Motion Control of Parallel Manipulators Using Acceleration Feedback

This paper addresses the kinematic and dynamic models of a 3-PPR parallel manipulator, which are the foundation of parallel manipulator dynamic control. Then, based on the Udwadia-Kalaba equation, a three-step procedure is exploited to realize the perfect trajectory tracking of 3-PPR parallel manipulator involving the known uncertainty. In addition, when the initial conditions are incompatible and system parameters are uncertain, we adopt the adaptive robust control method to realize approximate trajectory tracking of the planar parallel manipulator. The controller consists of three parts. The first part is the perfect control of dynamic model based on the Udwadia-Kalaba equation. The second part deals with the incompatibility of initial conditions. The third part is the robust control for system uncertainty regulated by adaptive law. Finally, on the basis of theoretical analysis, the adaptive robust control algorithm is demonstrated by simulation.

Zeroing dynamics (ZD), as a powerful method proposed for time-varying problems solving, has found successful applications in motion control of serial manipulators. Compared with serial manipulators, parallel manipulators possess some attractive advantages such as high carrying capacity and high operation accuracy. However, the inherent differences between parallel and serial manipulators set great difficulties on the applications of ZD to the control of parallel manipulators. Making progress along this direction, the first ZD based motion controller of parallel manipulators is proposed and the design procedure of the ZD based scheme is presented. As a typical application, the proposed scheme is utilised to control a Stewart platform for tracking a quatrefoil-shaped path, which illustrates the effectiveness of the ZD based scheme.

Trajectory planning and tracking are crucial tasks in any application using robot manipulators. These tasks become particularly difficult when obstacles are present in the manipulatorpsilas workspace. In this paper it is assumed that the obstacles can be approximated in a conservative way with discs. The goal is to represent the obstacles in the robot configuration space, in order to allow an efficient and accurate trajectory planning and tracking. Moreover, the paper provides the methods for checking the collision between the n-joint manipulator and the obstacles. Trajectory planning depends on tracking accuracy. In this paper an adequate tracking accuracy is guaranteed assuming the use of a suitably designed robust controller.

Brain–machine interface control of a manipulator using small-world neural network and shared control strategy

This paper presents a decoupled nonsingular terminal sliding mode controller (DNTSMC) for a novel 3-DOF parallel manipulator with actuation redundancy. According to kinematic analysis, the inverse dynamic model for a novel 3-DOF redundantly actuated parallel manipulator is formulated in the task space using Lagrangian formalism and decoupled into three entirely independent subsystems under generalized coordinates to significantly reduce system complexity. Based on the dynamic model, a decoupled sliding mode control strategy is proposed for the parallel manipulator; the idea behind this strategy is to design a nonsingular terminal sliding mode controller for each subsystem, which can drive states of three subsystems to the original equilibrium points simultaneously by two intermediate variables. Additionally, a RBF neural network is used to compensate the cross-coupling force and gravity to enhance the control precision. Simulation and experimental results show that the proposed DNTSMC can achieve better control performances compared with the conventional sliding mode controller (SMC) and the DNTSMC without compensator.

In this paper, the problem of robust control of robot manipulators which perform noncontact and contact tasks is considered. Using the hybrid control strategy, two variable structure control algorithms are developed in task space. One of the algorithms is developed for control of robot manipulators in constrained motion; the other is proposed for control of manipulators in unconstrained and constrained motion. Computer simulation results are presented for illustration. >

Cable-driven parallel robots (CDPRs) are a new type of parallel robots that use cables to control a mobile platform. They possess several advantages, including large workspace, low inertia, and high payload capacity. However, there are several problems in the high-precision trajectory tracking control of CDPRs. On the one hand, all the cables must remain in tension during the entire motion process. On the other hand, the controller design is subjected to model uncertainties and external disturbances. Accordingly, this article proposes a robust synchronization control (RSC) scheme in the cable length space to achieve high-precision trajectory tracking. The synchronization control ensures motion coordination among all the cables and prevents cable relaxation, whereas the robust control eliminates modeling errors and restrains external disturbances. The uniformly ultimate boundedness of the tracking and synchronization errors in the closed-loop system equation was proved using the Lyapunov theory. Simulations and experiments of the trajectory tracking control were both implemented on a three-degree-of-freedom CDPR. Compared with the adaptive robust control scheme and the augmented proportional derivative scheme on the premise of the approximate energy consumption, the proposed RSC scheme could reduce not only the tracking errors of the cables but also the synchronization errors between adjacent cables. Moreover, the RSC scheme could significantly improve the trajectory tracking accuracy of the mobile platform. The robustness of this scheme was verified using load experiments and torque-disturbance experiments.

This paper mainly focuses on dynamic modelling and real-time control for a parallel manipulator with flexible link. The Lagrange principle and assumed modes method (AMM) substructure technique is presented to formulate the dynamic modelling of a two-degrees-of-freedom (DOF) parallel manipulator with flexible links. Then, the singular perturbation technique (SPT) is used to decompose the nonlinear dynamic system into slow time-scale and fast time-scale subsystems. Furthermore, the SPT is employed to transform the differential algebraic equations (DAEs) for kinematic constraints into explicit ordinary differential equations (ODEs), which makes real-time control possible. In addition, a novel composite control scheme is presented; the computed torque control is applied for a slow subsystem and the H ∞ technique for the fast subsystem, taking account of the model uncertainty and outside disturbance. The simulation results show the composite control can effectively achieve fast and accurate tracking control.

A parallel manipulator provides an alternative design to serial manipulators, and can be found in many applications such as mining machines (Arai et al., 1991). Through the design of active joints such that actuators are fixed to the manipulator base, the mass of moving components of the parallel manipulator is greatly reduced, and high speed and high acceleration performance may be achieved. Parallel manipulators, comprised of closed-loop chains due to multiple linkages of the parallel structure, also provide high mechanical rigidity, but adversely exhibit smaller workspace and associated singularities. Considerable research has focused on kinematic analysis and singularity characterization of these devices (Gosselin & Angeles, 1990, Merlet, 1996). Planar parallel manipulators typically consist of three closed chains and a moving platform. According to the arrangement of their joints in a chain, these mechanisms are classified as PRR, RRR etc. where P denotes a prismatic joint and R denotes a revolute joint respectively. An assembly industry, such as the electronic fabrication, demands high-speed, high acceleration placement manipulators, with corresponding lightweight linkages, hence these linkages deform under high inertia forces leading to unwanted vibrations. Moreover, such multiple flexible linkages of a parallel manipulator propagate their oscillatory motions to the moving platform where a working gripper is located. Therefore, such vibration must be damped quickly to reduce settling time of the manipulator platform position and orientation. A number of approaches to develop the dynamic model of parallel manipulators with structural flexibility have been presented in the literature(Fattah et al., 1995, Toyama et al. 2001), but relatively few works related to vibration reduction of a parallel manipulator have been published. Kozak (Kozak et al., 2004) linearized the dynamic equations of a two-degree-of-freedom parallel manipulator locally, and applied an input shaping technique to reduce residual vibrations through modification of the reference command given to the system. Kang (Kang et al., 2002) modeled a planar parallel manipulator using the assumed modes method, and presented a two-time scale controller for linkage vibration attenuation of the planar parallel manipulator. Since both the input shaping technique and the two-time scale control scheme, applied to parallel manipulators,

This paper discusses the use of acceleration measurements to improve the performance and robustness of controllers for mechanical systems. To use acceleration signals there are at least two approaches: direct use in a feedback loop to improve the tracking error, and indirect use by an observer to improve the estimates of position and speed. Several proposals for the use of the acceleration in a feedback loop, resulting in slightly different controllers, are discussed. The design of the controllers for the experimental system, a flexible multiple degrees-of-freedom XY-table, uses a simplified two degrees-of-freedom model. The observer is of the predictive type to compensate for the time delay in the implementation, and its design is based in part on Kalman filter theory. Simulations and experiments show that both acceleration feedback and an acceleration assisted observer can improve the performance of the control system, but the robustness does not change significantly. A combination of both approaches did not give any improvement in the experiments, but some in the simulations. Disturbances in the acceleration signal (especially motor torque ripple), phase lag introduced by the signal processing equipment, time delay caused by the sampled data implementation of the controller and observer, and the non-colocated position and acceleration sensors are believed to be limitations for the usefulness of the acceleration signal. A performance improvement up to a factor of 1.5 was possible in the author's application, so to consider the use of acceleration measurements in tracking control is recommended.

The workspace of a spatial 6-DOF electro-hydraulic parallel manipulator is strongly coupled, due to its multi-closed-loop kinematic structure and the coupling complicates motion planning and control of the parallel manipulator. This paper clearly analyses the strong dynamic coupling property in the workspace of a spatial 6-DOF parallel manipulator, using modal decoupling theory and a frequency responses characteristics analysis method. The dynamic model of a spatial 6-DOF electro-hydraulic parallel manipulator is expressed with the Kane method and hydromechanics principles. The modal analysis method is used to establish the map between strong coupling workspace and decoupled modal space and the dynamic coupling relationship and coupling strength between workspaces are exactly revealed. The quantitative evaluation index of dynamic coupling is presented. Moreover, the relationship between dynamic coupling effects and input is discussed through applying frequency characteristics analysis. Experimental results show the workspace of the parallel manipulator is strongly coupled and the coupling property is coincident with theoretical results.

In this article, an orthogonal 6-degree-of-freedom (DOF) parallel robot with redundant actuation is studied as an earthquake motion simulator. Taking the practical simulation of earthquake waves into consideration, the general characteristics of natural earthquakes are analysed and complexity and variety of seismic waves, three-dimensional and multi-DOF movement, and strong devastating force are regarded as the three obvious features in this article. Based on the characteristics of this orthogonal 6-DOF parallel robot with redundant actuation and the features of earthquakes, the feasibility of using this parallel robot as an earthquake motion simulator is analysed from three aspects: orthogonal 6-DOF structure, decoupling feature, and redundant actuation module. In order to simulate an earthquake motion using this parallel robot, its inverse kinematics and dynamics models are derived. The control system of this earthquake simulator is developed based on the PXIbus development platform. The computed-torque control algorithm based on the inverse dynamics is used in the controller of this equipment. A typical three-directional earthquake motion, the El Centro earthquake, is simulated on the end-effector of this parallel robot by means of its mathematical models and control system. Three main motion parameters of simulated seismic waves, displacements, velocities, and accelerations, are measured, respectively, by laser tracker and acceleration sensors. The experimental results show this equipment is appropriate to be used as an earthquake simulator.

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for motion control of multilink robot manipulators. The proposed controller has the following salient features: (1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically according to their significance to the control system and the complexity of the mapped system and no predefined fuzzy rules are required; (2) fast online learning ability, i.e., no prescribed training models are needed for online learning and weights of the fuzzy neural controller are modified without any iterations; (3) fast convergence of tracking errors, i.e., manipulator joints can track the desired trajectories very quickly; (4) adaptive control, i.e., structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; and (5) robust control, where asymptotic stability of the control system is established using the Lyapunov theorem. Experimental evaluation conducted on an industrial selectively compliant assembly robot arm demonstrates that excellent tracking performance can be achieved under time-varying conditions.

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

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