efficient methods for the optimum selection among different types of mechanism candidates. This paper presents a new strategy for the purpose of optimum mechanism type selection based on the modified particle swarm optimization method. The concept of sub-swarm is introduced to represent the different mechanisms generated by the type synthesis, and a competitive mechanism is employed between the sub-swarms to reassign their population size according to the relative performances of the mechanism candidates to implement the optimization. Combining with a modular modeling approach for fast calculation of the performance index of the potential candidates, the proposed method is applied to determine the optimum mechanism type among the potential candidates for the desired manipulator. The effectiveness and efficiency of the proposed method is demonstrated through a case study on the optimum selection of mechanism type of a heavy manipulator where six feasible candidates are considered with force capability as the specific performance index. The optimization result shows that the fitness of the optimum mechanism type for the considered heavy manipulator can be up to 0.578 5. This research provides the instruction in optimum selection of mechanism types for robotic manipulators.