基于活动标架的喷涂机器人喷枪轨迹规划研究
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摘要
喷枪轨迹自动规划是喷涂机器人智能化的重要研究内容。目前在喷涂机器人喷枪轨迹规划研究中,喷涂曲面CAD几何模型大都基于网格模型,网格模型缺少边、曲线等几何信息,存在大量冗余信息,网格化方法对于规则曲面过于繁琐,对大曲率复杂曲面则容易出现网格丢失或重叠等情况,增加了网格修补和小曲面上短喷涂路径连接的轨迹规划难度,造成喷涂轨迹规划效率和喷涂质量的下降。本研究针对喷涂产品的CAD参数化模型,运用微分几何理论并结合喷涂工艺,从喷枪模型、路径模式、喷涂累积模型、喷涂轨迹规划、喷涂轨迹到喷枪轨迹的转化、组合曲面路径等方面进行了研究。主要研究内容如下：
1.针对喷涂曲面CAD参数化模型,以产品模型数据交换标准STEP格式作为数据交换中性格式,利用从STEP标准中提取的产品几何模型数据,转换为喷涂轨迹规划所需的曲面表达参数。
2.运用微分几何曲线论和曲面论,以空气喷枪椭圆双α分布模型为喷涂沉积厚度模型,对平面上直线路径模式和曲线路径模式的连续累积喷涂厚度进行了对比研究；通过对曲面上一点喷涂厚度和曲面度量关系分析,得出了曲面上喷枪沉积模型和曲面度量的关系。
3.基于微分几何活动标架法,以规则曲面上给定喷涂路径下的累积喷涂厚度模型为对象,定义了速比系数和喷涂方向系数,建立了喷涂区域内一点与喷涂区域中心点累积厚度模型沿曲面喷涂轨迹方向法曲率的关系。对规则曲面给出可行喷涂路径,在喷枪等高度、匀速喷涂条件下,以曲面上实际涂层厚度与理想喷涂厚度偏差最小为优化目标,基于活动标架法对喷枪速度和轨迹间距进行了优化计算,根据喷涂速度和涂层累积厚度关系将喷涂速度转化为路径间距的函数,使优化问题转变为一维变量优化,简化了优化问题,并给出了参数曲面上喷涂轨迹优化的详细计算过程和公式,比较了柱面上不同路径和间距对喷涂厚度和均匀度的影响。
4.基于微分几何Gauss-Bonnet理论,确立了偏移起始测地曲线和偏移起始截面且测地曲率最小的喷涂轨迹规划方法。通过理论分析和公式推导得出了偏移起始曲线轨迹规划方法中起始测地曲线的特性和计算公式,结合喷涂曲面上喷涂厚度均匀性和喷涂时间最小的优化目标确定了偏移起始截面法中最优化的起始截面。基于活动标架和外微分法推导了喷涂轨迹到喷枪轨迹的转化关系,并给出了喷枪位置和姿态的运动公式。
5.对组合曲面,根据单曲面片喷涂轨迹和曲面片交线的关系,给出交线区域的喷枪沉积模型和喷涂路径规划公式。利用图论,将组合曲面喷涂路径顺序看作开环哈密顿图,基于遗传算法对组合曲面喷涂路径序列和方向进行优化,给出了组合曲面上最短喷涂路径。
The auto-trajectory planning of spray gun is an important research in intelligent spray robot field. Currently the format of CAD model of the part to be painted is mostly based on tessellated models, which has the disadvantages such as lack of geometrical information about edges and curve and existing of much redundant information. Mesh model is too complicated for ruled surface and causes missing and overlapping facets for large curvature surface which increases the trajectory planning difficulty for mesh repairing and spray path connections of mall facets. It causes the lower trajectory planning efficiency and spray quality. For CAD parameterized model of spray surface, differential geometry theory combining with spray process is applied to the spray gun model, path pattern, spray accumulation model, spray trajectory planning, conversion of spray trajectory and spray gun trajectory optimization, and trajectory planning of compound surfaces. The major research content of this dissertation is as follows:
1. For CAD parametric model of part to be painted, using the standard for exchange of product STEP as the format of model in spray path planning, data drawn from STEP format of the part to be painted is converted into the parameters of surface expression required in spray trajectory planning.
2. Based on curve and surface theory of differential geometry, elliptic double-(3distribution model of air gun is used to generate the spray paths, a comparison between the raster pattern and spiral patterns path regarding continuous material deposion is made and draw a conclusion on the relationship between continuous material deposion and surfaces measurement.
3. Given the path of the regular surface, the relations of continuous material deposion model between a point and the center in the spary region along the normal curvature direction is specified based on the moving frames of differential geometry. The coefficients of velocity of one point to the center and sparying direction are defined. Spraying in equal height and constant velocity, regarding the mean square error of the material thickness deviation form required material thicknes as optimized objective, and spraying velocity is expressed as a function of overlapping distance, the optimization problem become a one-dimensional variable optimization, optimal spary gun velocity and overlapping distance are calculated. Material thickness and uniformity of two kinds of path and different overlapping distance on cylindrical surface are compared.
4. Based on Gauss-Bonnet theory of differential geometry, the method offseting start geodesic and offseting start section with minimum geodesic curvature on freeform surface are adopted to generate spraying trajectory. Considering uniformity of material thickness and a minimum spray time the start geodesic curve and the start section are specified by theoretical analysis and formula reduction. Based on the moving frame and exterior differentiation conclude relationship between the frames of spray trajectory on surface and tool ones, and gives motion formula of the position and oriention of spray gun.
5. According to the relationship between the spray path of single patch and the intersection line of the composite surface, material deposition model on intersection region is given. Using graph theory, the spray paths sequence on the composite surface is regarded as open-loop Hamiltonian graph, based on genetic algorithm the sequence and direction of spraying path of the composite surface are optimized, and the optimal results is obtained.
1.针对喷涂曲面CAD参数化模型,以产品模型数据交换标准STEP格式作为数据交换中性格式,利用从STEP标准中提取的产品几何模型数据,转换为喷涂轨迹规划所需的曲面表达参数。
2.运用微分几何曲线论和曲面论,以空气喷枪椭圆双α分布模型为喷涂沉积厚度模型,对平面上直线路径模式和曲线路径模式的连续累积喷涂厚度进行了对比研究；通过对曲面上一点喷涂厚度和曲面度量关系分析,得出了曲面上喷枪沉积模型和曲面度量的关系。
3.基于微分几何活动标架法,以规则曲面上给定喷涂路径下的累积喷涂厚度模型为对象,定义了速比系数和喷涂方向系数,建立了喷涂区域内一点与喷涂区域中心点累积厚度模型沿曲面喷涂轨迹方向法曲率的关系。对规则曲面给出可行喷涂路径,在喷枪等高度、匀速喷涂条件下,以曲面上实际涂层厚度与理想喷涂厚度偏差最小为优化目标,基于活动标架法对喷枪速度和轨迹间距进行了优化计算,根据喷涂速度和涂层累积厚度关系将喷涂速度转化为路径间距的函数,使优化问题转变为一维变量优化,简化了优化问题,并给出了参数曲面上喷涂轨迹优化的详细计算过程和公式,比较了柱面上不同路径和间距对喷涂厚度和均匀度的影响。
4.基于微分几何Gauss-Bonnet理论,确立了偏移起始测地曲线和偏移起始截面且测地曲率最小的喷涂轨迹规划方法。通过理论分析和公式推导得出了偏移起始曲线轨迹规划方法中起始测地曲线的特性和计算公式,结合喷涂曲面上喷涂厚度均匀性和喷涂时间最小的优化目标确定了偏移起始截面法中最优化的起始截面。基于活动标架和外微分法推导了喷涂轨迹到喷枪轨迹的转化关系,并给出了喷枪位置和姿态的运动公式。
5.对组合曲面,根据单曲面片喷涂轨迹和曲面片交线的关系,给出交线区域的喷枪沉积模型和喷涂路径规划公式。利用图论,将组合曲面喷涂路径顺序看作开环哈密顿图,基于遗传算法对组合曲面喷涂路径序列和方向进行优化,给出了组合曲面上最短喷涂路径。
The auto-trajectory planning of spray gun is an important research in intelligent spray robot field. Currently the format of CAD model of the part to be painted is mostly based on tessellated models, which has the disadvantages such as lack of geometrical information about edges and curve and existing of much redundant information. Mesh model is too complicated for ruled surface and causes missing and overlapping facets for large curvature surface which increases the trajectory planning difficulty for mesh repairing and spray path connections of mall facets. It causes the lower trajectory planning efficiency and spray quality. For CAD parameterized model of spray surface, differential geometry theory combining with spray process is applied to the spray gun model, path pattern, spray accumulation model, spray trajectory planning, conversion of spray trajectory and spray gun trajectory optimization, and trajectory planning of compound surfaces. The major research content of this dissertation is as follows:
1. For CAD parametric model of part to be painted, using the standard for exchange of product STEP as the format of model in spray path planning, data drawn from STEP format of the part to be painted is converted into the parameters of surface expression required in spray trajectory planning.
2. Based on curve and surface theory of differential geometry, elliptic double-(3distribution model of air gun is used to generate the spray paths, a comparison between the raster pattern and spiral patterns path regarding continuous material deposion is made and draw a conclusion on the relationship between continuous material deposion and surfaces measurement.
3. Given the path of the regular surface, the relations of continuous material deposion model between a point and the center in the spary region along the normal curvature direction is specified based on the moving frames of differential geometry. The coefficients of velocity of one point to the center and sparying direction are defined. Spraying in equal height and constant velocity, regarding the mean square error of the material thickness deviation form required material thicknes as optimized objective, and spraying velocity is expressed as a function of overlapping distance, the optimization problem become a one-dimensional variable optimization, optimal spary gun velocity and overlapping distance are calculated. Material thickness and uniformity of two kinds of path and different overlapping distance on cylindrical surface are compared.
4. Based on Gauss-Bonnet theory of differential geometry, the method offseting start geodesic and offseting start section with minimum geodesic curvature on freeform surface are adopted to generate spraying trajectory. Considering uniformity of material thickness and a minimum spray time the start geodesic curve and the start section are specified by theoretical analysis and formula reduction. Based on the moving frame and exterior differentiation conclude relationship between the frames of spray trajectory on surface and tool ones, and gives motion formula of the position and oriention of spray gun.
5. According to the relationship between the spray path of single patch and the intersection line of the composite surface, material deposition model on intersection region is given. Using graph theory, the spray paths sequence on the composite surface is regarded as open-loop Hamiltonian graph, based on genetic algorithm the sequence and direction of spraying path of the composite surface are optimized, and the optimal results is obtained.
引文
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