Stiffness analysis of hexaslide machine tools

This paper presents stiffness analysis of hexaslides, a class of parallel manipulators with six constant length legs, the base joints of which move along six distinct rail-axes. In the design of hexaslides for machine tool applications, stiffness as well as its variation within the workspace is important. The stiffness of any parallel kinematic machine and, thus, the accuracy depends on the pose of the tool platform. A stiffness model of a generic hexaslide is developed here considering the flexibilities in both the actuator and the legs of the hexaslide. The methodology adopted is based on the concept of the determination of stiffness of a group of serially connected linear springs. Based on the proposed model, the average stiffness and its variation along and about the Cartesian coordinate axes offered by three typical hexaslides, having the same foot print size, are estimated and compared. Other typical performance indices, i.e. workspace volume, workspace volume index (ratio of workspace volume to machine size), global dexterity index and global stiffness index, are also compared.     

A recursive,numerically stable,and efficient simulation algorithm for serial robots

Traditionally, the dynamic model, i.e., the equations of motion, of a robotic system is derived from Euler–Lagrange (EL) or Newton–Euler (NE) equations. The EL equations begin with a set of generally independent generalized coordinates, whereas the NE equations are based on the Cartesian coordinates. The NE equations consider various forces and moments on the free body diagram of each link of the robotic system at hand, and, hence, require the calculation of the constrained forces and moments that eventually do not participate in the motion of the coupled system. Hence, the principle of elimination of constraint forces has been proposed in the literature. One such methodology is based on the Decoupled Natural Orthogonal Complement (DeNOC) matrices, reported elsewhere. It is shown in this paper that one can also begin with the EL equations of motion based on the kinetic and potential energies of the system, and use the DeNOC matrices to obtain the independent equations of motion. The advantage of the proposed approach is that a computationally more efficient forward dynamics algorithm for the serial robots having slender rods is obtained, which is numerically stable. The typical six-degree-of-freedom PUMA robot is considered here to illustrate the advantages of the proposed algorithm.     

Dimensional design of hexaslides for optimal workspace and dexterity

The paper presents the dimensional design of a class of parallel manipulators, namely, Hexaslides. The design of hexaslides is formulated as a multiobjective optimization problem considering workspace and dexterity as dual objectives. As the relative emphasis on workspace and dexterity varies depending on the application, a set of Pareto-optimal solutions is found. The present analysis is a useful tool for designers to select suitable hexaslide parameters for a given application, particularly, in machine tool applications.     

Reduced-order forward dynamics of multiclosed-loop systems

In this work, a reduced-order forward dynamics of multiclosed-loop systems is proposed by exploiting the associated inherent kinematic constraints at acceleration level. First, a closed-loop system is divided into an equivalent open architecture consisting of several serial and tree-type subsystems by introducing cuts at appropriate joints. The resulting cut joints are replaced by appropriate constraint forces also referred to as Lagrange multipliers. Next, for each subsystem, the governing equations of motion are derived in terms of the Lagrange multipliers, which are based on the Newton–Euler formulation coupled with the concept of Decoupled Natural Orthogonal Complement (DeNOC) matrices, introduced elsewhere. In the proposed forward dynamics formulation, Lagrange multipliers are calculated sequentially at the subsystem level, and later treated as external forces to the resulting serial or tree-type systems of the original closed-loop system, for the recursive computation of joint accelerations. Note that such subsystem-level treatment allows one to use already existing algorithms for serial and tree-type systems. Hence, one can perform the dynamic analyses relatively quickly without rewriting the complete model of the closed-loop system at hand. The proposed methodology is in contrast to the conventional approaches, where the Lagrange multipliers are calculated together at the system level or simultaneously along with the joint accelerations, both of which incur higher order computational complexities, and thereby a greater number of arithmetic operations. Due to the smaller size of matrices involved in evaluating Lagrange multipliers in the proposed methodology, and the recursive computation of the joint accelerations, the overall numerical performances like computational efficiency, etc., are likely to improve. The proposed reduced-order forward dynamics formulation is illustrated with two multiclosed-loop systems, namely, a 7-bar carpet scrapping mechanism and a 3-RRR parallel manipulator.     

Modular and Recursive Kinematics and Dynamics for Parallel Manipulators

Constrained multibody systems typically feature multiple closed kinematic loops that constrain the relative motions and forces within the system. Typically, such systems possess far more articulated degrees-of-freedom (within the chains) than overall end-effector degrees-of-freedom.Thus, actuation of a subset of the articulations creates mixture of active and passive joints within the chain.The presence of such passive joints interferes with the effective modular formulation of the dynamic equations-of-motion in terms of a minimal set of actuator coordinates as well the subsequent recursivesolution for both forward and inverse dynamics applications. Thus, in this paper, we examine the development of modular and recursive formulations of equations-of-motion in terms of a minimal set of actuated-joint-coordinates for an exactly-actuated parallel manipulators. The 3 RRR planar parallel manipulator, selected to serve as a case-study, is an illustrative example of a multi-loop, multi-degree-of-freedom system with mixtures of active/passive joints. The concept of decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism inherent in parallel mechanisms to develop a dynamics formulation that is both recursive and modular. An algorithmic approach to the development of both forward and inverse dynamics is highlighted. The presented simulation studies highlight the overall good numerical behavior of the developed formulation, both in terms of accuracy and lack of formulation stiffness.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains

The dynamic model, particularly with reference to controller design, is an important issue in mechanical control and design. However, this model is often difficult to achieve in complex multi-closed-loop mechanisms, such as parallel mechanisms or forging manipulators. A new approach on the dynamic modeling of a multi closed-chain mechanism in a forging manipulator, which applies screw theory and the reduced system model, is proposed in this paper. The proposed method not only allows a straightforward calculation of actuator forces but also obtains the dynamic equation of the multi-closed-loop mechanism easily. The structure of dynamic model obtained is similar to that of standard Lagrangian formulations, which can extend vast control strategies developed for serial robots to complex multi-closed-loop mechanisms. A complex multi-closed-loop mechanism on a forging manipulator is decomposed into several serial mechanisms or simpler subsystems. The Lagrangian equations associated with each subsystem are directly derived from the local generalized coordinates of the sub-mechanisms. Jacobian matrices are used to interpret the differential equations of the sub-mechanisms into the generalized coordinate or the actuated pairs according to the D’Alembert principle. Hessian matrices are also applied to form a standard Lagrangian formulation. The screw theory is introduced to overcome the difficulties of solving transformed Jacobian matrices, thereby simplifying the calculation of the matrices. Computation difficulties of transformation matrices may decrease considerably by choosing suitable generalized coordinates instead of direct actuator variables. The full dynamics of the complex multi-closed-loop mechanism in a forging manipulator is presented. Simulations and experiments illustrate the reliability of the proposed method and the correctness of the dynamic model of the forging manipulator.     

A recursive, numerically stable, and efficient simulation algorithm for serial robots with flexible links

A methodology for the formulation of dynamic equations of motion of a serial flexible-link manipulator using the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere for rigid bodies, is presented in this paper. First, the Euler Lagrange (EL) equations of motion of the system are written. Then using the equivalence of EL and Newton–Euler (NE) equations, and the DeNOC matrices associated with the velocity constraints of the connecting bodies, the analytical and recursive expressions for the matrices and vectors appearing in the independent dynamic equations of motion are obtained. The analytical expressions allow one to obtain a recursive forward dynamics algorithm not only for rigid body manipulators, as reported earlier, but also for the flexible body manipulators. The proposed simulation algorithm for the flexible link robots is shown to be computationally more efficient and numerically more stable than other algorithms present in the literature. Simulations, using the proposed algorithm, for a two link arm with each link flexible and a Space Shuttle Remote Manipulator System (SSRMS) are presented. Numerical stability aspects of the algorithms are investigated using various criteria, namely, the zero eigenvalue phenomenon, energy drift method, etc. Numerical example of a SSRMS is taken up to show the efficiency and stability of the proposed algorithm. Physical interpretations of many terms associated with dynamic equations of flexible links, namely, the mass matrix of a composite flexible body, inertia wrench of a flexible link, etc. are also presented. The work has been carried out in the Dept. of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India.     

Simulation study on the improvements of machining accuracy by using smart materials

This work utilizes smart material to counteract the radial disturbing cutting forces and reduce machining error in the turning process. The finite element method (FEM) is employed to explore the capability of such a method in controlling tool position. Toolpost dynamic response is investigated where the pulse width modulation (PWM) technique is launched for actuator voltage input. The result from tool response using dynamic absorber does not encourage the use of such a vibration attenuator in error elimination in the presence of the PWM voltage input. Even though increasing toolpost damping within a reasonable range shows a reduction in toolpost error, major improvement is noticed by modifying the PWM voltage level and its time duration. For error elimination, the estimate of static actuator voltage does not reflect the actual level of required dynamic applied voltage. This work also emphasizes the importance of tool bit to actuator stiffness and tool carrier (holder) to actuator stiffness in reducing tool positional error.     

Dynamic loading criteria in actuator selection for desired dynamic performance

This article presents two methods for selecting actuators based on the dynamic loading criteria which yield a manipulator with a desired level of dynamic performance. Here, dynamic performance is measured in terms of a robot's acceleration and force capabilities, which describe its ability to accelerate the end-effector and to apply forces to the environment, given the limitations on its actuator torques. The Dynamic Capability Equations are used to model the relationship between actuator torque capacities and the acceleration and force capabilities, because they treat linear and angular quantities in a consistent and physically meaningful way. This article discusses actuator selection for a single configuration, as well as for multiple configurations.     

Trajectory tracking control of a pneumatically actuated 6-DOF Gough–Stewart parallel robot using Backstepping-Sliding Mode controller and geometry-based quasi forward kinematic method

In this paper, the trajectory tracking control of a 6-DoF pneumatically actuated Gough–Stewart parallel robot is investigated. The dynamic model of each link, comprising of a pneumatic actuator and a proportional electrical valve is extracted with the aim of obtaining the corresponding state space representation of the pneumatic system. Unknown parameters of the dynamic model consisting friction force of the cylinder and parameters of the proportional valve are identified by employing genetic algorithm. Position control of the pneumatic actuator is performed based on Back-Stepping Sliding Mode controller according to the dynamic model of the system. As such trajectory tracking control is performed for different trajectories by employing a rotation sensor and calculated position based on joint space and task space simultaneously. Desired sinusoidal trajectories with pure motions are tracked with root mean square error of the pure translations and rotations lower than 0.85 (cm) and 1.9 (deg), respectively. The results reveal that the trajectory is tracked by the Back-Stepping Sliding Mode controller properly. This shows the efficiency of the control strategy and the proposed method for calculating the position of the end-effector.     

An integrated physical model that characterizes creep and hysteresis in piezoelectric actuators

In this paper, a model that can precisely portray hysteresis and creep in piezoelectric actuators is proposed. The model, which is originally constructed using bond-graph representation, describes the actuator’s various physical effects and energy interaction between physical domains. Specifically, the model utilizes a parallel connection of Maxwell-slip elements and a nonlinear spring to describe hysteresis, and a series connection of Kelvin–Voigt units to describe creep. Using the experimental data, the constitutive relation of the nonlinear spring and the parameters of linear, physical elements in the model can be systematically identified via the linear programming method. To further account for the frequency-dependent hysteresis behavior, a dynamic damper is incorporated. By analyzing the model, the influence of initial strain/charges on the creep response is revealed and an initialization procedure is devised to eliminate such an influence. An inverse model control, in the sense of feedback linearization, is constructed based on the identified model to make the actuator track reference trajectories. Experiments show that both creep and hysteresis are effectively cancelled and accurate tracking of selected reference trajectories is achieved.     

Swing-arm-type PZT dual actuator with fast seeking for optical disk drive

 In this paper, a swing-arm-type dual positioning mechanism using a voice coil motor (VCM) and bimorph PZT actuators is proposed for the possible application to the future optical disc drive actuator. A VCM is used as a coarse motion actuator, and a set of piezoelectric actuators is used for fine motion. The two pairs of PZT actuators are arranged in parallel and are carefully designed to deflect in `S' shape such that tension and compression forces are generated simultaneously and thus the hysteresis is minimized. The static and dynamic analyses are performed and the parameter studies on the key dimensions of the set of PZT actuators are investigated. For fast seeking motion, time optimal control scheme combined with PD algorithm is adopted for the fast seeking motion of VCM. Positive position feedback (PPF) control is used to suppress residual vibration for the PZT actuator beams by activating it at the end of VCM swing motion. The feasibility of the suggested actuator system and the control scheme is demonstrated through simulations and experiments. Received: 5 July 2001/Accepted: 21 December 2001     

基于混合神经网络的压电陶瓷微位移执行器动态迟滞建模

提出了两个动态神经网络串联的混合神经网络动态迟滞模型,用以逼近压电陶瓷的迟滞特性.混合模型由两个动态RBF神经网络构成,前者形成一个相位超前的动态模型,其特性与压电陶瓷的输出特性类似,但在相位和幅值上有所区别;后者实现相位滞后的变换和幅值的非线性变换,以达到对压电陶瓷实际输出的逼近.仿真和实验表明,所提出的描述动态迟滞特性的动态迟滞模型是有效的.与PI模型相比较,具有较高的模型精度.     

A robust adaptive control of a parallel robot

The work presented in this article deals with the robust adaptive control tracking of a 6 degree of freedom parallel robot, called C5 parallel robot. The proposed approach is based on the coupling of sliding modes and multi-layers perceptron neural networks (MLP-NNs). It does not require the inverse dynamic model for deriving the control law. The MLP-NN is added in the control scheme to estimate the gravitational and frictional forces along with the non-modelled dynamic effects. The nonlinearity problem, present in neural networks, is resolved using Taylor series expansion. The proposed approach allows to adjust the parameters of neural network and sliding mode control terms by taking into account a reference model and the closed-loop stability in the Lyapunov sense. We implemented our approach on the C5 parallel robot of LISSI laboratory and performed experiments to observe its effectiveness and the robust behaviour of the controller against external disturbances.     

Adaptive Dynamic Surface control of An electrohydraulic Actuator with Friction Compensation

In this paper, an adaptive nonlinear control scheme with a friction observer for position control of an electrohydraulic actuator is proposed. The observer based on the LuGre friction model is employed to compensate for the friction. Adaptation laws are used to handle parameter uncertainties in the actuator and friction model. The control law including dynamics of the observer is developed through a backstepping‐like dynamic surface control (DSC) technique. Experimental results have illustrated the success of the control scheme. The results also show that the adaptive DSC controller has better tracking performance than an adaptive backstepping and conventional PI controllers.     

Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay

This article is concerned with the problem of multi-objective H _∞ control for vehicle active suspension systems with random actuator delay, which can be represented by signal probability distribution. First, the dynamical equations of a quarter-car suspension model are established for the control design purpose. Secondly, when taking into account vehicle performance requirements, namely, ride comfort, suspension deflection and the probability distributed actuator delay, we present the corresponding dynamic system, which will be transformed to the stochastic system for the problem of multi-objective H _∞ controller design. Third, based on the stochastic stability theory, the state feedback controller is proposed to render that the closed-loop system is exponentially stable in mean-square while simultaneously satisfying H _∞ performance and the output constraint requirement. The presented condition is expressed in the form of convex optimisation problems so that it can be efficiently solved via standard numerical software. Finally, a practical design example is given to demonstrate the effectiveness of the proposed method.     

含时滞记忆的非线性时滞系统满意容错控制

针对一类基于T-S模糊模型描述的非线性时滞系统,研究在一般执行器故障模式下的含时滞记忆的鲁棒H∞容错控制器设计问题.针对任意连续型执行器故障模式,采用并行分布式补偿原理设计含记忆型状态反馈控制器,给出非线性时滞系统在执行器发生故障情况下的鲁棒镇定准则.然后给出H∞性能指标约束下的满意容错控制器的设计方法和设计步骤.提出的含时滞记忆的状态反馈控制方法可以确保当执行器发生故障时,闭环系统不仅具有渐近稳定性,而且有一定的抗扰动性能,状态反馈控制器设计的保守性较不含时滞记忆控制器设计方法大大降低.仿真实例验证了鲁棒容错控制策略的有效性.     

Kinematics and dynamics of Jansen leg mechanism: A bond graph approach

The Jansen mechanism is a one degree-of-freedom, planar, 12-link, leg mechanism that can be used in mobile robotic applications and in gait analysis. This paper presents the kinematics and dynamics of the Jansen leg mechanism. The forward kinematics, accomplished using circle intersection method, determines the trajectories of various points on the mechanism in the chassis (stationary link) reference frame. From the foot point trajectory, the step length is shown to vary linearly while step height varies non-linearly with change in crank radius. A dynamic model for the Jansen leg mechanism is proposed using bond graph approach with modulated multiport transformers. For given ground reaction force pattern and crank angular speed, this model helps determine the motor torque profile as well as the link and joint stresses. The model can therefore be used to rate the actuator torque and in design of the hardware and controller for such a system. The kinematics of the mechanism can also be obtained from this dynamic model. The proposed model is thus a useful tool for analysis and design of systems based on the Jansen leg mechanism.     

四旋翼无人机姿态系统的非线性容错控制设计

本文研究了四旋翼无人机执行器发生部分失效时的姿态控制问题.通过分析其动力学特性,将执行器故障以乘性因子加入系统模型,得到执行器故障情况下四旋翼无人机的姿态动力学模型.在同时存在未知外部扰动和执行器故障的情况下,设计了一种基于自适应滑模控制的容错控制器.利用基于Lyapunov的分析方法证明了所设计控制器的渐近稳定性.在四旋翼无人机实验平台上进行了实验,验证了该算法对存在未知外部扰动和执行器部分失效时四旋翼无人机的姿态控制具有较好的鲁棒性.