Showing papers by "Zexiang Li published in 2007"

A Geometric Theory for Analysis and Synthesis of Sub-6 DoF Parallel Manipulators

Abstract: Mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.

Modeling, Identification and Control of a Redundant Planar 2-DOF Parallel Manipulator

Abstract: In this paper, the dynamic controller design problem of a redundant planar 2-dof parallel manipulator is studied. Using the Euler-Lagrange equation, we formulate the dynamic model of the parallel manipulator in the joint space and propose an augmented PD controller with forward dynamic compensation for the parallel manipulator. By formulating the controller in the joint space, we eliminate the complex computation of the Jacobian matrix of joint angles with end-effector coordinate. So with less computation, our controller is easier to implement, and a shorter sampling period can be achieved, which makes the controller more suitable for high- speed motion control. Furthermore, with the combination of static friction model and viscous friction model, the active joint friction of the parallel manipulator is studied and compensated in the controller. Based on the dynamic parameters of the parallel manipulator evaluated by direct measurement and identification, motion control experiments are implemented. With the experiments, the validity of the dynamic model is proved and the performance of the controller is evaluated. Experiment results show that, with forward dynamic compensation, the augmented PD controller can improve the tracking performance of the parallel manipulator over the simple PD controller.

Auto-calibration of a redundant parallel manipulator based on the projected tracking error

Abstract: Utilizing the projected tracking error of the redundant joint angles, we studied the calibration problem of the sensor zero positions of a planar 2-dof parallel manipulator in this paper. Based on the study of the relationship between the projected tracking error of the joint angles and the error of the sensor zero positions, a new error function is proposed for the calibration of the sensor zero positions of the parallel manipulator. It is proved that the error function is robust to the measurement error of the joint sensors, so accurate calibration results can be obtained by minimizing the error function even if the measurement of the joint angles is not accurate. With a simple searching strategy for the minimal value of the error function, we designed an auto-calibration procedure and verified the validity of the calibration procedure through real experiments on a real redundant planar 2-dof parallel manipulator.

Force Analysis of Whole Hand Grasp by Multifingered Robotic Hand

Abstract: Under a whole hand grasp, it may not be possible to generate grasping forces in all directions. Thus, the traditional techniques developed based on fingertip contacts is inadequate. In this paper, we decompose the contact force space into four orthogonal subspaces, each with a clear physical interpretation. Based on linear matrix inequalities (LMI's) representations of grasping constraints, we address and formulate the active force closure and the active grasp feasibility problems as LMI feasibility problems. Combining the effects of both active and passive forces, we propose a new cost index for the whole hand grasping force optimization problem. We further simply the force optimization problem for a whole hand grasp, which is active force closure.

Analysis of absolute stability for time-delay teleoperation systems

Abstract: In this paper, a new bilateral control algorithm based on absolute stability theory is put forward, which aims at the time-delay teleoperation system with force feedback from the slave directly. In the new control algorithm, the delay-dependent stability, instead of delay-independent stability, is taken as the aim of control design. It improves the transparency of the system at the price of unnecessary stability. With this algorithm, the time-delay teleoperation systems have good transparency and stability. A simulation system is established to verify the effect of this algorithm.

Finger gaits planning for multifingered manipulation

Abstract: A robotic hand may change its grasp status and relocate some of its fingers in order to perform a large scale manipulation. Such a strategy is called a finger gait. In this paper, a randomized manipulation planning algorithm is proposed to solving the finger gait planning problem. One of the most used finger gaiting primitives, finger substitution, is introduced. Because of its discrete-continuous characteristics, the kinematics model of a finger substitution is formulated into a hybrid automaton. Considering the discrete and continuous topology of the automaton, both the discrete metric and continuous metric are defined on the state space. An improved RRT based planner is proposed to find a feasible finger substitution. Finally, simulation results verify the validity of the proposed finger gait planner.

Development of a Novel 3-DoF Purely Translational Parallel Mechanism

Abstract: In view of the successful application of planar parallelogram in the Delta robot and its variants, we are interested to investigate mechanisms consisting of spatial parallelograms. The spatial parallelogram, denoted by Pscra*, is a 2-SS (S stands for a spherical joint) parallel mechanism having identical length for opposite links. We show that a 3-PPscr a* mechanism is generically undergoes 3-dimensional purely translational motion. Based on the 3-PPscr a* topology, an integrated optimal design on both architecture and geometry design is carried out. Using the formulation of maximizing effective cubic workspace, the Orthopod, which has three orthogonally arranged linear joint axes, is found to be the best in our settings. A prototype machine of the Orthopod is thus designed and manufactured.

Accuracy Analysis of General Parallel Manipulators with Joint Clearance

Abstract: Due to the joint clearance, parallel manipulators always exhibit some position and orientation errors at the mobile platform. This paper aims to provide a systematic framework for the error analysis problem of general parallel mechanisms influenced by the joint clearance. A novel and efficient method is proposed to evaluate the maximal pose errors of general spatial parallel manipulators with joint clearance.

Assembly Problem of Overconstrained and Clearance-free Parallel Manipulators

Abstract: To avoid deteriorating the mechanism's performance, joint clearance can be eliminated by preloading the pairing elements of the joint. However, this paper proves rigorously that in the real world, the unavoidable assembly and manufacturing errors will cause overconstrained parallel manipulators to lose degree of freedoms, or even unable to be assembled if they are composed of purely clearance-free pairs (e.g., preloaded pairs). Introducing joint clearance is an essential and efficient way for the correct functioning and easy assembly of overconstrained parallel manipulators.

A Study on Integrated Design Methodology: A Single Beam Case

Abstract: As a preliminary study for a 4 degree of freedom wafer handling robot, an integrated design methodology for high-speed high precision single beam system is proposed in this paper Strict mathematical modelling and identification processes of the actuating subsystem are performed Parametric studies and experiments of step response of the system are conducted to investigate the influence of the interactions between control and mechanical parameters on the system, where the stiffness and inertia of the system is taken as the mechanical design variables According to the analysis of the system performance, a multi-objective optimization problem together with nonlinear constraints is formulated Two algorithms to solve such optimization problem, CRS (controlled random search) and SQP (sequential quadratic programming), are programmed and the optimizing results respectively are compared and discussed Some conclusions was drawn at last

Development and implementation of NURBS interpolator with look-ahead technique

Abstract: With recent advances in high accuracy and high speed machining, the NURBS interpolator has shown significant effect on dealing with the free form curves and surfaces. The present study aims at developing the speed-controlled interpolator and implementing the real-time hardware. However, the system vibration at sharp corner is unavoidable, it reduces the tracking accuracy. This paper proposes and implements a NURBS interpolation algorithm with look-ahead technique to generate smooth trajectory command under the corner error constraints, the average feedrate is increased and so as to shorten the motion time. Experimental results indicate that the proposed NURBS interpolation algorithm is able to provide a satisfactory performance.

Two-Degree-of-Freedom Based Cross-Coupled Control for High-Accuracy Tracking Systems

Abstract: Recent work recognizes that cross-coupled control (CCC) can significantly improve the accuracy of contour tracking in biaxial systems. However, it's complicated to apply CCC to arbitrary contour because of extra requirements to calculation and switching the cross-coupled gains. In addition, since most of CCC are based on the PID controlled loops of the individual axes, performances are conserved in some sense. In this paper, we propose a structure for arbitrary regular contours by efficiently determining the cross-coupling gains for CCC with the two-degree-of-freedom (2DOF) controlled to the single axes. Furthermore, an approach for stability analysis of the CCC is posed. Experimental results for a two-axial motion system indicate that the proposed structure eliminates the contouring error significantly.

Analysis of delay-dependent stability for time-delay teleoperating systems with force-reflection

Abstract: When there exist a time-delay between the master and slave of bilateral systems with force-reflection,the stability and transparency of system gets worse.The algorithm based on passivity can guarantee the delay-independent stability.However,because the stability and transparency are in conflict,the transparency of this algorithm gets worse. In this papers,a new bilateral control algorithm based on absolute stable theory is put forward,which aims at the time- delay teleoperating system with force reflection from slave directly.In the new control algorithm,delay-dependent stability instead of delay-independent stability was taken as the aim of control design,it sacrifices some excessive stability to improve transparency.This control algorithm guarantees the stability and better transparency.Finally,a simulation is given to illustrate this approach.

Modeling and Identification for High-Speed Milling Machines

Abstract: Accurate modeling and identification to the dynamics of the feed drive system is significant in designing a high performance milling machine. In this paper, mathematical model of the feed drive system, including electromagnetic and mechanical aspects, is concluded. To be consistent with the controller design techniques, two different grey-box identification methods are discussed to estimate the model of a practical milling machine. It turns out that the sampled-data control system with a slower sample rate fits the system better than the faster one. Moreover, compared with the model estimated by partial continuous approach, the total discrete-time model achieves better results in the model validation.