Dongjun Zhang

Accuracy Analysis of Parallel Manipulators With Joint Clearance

Due to joint clearance, a parallel manipulators end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or non-overconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Geometric Contouring Control on the Smooth Surface

In this paper we concentrate on contouring control for surface machining. The object of the motion control system is tracking the spatial curve lying on the surface. Observing that the contour error can be approximated by the tracking error (projected to the normal subspace of the surface), we propose a new design procedure based on the geometrical properties of the curves and surfaces. Essentially the controllers look ahead using the information provided by the curvature of the curves and surfaces. The simulation results show the efficiency of the design method

Accuracy Analysis of General Parallel Manipulators with Joint Clearance

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.

Position loop-based cross-coupled control for high-speed machining

Recent work recognizes that cross-coupled control (CCC) can improve the accuracy of contour tracking in biaxial systems evidently. In this paper, a structure, ejecting the cross compensated control effort into the position input directly, is proposed. In order to obtain the cross-coupling gains, an approach for contour error approximation to arbitrary regular curve is set up. Furthermore, it turns to deal with an equivalent robust system when analyze the stability of the proposed CCC structure. The experimental results indicate that the contouring error is reduced by half when the introduced structure is applied.

Tracking controller design by relay method

For high speed high accuracy 3D machining, the controller design is very important. The object of the control system is to minimize the contour error which is related to the tracking error of each individual servo axis. From the analysis of the tracking error, both the phase delay and the gain difference generate tracking error. In this paper we propose a new relay auto-tuning method for the tracking control. First the critical points on the Nyquist graph of the servo dynamic is identified using the relay feedback method, then the PID controller and the feedforward controller is designed based on the system performance criteria. The simulation and the experimental results show the performance of the control system.

Assembly Problem of Overconstrained and Clearance-free Parallel Manipulators

To avoid deteriorating the mechanisms 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 unified contouring control in the task space

In the contouring control, the trajectory and the tolerance information are specified in the task space. Based on this observation we propose to design the controller in the task space directly. First, by defining the projection map on the cotangent space of the mechanical system the equation of motion is derived in the task space. Then a novel contouring controller is got based on the geometric control theory. The controller is transferred into the joint space for implementation. The simulation results show the performance of the controller.

Advanced path interpolation in high performance motion control systems

In the path following motion control system, the reference tool path of the machine tool is geometric curves predetermined by applications. The reference motion command for servo control system is generated based on the geometric tool path and the feedrate. The command generation module is called path interpolation. It is a classical problem in the motion control system. However, a clear formula is still missing in the literature. In this paper, path interpolation problem for the generic parametric tool path is formulated clearly in a mathematical way. By examining the parametrization of the tool path, the problem turns out to be an initial value problem for the ordinary differential equation system (ODE). From this formula, traditional interpolation algorithms, like digital differential analyzer (DDA) and digital increment algorithm, are easily derived. Numerical computation algorithms, such as the truncated Taylor expansion algorithm, the Runge-Kutta algorithm and the predictor-corrector algorithm, can be utilized. Considering reliability, accuracy and complexity, all those algorithms are analyzed and compared from three perspectives - theoretical comparison based on numerical analysis, simulation and experiments. Although the Taylor expansion algorithms and the predictor-corrector algorithms are widely used in the literature, the Runge-Kutta algorithms are highly recommended from our analysis and comparison. The Runge-Kutta algorithm of order 4 is recommended, if the computation resource is available.

Advanced contouring error compensation in high performance motion control systems

Because of nonlinearities, uncertainties and inherent performance limitations of the mechatronic system, there is a trade-off between tracking error minimization and robust stabilization. This implies that the tracking error is unavoidable in practice. Fortunately, in the path following motion control system, it is the geometric error that measures the quality of the product. Since the tracking error gives an upper bound on the geometric error, by the principle of uncertainty, more preference can be given to the geometric error dynamics to improve the quality of the product. For generic parametric tool path, although the geometric error is hard to be computed numerically, it can be estimated by a projection operator on the tracking error vector. Then the tasks of contouring error compensation are twofold: to internally stabilize the feedback system, and to minimize the estimated contouring error. A novel multiple-loop structure is proposed in this paper. By using this structure, the internal stability of the feedback system is guaranteed, if the norm of the compensator is less than a function value on the infinity norm of the tracking error dynamics. Experiments were done on milling machines to verify the feasibility of the proposed structure. Low order compensators were designed and compared with each other. In the experiments, the estimated contouring error was reduced by more than 20%, while the tracking error did not change too much.

Modeling and Identification for High-Speed Milling Machines

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.