Motion Planning for Industrial Robots Based on Task Process Decomposition

The existing research of the industrial robotic motion planning mainly focuses on the trajectory planning and the path planning, which aim at obtaining a minimum-time trajectory and finding an obstacle-free path respectively. In the trajectory planning, the jerks of robotic joints are usually not considered, so the smoothness of the robotic motion cannot be ensured. In the path planning, the complex spatial curves generally cannot be tracked easily, and it needs the fussy teach-and-playback operation. In this paper, based on the different constraint characteristic of the variable motion phases in the practical robotic task, the complicated task is decomposed into two kinds of sub processes, which are the free motion process and the constrained motion process. In the free motion process, the kinematic models of quasi trapezoidal waveform and quasi triangular waveform are proposed with the dynamic limits of maximum velocities, accelerations and jerks of robotic joints, so the minimum-time trajectory can be obtained with the motion smoothness. In the constrained motion process, the mathematical presentation of the task paths is extracted from the CAD models of the workpieces, so the complex spatial curves can be tracked autonomously without much teaching operation. In addition to the theoretical research, a robotic virtual prototyping system is also developed for the industrial arc welding production. The proposed research ensures the robotic motion smoothness, enhances the ability for tracking the complex spatial curves, and improves the quality and efficiency of the robotic motion planning.

SELF-ORGANIZED SEMANTIC FEATURE EVOLUTION FOR AXIOMATIC DESIGN

Aiming at the problem existing in the computer aided design process that how to express the design intents with high-level engineering terminologies, a mechanical product self-organized semantic feature evolution technology for axiomatic design is proposed, so that the constraint relations between mechanical parts could be expressed in a semantic form which is more suitable for designers. By describing the evolution rules for semantic constraint information, the abstract expression of design semantics in mechanical product evolution process is realized and the constraint relations between parts are mapped to the geometric level from the semantic level; With semantic feature relation graph, the abstract semantic description, the semantic relative structure and the semantic constraint information are linked together; And the methods of semantic feature self-organized evolution are classified. Finally, combining a design example of domestic high-speed elevator, how to apply the theory to practical product development is illustrated and this method and its validity is described and verified. According to the study results, the designers are able to represent the design intents at an advanced semantic level in a more intuitional and natural way and the automation, recursion and visualization for mechanical product axiomatic design are also realized.

COLLISION AVOIDANCE DECISION-MAKING MODEL OF MULTI-AGENTS IN VIRTUAL DRIVING ENVIRONMENT WITH ANALYTIC HIERARCHY PROCESS

Collision avoidance decision-making models of multiple agents in virtual driving environment are studied. Based on the behavioral characteristics and hierarchical structure of the collision avoidance decision-making in real life driving, delphi approach and mathematical statistics method are introduced to construct pair-wise comparison judgment matrix of collision avoidance decision choices to each collision situation. Analytic hierarchy process （AHP） is adopted to establish the agents＇ collision avoidance decision-making model. To simulate drivers＇ characteristics, driver factors are added to categorize driving modes into impatient mode, normal mode, and the cautious mode. The results show that this model can simulate human＇s thinking process, and the agents in the virtual environment can deal with collision situations and make decisions to avoid collisions without intervention. The model can also reflect diversity and uncertainly of real life driving behaviors, and solves the multi-objective, multi-choice ranking priority problem in multi-vehicle collision scenarios. This collision avoidance model of multi-agents model is feasible and effective, and can provide richer and closer-to-life virtual scene for driving simulator, reflecting real-life traffic environment more truly, this model can also promote the practicality of driving simulator.

A new algorithm for designing developable Bézier surfaces

A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.

TECHNOLOGY AND APPLICATION OF PRODUCT EVOLUTIONARY DESIGN BASED ON CONFIGURATION IN MASS CUSTOMIZATION MODE

Product customization has been recognized as an effective means to implement mass cus-tomization （MC）. A new theory and method for MC-oriented evolutionary design of configuration product is presented based on the study of developing law of evolutionary design in integrated envi-ronment, which focuses on the innovation and reuse properties of configuration product. The key technologies for general requirement modeling in quick response to customer requirement, multi-level stepwise configuration optimization driven by customer requirement and evolutionary deduction of product variable structure based on configuration association are thoroughly investigated. The suc-cessful application of the presented method in the development of real-life products demonstrates its utility, flexibility and robusticity.

Generalization of 3D Mandelbrot and Julia sets

In order to further enrich the form of 3D Mandelbrot and Julia sets, this paper first presents two methods of generating 3D fractal sets by utilizing discrete modifications of the standard quaternion algebra and analyzes the limitations in them. To overcome these limitations, a novel method for generating 3D fractal sets based on a 3D number system named ternary algebra is proposed. Both theoretical analyses and experimental results demonstrate that the ternary-algebra-based method is superior to any one of the quad-algebra-based methods, including the first two methods presented in this paper, because it is more intuitive, less time consuming and can completely control the geometric structure of the resulting sets. A ray-casting algorithm based on period checking is developed with the goal of obtaining high-quality fractal images and is used to render all the fractal sets generated in our experiments. It is hoped that the investigations conducted in this paper would result in new perspectives for the generalization of 3D Mandelbrot and Julia sets and for the generation of other deterministic 3D fractals as well.

REVERSE DESIGN APPROACH FOR MECHANISM TRAJECTORY BASED ON CODE-CHAINS MATCHING

Aiming at the problem of reverse-design of mechanism, a method based on the matching of trajectory code-chains is presented. The motion trajectory of mechanism is described with code-chain, which is normalized to simplify the operation of geometric transformation. The geometric transforma-tion formulas of scale, mirror and rotation for trajectory code-chain are defined, and the reverse de-sign for mechanism trajectory is realized through the analysis and solution of similarity matching between the desired trajectory and the predefined trajectory. The algorithm program and prototype system of reverse design for mechanism trajectory are developed. Application samples show that the method can break the restriction of trajectory patterns in matching, meet the demand of partial match-ing, and overcome the influence of geometric transformation of trajectory on the reverse design for mechanism.

Image-based Virtual Exhibit and Its Extension to 3D

In this paper we introduce an image-based virtual exhibition system especially for clothing product. It can provide a powerful material substitution function, which is very useful for customization clothing-built. A novel color substitution algorithm and two texture morphing methods are designed to ensure realistic substitution result. To extend it to 3D, we need to do the model reconstruction based on photos. Thus we present an improved method for modeling human body. It deforms a generic model with shape details extracted from pictures to generate a new model. Our method begins with model image generation followed by silhouette extraction and segmentation. Then it builds a mapping between pixels inside every pair of silhouette segments in the model image and in the picture. Our mapping algorithm is based on a slice space representation that conforms to the natural features of human body.

An efficient method for tracing planar implicit curves

This paper presents a method for tracing a planar implicit curve f（x, y）=0 on a rectangular region based on continuation scheme. First, according to the starting track-point and the starting track-direction of the curve, make a new fimction F（x, y）=0 where the same curve withf（x, y）=0 is defined. Then we trace the curve between the two domains where F（x, y）〉0 and F（x, y）〈0 alternately, according to the two rules presented in this paper. Equal step size or adaptive step size can be used, when we trace the curve. An irregular planar implicit curve （such as the curve with large curvatures at some points on the curve）, can be plotted if an adaptive step size is used. Moreover, this paper presents a scheme to search for the multiple points on the curve. Our method has the following advantages： （1） it can plot Co planar implicit curves; （2） it can plot the planar implicit curves with multiple points; （3） by the help of using the two rules, our method does not need to compute the tangent vector at the points on the curve, and directly searches for the direction of the tracing curve; （4） the tracing procedure costs only one of two evaluations of function f（x, y）=0 per moving step, while most existing similar methods cost more evaluations of the function.

Constrained multi-degree reduction of rational Bézier curves using reparameterization

Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.

ADAPTIVE LAYERED CARTESIAN CUT CELL METHOD FOR THE UNSTRUCTURED HEXAHEDRAL GRIDS GENERATION

Adaptive layered Cartesian cut cell method is presented to solve the difficulty of the tmstructured hexahedral anisotropic Cartesian grids generation from the complex CAD model. ＂Vertex merging algorithm based on relaxed AVL tree is investigated to construct topological structure for stereo lithography （STL） files, and a topology-based self-adaptive layered slicing algorithm with special features control strategy is brought forward. With the help of convex hull, a new points-in-polygon method is employed to improve the Cartesian cut cell method. By integrating the self-adaptive layered slicing algorithm and the improved Cartesian cut cell method, the adaptive layered Cartesian cut cell method gains the volume data of the complex CAD model in STL file and generates the unstructured hexahedral anisotropic Cartesian grids.

MODELING METHOD FOR PRODUCT STRUCTURE MAPPING BASED ON REVERSE SOLVING OF LOCUS AND MOTION

Aiming at the problem of structure design in reverse-design of mechanism, a structure mapping method based on reverse solving of locus and motion （RSLM） is presented. The mechanism scheme meeting the requirements of geometric and structural features is obtained through RSLM. The element instance subsets related to component are established based on the element type mapping, pair structure type mapping and design knowledge mapping between components and elements layer by layer. The assembly position mapping of elements is established based on the topological structure information of mechanism scheme, and the product modeling of structure mapping is realized. The algorithm program and prototype system of product structure mapping based on RSLM are developed. Application samples show that the method implements the integration of scheme design, assembly design and structure design, and modeling for product structure mapping based on RSLM. The feasibility of assembly is analyzed in scheme design that contributes to reducing the design error, and raising the design efficiency and quality.

Trimming self-intersections in swept volume solid modeling

Swept volume solid modeling has been applied to many areas such as NC machining simulation and verification, robot workspace analysis, collision detection, and CAD. But self-intersections continue to be a challenging problem in the boundary representation of swept volume solids. A novel algorithm is presented in this paper to trim self-intersection regions in swept volume solids modeling. This trimming algorithm consists of two major steps: (1) roughly detecting self-intersection regions by checking intersections or overlapping of the envelop profiles; (2) splitting the whole envelop surfaces of the swept volume solid into separate non-self-intersecting patches to trim global self-intersections, and to trim local self-intersections, dividing local self-intersecting regions into patches and replacing self-intersecting patches with non-self-intersecting ones. Examples show that our algorithm is efficient and robust.

Self-organized evolution of mechanism kinetic scheme based on axiomatic design

The self-organized evolution technology of the mechanism kinetic scheme based on axiomatic design is presented. This technology tries to express the constraints between kinetic mechanisms briefly in a semantic form which is more familiar to the designers. Through the mapping process between the kinetic chain unit and the unit instance, the evolution from abstract unit to concrete engineering instance is achieved. The subdivision of unit coupling semantics is studied, and the evolution of semantics is finished. Also, the semantic constraints evolution of unit coupling semantics is described. The product structure models with function and assembly meanings are constructed based on the kinematic chain unit and unit coupling. It provides a basis to realize the inheritance and transfer of constraint information from conceptual design to design for assembly （DFA）. As the engineering practice result shows, the method can help the engineers express their And the automation, recursion and design intension more clearly and naturally in a high semantic level. visualization of the mechanism kinetic scheme design are realized

STABLE PROGRAMMED MANIFOLD SOLVER FOR VIRTUAL PROTOTYPING MOTION SIMULATION

Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its mtmerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.

REQUIREMENT PRODUCT CONFIGURATION IN MASS CUSTOMIZATION

On the basis of researching on requirement product configuration in mass customization, the concept of product family requirement class （PFRC） and requirement-matching template are put forward. A case-based requirement product configuration （CB-RPC） model and corresponding requirement product model are established. The result of requirement product configuration is obtained by using the method of two-level similar matching. In addition, the effect of the method on requirement responding is analyzed. Finally, the model and the method given are applied in elevator industry, and have improved the enterorise＇s ability of rapid responding to customer＇s reouirements.

Constrained multi-degree reduction of triangular Bézier surfaces

This paper proposes and applies a method to sort two-dimensional control points of triangular Bezier surfaces in a row vector. Using the property of bivariate Jacobi basis functions, it further presents two algorithms for multi-degree reduction of triangular Bezier surfaces with constraints, providing explicit degree-reduced surfaces. The first algorithm can obtain the explicit representation of the optimal degree-reduced surfaces and the approximating error in both boundary curve constraints and corner constraints. But it has to solve the inversion of a matrix whose degree is related with the original surface. The second algorithm entails no matrix inversion to bring about computational instability, gives stable degree-reduced surfaces quickly, and presents the error bound. In the end, the paper proves the efficiency of the two algorithms through examples and error analysis.

Model evolvement and reuse technology of injection molding machine based on performance knowledge

To illuminate the necessity of model evolvement and reuse, dynamics of injection molding machine＇s product models are analyzed. The performance knowledge is used to support the model evolvement and reuse. The driven factors of mechanical product model are concluded. The dynamic characteristics of reuse. Finally, HT1800X1N series injection molding machines are taken as examples to illuminate that the arithmetic is correct and practical.

CONCEPTUAL MODELING BASED ON LOGICAL EXPRESSION AND EVOLVEMENT

Aiming at the problem of abstract and polytype information modeling in product conceptual design, a method of conceptual modeling based on logical expression and evolvement is presented. Based on the logic expressions of the product conceptual design information, a fimction/logic/strucmre mapping model is set up. First, the fimction semantics is transformed into logical expressions through fimction/logic mapping. Second, the methods of logical evolvement are utilized to describe the fimction analysis, fimction/strucmre mapping and structure combination. Last, the logical structure scheme is transformed into geometrical sketch through logic/structure mapping. The conceptual design information and modeling process are described uniformly with logical methods in the model, and an effective method for computer aided conceptual design based on the model is implemented.

METABALL-BASED TRANSITION SURFACES

Metaball-based constraint deformation technique is used to change the definition of r, the straight-line distance from a space point to a constraint center in the original calculation of the potential function. By replacing the parameter of the pararnetrized surface w with the straight-line distance r, a method of building transition surfaces according to cormected boundary curves and skeleton curves is proposed. The method has no restrictions on boundary curves that control the space shapes of transition surfaces or on types of skeleton curves, thus transition surfaces, which reach C^1 continuity and are more abundant in shapes and natural, can be obtained.