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.     

A flexible quantitative method for NC machining verification using a space-division based solid model

A geometric-modeling method called Graftree and a system design of an NC (numerical control) machining verifier based on Graftree are proposed. Graftree is constructed by combining Oct-tree and constructive solid geometry (CSG) so as to simulate machining processes precisely in three-dimensional space. Using Graftree, the Boolean operation produces no risk of yielding topological conflicts, which often cause the simulation to stop abnormally. Based on the properties of Graftree, an NC machining verifier is designed to consist of three individual subsystems: data-input operations, geometric simulation, and interactive verification, i.e., visuluatzation of machining scenes and evaluation of the machined product using models of the measuring instruments. This design lets the users watch selectively only the machining steps they want to check precisely, and verify the machining according to dimensional tolerance.     

Computer aided contouring operation for traveling wire electric discharge machining (EDM)

This paper develops a computational method for numerical control (NC) of traveling wire electric discharge machining (EDM) operation from geometric representation of a desired cut profile in terms of its contours. Normalized arc length parameterization of the contour curves is used to represent the cut profile and a subdivision algorithm is developed together with kinematic analysis to generate the required motions of the machine tool axes. In generating the tool motions for cutting sections with high curvatures such as corners with small radii, a geometric path lifting method is presented that increases the machining gap and prevents gauging or wire breakage.     

Iso-planar interpolation for the machining of implicit surfaces

The paper presents an approach for on-line path generation and interpolation for the machining of implicit surfaces. For a given implicit surface, once the cutting plane direction and cut-in points have been selected, iso-planar tool paths and interpolated points can be calculated on-line according to the feedrate and scallop height requirements. The approach enables the tool position and orientation to be correctly calculated at each interpolated point. Validation examples are provided for the interpolation of cyclide surfaces with planar and curved boundaries.     

Simulation refinement for concurrency verification

In recent years, we applied and extended the theory of Abadi and Lamport (1991) [1] on the existence of refinement mappings. The present paper presents an overview of our extensions of the theory. For most concepts we provide examples or pointers to case studies where they occurred. The paper presents the results on semantic completeness. It sketches out how the theory is related to the other formalisms in the area. It discusses the tension between semantic completeness and methodological convenience. It concludes with our experience with the theorem provers NQTHM and PVS that were used during these projects.     

Discrete simulation of NC machining

We describe a method for simulating and verifying the correctness of Numerical Control (NC) programs. NC programs contain the sequence of cutting tool movements which machine raw stock into a finished object. Our method is based on a discrete approximation of the object by a set of points. A vector is passed through each of the points and machining is simulated by finding the intersections of tool movements with these vectors. We present a point-selection method and an analysis that shows that the error introduced by the approximation can be made as small as desired. The run time is inversely proportional to the allowable error and the size of the cutting tool, and directly proportional to the distance that the cutting tool moves.This research was supported in part by the National Science Foundation under Contract No. DMC 8512621 and by the Ford Motor Company.     

Machine models and tool motions for simulating five-axis machining

This paper presents a method of determining the tool motion of a five-axis machine. The method is motivated by the imprint point method, where points on the machined surface are computed based on the tool position and tool motion. While simple linear motion can be used as a coarse approximation to this motion, this paper looks at more accurate models of tool motion based on machine kinematics that can be generalized and applied to any CNC machine with one tool head. A kinematic chain is created by decomposing the linear motion of a machine’s translational and rotational axes into parameterized affine transformations, and a hierarchical model of the machine combines the transformations to provide an accurate model of machine motion.     

A study on three-dimensional vision system for machining setup verification

In computerized numerical control (CNC) machine tools, it is often a time-consuming and error-prone process to verify the Euclidean position accordance between the actual machining setup and its designed three-dimensional (3D) digital model. The model mainly contains the work piece and jigs. The mismatch between them will cause a failure of simulation to precisely detect the collision. The paper presents an on-machine 3D vision system to quickly verify the similarity between the actual setup and its digital model by real and virtual image processing. In this paper, the system is proposed first. Afterwards, a simple on-machine camera calibration process is presented. This calibration process determines all the camera's parameters with respect to the machine tool's coordinate frame. The accurate camera mathematical model (or virtual camera) is derived according to the actual imaging projection. Both camera-captured real images and system-generated virtual images are compensated to make them theoretically and practically identical. The mathematical equations have been derived. Using the virtual image as a reference and then superimposing the real image onto it, the operator can intuitively verify the Euclidean position in accordance to the actual setup and its 3D digital model.     

Fast and numerically stable methods for the computation of Zernike moments

Zernike moments (ZMs) are used in many image processing applications due to their superior performance over other moments. However, they suffer from high computation cost and numerical instability at high order of moments. In the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved. The analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property. There are three recursive methods which are normally used in ZMs calculation—Prata’s, Kintner’s and q-recursive methods. The earlier studies have found the q-recursive method outperforming the two other methods. In this paper, we modify Prata’s method and present a recursive relation which is proved to be faster than the q-recursive method. Numerical instability is observed at high orders of moments with the q-recursive method suffering from the underflow problem while the modified Prata’s method suffering from finite precision error. The modified Kintner’s method is the least susceptible to these errors. Keeping in view the better numerical stability, we further make the modified Kintner’s method marginally faster than the q-recursive method. We recommend the modified Prata’s method for low orders (≤90) and Kintner’s fast method for high orders (>90) of ZMs.     

命令式程序终止性验证方法综述

作为软件完全正确性的重要组成部分,程序终止性受到越来越多的关注。旨在跟踪国内外针对命令式程序的终止性验证方法,调研该领域的最新研究成果,同时提出解决该问题的建议性方法框架,对命令式程序终止性研究提供有意义的帮助。给出了程序终止性问题的定义,介绍了已有的数值程序、堆操作程序终止性验证方法,并分别进行了分析与对比。总结了当前研究中存在的难点与热点问题,给出了一种基于模型检验的C程序终止性验证框架,该框架可以作为研究命令式程序终止性的基本框架。     

A comparison of simulation techniques and algebraic techniques for verifying concurrent systems

Simulation-based assertional techniques and process algebraic techniques are two of the major methods that have been proposed for the verification of concurrent and distributed systems. It is shown how each of these techniques can be applied to the task of verifying systems described as input/output automata; both safety and liveness properties are considered. A small but typical circuit is verified in both of these ways, first using forward simulations, an execution correspondence lemma, and a simple fairness argument, and second using deductions within the process algebra DIOA for I/O automata. An extended evaluation and comparison of the two methods is given.Supported by NSF grant CCR-89-15206, by DARPA contracts N00014-89-J-1988 and N00014-92J-4033, and by ONR contract N00014-91-J-1046.     

An innovative approach for automatic generation,verification and optimization of part programs in turning

Continuous innovation of products and optimization of manufacturing processes are of fundamental importance for preserving competitiveness. In the last decades, several approaches based on analytic models for optimization of basic machining operations such as cylindrical turning and face milling have been developed. However, the analytic approaches may not be adequate for real industrial applications, since they are based on average cutting parameters and thus they are not capable of taking into account the effect of complex geometries and instantaneous cutting conditions. In this paper, an innovative integrated system for automatic generation of optimized part programs in turning based on realistic machining simulation is proposed. The system components are described in detail and the machining simulator is validated by comparison with the results of real cutting tests. Then, the optimization approach is applied to a simple case study. The results show that the behavior of the cost function is rather complex, even for simple workpieces. Moreover, the simulator can detect unfeasible combinations of cutting parameters and thus reduce inline part program refinement and optimization. The optimal combination of cutting parameters determined by the new system was competitive with the solutions derived from tool specifications or proposed by a machining expert.     

3-D object decomposition with extended octree model and its application in geometric simulation of NC machining

The paper discusses the development of a prototype solid modeling system based on the extended octree modeling approach and its applications in 3-D NC machining simulation and automatic verification. Along with a simple hierarchical data structure, the extended octree model uses the face boundary information (i) to represent complex objects, (ii) to improve object representational accuracy, and (iii) to accelerate the model updating procedures in a graphic simulation process. The improved representational accuracy makes it possible to carry out automatic NC program verification by generating the machined model of the part through the simulation and comparing it with the designed model of the part. The paper also addresses the issues of model conversions from CSG and B-Rep schemes to the corresponding extended octree models and the issues of carrying out Boolean operations on those extended octree models. A prototype system has been implemented and is integrated with AutoCAD AME solid modeler for object modeling and for NC simulation purpose.     

Admissible simulation relations,set-valued feedback,and controlled invariance

This work is a continuation of the author’s study of simulation relations between nonlinear input–output systems with disturbances. Previously we derived a criterion under which a “pointwise” simulation condition implies simulation by so-called “admissible” inputs and disturbances (that is, inputs and disturbances that yield time-dependent vector fields satisfying C ¹ Carathéodory conditions). This criterion included a certain constant-rank assumption. In this paper we use the theory of set-valued mappings and differential inclusions to derive analogous results in which the constant-rank assumption is replaced by a compactness provision that augments the pointwise simulation condition. We illustrate our simulation results by deriving a sufficient condition for achieving global controlled invariance of a (possibly singular) nonlinear system through the use of a set-valued feedback law.     

Remote real-time CNC machining for web-based manufacturing

Today's machining shop floors, characterized by large variety of products in small batch sizes, require dynamic control and real-time monitoring capabilities that are responsive and adaptive to the rapid changes of production capability and functionality. It is especially true when the shop floors are combined with the e-manufacturing concept. However, a highly efficient infrastructure that can integrate the pieces of automated equipment together and link them to the e-manufacturing is still missing. The objective of this research is to develop an appropriate methodology with open architecture for real-time monitoring and remote control of networked CNC machines. A framework named Wise-ShopFloor (Web-based-integrated sensor-driven e-ShopFloor) is designed for this purpose. Within the context, this paper presents a new enabling technology to bring traditional CNC machine tools on-line with combined monitoring and control capability. Issues such as architecture design, methodology development, and prototype implementation are addressed through a milling machine case study. It is expected that the developed technology can be readily applied to real shop floor environments with increased productivity, flexibility, and responsiveness.     

Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification

This paper presents an algebraic based approach and a computational framework for the simulation of multi-axis CNC machining of general freeform tools. The boundary of the swept volume of the tool is precisely modeled by a system of algebraic constraints, using B-spline basis functions. Subdivision-based solvers are then employed to solve these equations, resulting in a topologically guaranteed construction of the swept volume. The presented algebraic-based method readily generalizes to accept tools of arbitrary free-form shape as input, and at the same time, delivers high degree of precision.Being a common representation in CNC simulations, the computed swept volume can be reduced to a dexels’ representation. Several multi-axis test cases are exhibited using an implementation of our algorithm, demonstrating the robustness and efficacy of our approach.     

Boolean operations for 3D simulation of CNC machining of drilling tools

This paper addresses the simulation of drilling tools CNC machining. It describes a novel approach for the computation of the boundary representation of the machined tools. Machining consists of a sequence of boolean operations of difference between the tool and the grinding wheels through time. The proposed method performs the dynamic boolean operations on cross sections of the tool and it reconstructs the 3Dmodel by tiling between the cross sections. The method is based on classical computational geometry algorithms such as intersection tests, hull computations, 2D boolean operations and surface tiling. This approach is efficient and it provides user control on the resolution of the operations.     

A verifiable simulation model for real-world microscopic traffic simulations

This article presents a scientific discussion about the ongoing progress in the development of traffic simulation system platforms. As part of the discussion, the presentation introduces a simulation model that is based on the fully functional, real-world online traffic information system OLSIMv4 which is the updated version of the traffic information platform for the highway network of North Rhine-Westphalia (Germany). The simulation model consists of a simulation engine and a combination of several subject-specific model families such as vehicle models, microscopic traffic models, detector models, and tuning element models. Additionally, it provides a data model for arbitrary road traffic networks in highway and urban environments.The presentation includes a demonstration of how to form and initialize all relevant system components by providing an example for each component. The demonstrations use the declarative programming language Maude to form and initialize the components due to its simplicity and expressive power. The components facilitate their enhancement by a verification and validation management approach. The goal of the enhancement effort is to optimize the further development of the underlying OLSIMv4 system. In addition, the presented methodology stands exemplarily for the design and implementation of a whole class of systems. Additionally, the definitions of the simulation model can be used as a specification for an implementation with sequential, parallel, and distributed operation. Therein, independent entities can be inferred automatically by the simulation engine as part of an automatic domain decomposition. It has been implemented as a sequential and a parallel simulation that exploits CPU thread-level parallelism.     

Safety verification and reachability analysis for hybrid systems

Safety verification and reachability analysis for hybrid systems is a very active research domain. Many approaches that seem quite different, have been proposed to solve this complex problem. This paper presents an overview of various approaches for autonomous, continuous-time hybrid systems and presents them with respect to basic problems related to verification.