大型复杂自由曲面的喷涂机器人喷枪轨迹优化研究
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摘要
本文针对大型复杂自由曲面的喷涂机器人喷枪轨迹优化研究存在的问题，分别从喷枪模型的建模及其应用、大曲率特征自由曲面的喷涂分片规划、自然二次曲面上喷涂轨迹优化及复杂曲面上喷枪轨迹组合优化等角度对问题进行了系统的研究。研究并在一定程度上解决了目前面向复杂自由曲面喷涂机器人喷枪轨迹优化研究中，从喷枪3D模型的建立、提高大曲率特征自由曲面涂层均匀度和提高复杂曲面喷枪轨迹组合优化时喷涂效果的关键技术和算法。
文章阐述了面向喷涂机器人离线编程系统的主要结构和技术路线，提出了喷涂机器人喷枪轨迹优化模块为本文研究的重点。
在喷枪模型的建模及其应用中，基于一组喷釉实验数据，对喷枪模型的建模方法及其在平面喷枪轨迹优化中的应用进行了论述。运用二次样条曲线描述平面上涂料的生长情况，并建立了单位时间内平面和圆弧面上的涂层厚度表达式。分析了平面相对于圆弧面上涂层厚度不一致的原因，并给出了涂层厚度一致性优化方法。由于该类喷枪模型在喷枪轨迹优化时的复杂性，运用最小二乘曲线拟合的方法将复杂涂层厚度模型拟合成表达式较为简单的β分布模型以提高其实用性，给出了拟合算法，并将该模型运用到了平面喷枪轨迹优化研究中。
在大曲率特征自由曲面喷涂分片规划中，研究了大曲率特征自由曲面分片造型方法和喷枪轨迹生成方法。首先，结合喷涂半径和几何拓扑分片法，给出了提取曲面中大曲率特征曲面的方法；然后，针对大曲率曲面组曲面，提出了运用最小二乘曲线曲面拟合的方法对大曲率组曲面进行拟合造型，生成面片面积较大，形状较匀整的自然二次曲面，提出了运用修正的Gauss-Newton法对非线性最小二乘问题进行求解，并给出了大曲率组曲面造型算法和整个复杂自由曲面的分片规划算法；最后，提出了运用自然二次曲面上的母线规划其上喷枪轨迹的方法。
在面向自然二次曲面的喷涂轨迹优化中，研究了提高自然二次曲面上涂层均匀度的喷涂轨迹优化方法。基于一种前人已有的喷枪模型，运用面积几何放大定理建立了自然二次曲面上的喷枪3D模型，基于该3D模型在指定的喷枪路径上建立了自然二次曲面上喷枪轨迹参数优化目标函数，并运用黄金分割法和可行方向法对特定的优化问题进行求解。基于PA-PA原则，提出了先优化喷涂半径变化范围，后优化喷枪轨迹参数的方法对不同组合面片交界处的喷枪轨迹进行优化，并建立了不同组合面片交界处的喷枪轨迹参数优化目标函数，并运用乘子法对该类优化问题进行求解。
在复杂曲面喷枪轨迹组合优化中，重点研究了提高整个复杂曲面上涂层均匀度和涂料利用率的方法。首先，针对喷枪路径规划方式和面片几何形状对喷涂效果的影响，提出了优化两种喷枪路径规划方式的全局路径规划算法。其次，针对影响涂层质量的面片之间的涂层分布干涉问题，运用直接修正轨迹间距法、修正喷枪喷射高度法和两者相结合的方法对交界线平行和近似平行时的涂层分布干涉问题进行论述，分别给出了优化目标函数，并运用非线性整数优化的蚁群算法对问题进行求解。再次，针对影响喷涂效果三要素中的涂料利用率问题，建立了喷涂路径规划时的涂料利用率近似表达式，在满足涂层质量要求的前提下，结合路径分段计算喷枪路径拐角处的涂层厚度法和扫描搜索算法优化了涂料利用率的影响因素，达到提高涂料利用率的目的。最后，基于优化喷涂效率和涂料利用率的矛盾，给出了最佳喷涂效果的评价函数。
本文对主要的设计方案进行了仿真研究。仿真结果表明，本文提出的数学模型以及各种喷枪轨迹优化方法均可以获得良好的效果。
Be aimed at the problem that spray tool trajectory optimization for large complexfree-form curved surface, separately from the spray tool modeling and its application, thepartition of large curvature complex free-form curved surface, the spray tool trajectoryoptimization for natural quadric surface and the combinatorial optimization of spray tooltrajectory for complex curved surface to study it. The key algorithms of spray tool3Dmodeling and improve the coating thickness uniformity of large curvature complex free-formcurved surface and the spray effect of complex free-form curved surface are investigated anddeveloped.
The main structure and technical route of off-line programming system for painting robotare introduced in this paper. The key research content is proposed that module of spray tooltrajectory optimization.
Based on a group of spray glaze experimental data, the method of spray tool modelingand its application are discussed. Quadratic spline is used to describe coating growth on aplane and the coating thickness expressions are developed within unit time when spray on aplane and on an arc surface. The inconsistent reason of coating thickness is analysed on planeand arc surface, the consistent optimization method of coating thickness is given. Because theapplied complexity of this tool model, the least-square curve fitting method is used togenerate a β distributed model which improves its practicability, the fitting algorithm isdeveloped and the spray tool model is used to tool trajectory optimization on a plane.
The partition of large curvature free-form curved surface and the method of tooltrajectory generation are studied. First, combination with spray radius and topological method,the extraction of large curvature features surface from free-form surface is developed. Than,the least square method is used to fit big curvature surfaces and natural quadric surface oflarge area, leveling shape is generated. The method is proposed that the amendatoryGauss-Newton is used to solve nonlinear least squares problem. The modeling algorithm oflarge curvature surfaces and the partition planning algorithm of a free-form surface are given.Finally, the generatrix of natural quadric surface is used to planning the tool trajectory on it.
The method of tool trajectory optimization that improves coating uniformity is studied.Based on a existing spray tool2D model, the geometry enlarge theorem is used to develop thespray tool3D model on natural quadric surface and use it to establish optimization objectivefunction of tool trajectory along designated path. The golden section method and feasibledirection method are used to solve optimization problems. Based on the PA-PA principle, themethod that combine optimze spray radius with optimize tool trajectory parameters isproposed to optimize the tool trajectory which at the junction of different combination patchesand optimization objective functions are established, the multiplier method is used to solveoptimization problems.
The methods that improve coating uniformity and coating utilization factor are studied. Frist, for tool path planning way and geometric shape of patch have an effect on spray effect,the global path planning algorithm is proposed that based on optimization of two pathplanning ways. Secondly, be aimed at the problem that coating distribution interference whichinfluence coating uniformity, the methods of adjust spacing distance, adjust spray height andcombine both are used to study coating distribution interference when border parallel andapproximate parallel, the optimization objective functions are given respectively and the antcolony optimization algorithm for nonlinear integer programming is used to solve them.Again, be aimed at the problem that coating utilization factor influence spray effect, theapproximate expression of coating utilizing factor is given when path planning, on conditionthat meet coating uniformity, The method is proposed that combine coating thicknessfunctions at corner of paths with search algorithm to optimize coating utilization factor.Finally, based on the contradiction between optimize spray efficiency and coating utilizationfactor.
In this paper, simulations are performed for main design schemes, simulations show thatmathematical model and a variety of tool trajectory optimization can obtain good results.
文章阐述了面向喷涂机器人离线编程系统的主要结构和技术路线，提出了喷涂机器人喷枪轨迹优化模块为本文研究的重点。
在喷枪模型的建模及其应用中，基于一组喷釉实验数据，对喷枪模型的建模方法及其在平面喷枪轨迹优化中的应用进行了论述。运用二次样条曲线描述平面上涂料的生长情况，并建立了单位时间内平面和圆弧面上的涂层厚度表达式。分析了平面相对于圆弧面上涂层厚度不一致的原因，并给出了涂层厚度一致性优化方法。由于该类喷枪模型在喷枪轨迹优化时的复杂性，运用最小二乘曲线拟合的方法将复杂涂层厚度模型拟合成表达式较为简单的β分布模型以提高其实用性，给出了拟合算法，并将该模型运用到了平面喷枪轨迹优化研究中。
在大曲率特征自由曲面喷涂分片规划中，研究了大曲率特征自由曲面分片造型方法和喷枪轨迹生成方法。首先，结合喷涂半径和几何拓扑分片法，给出了提取曲面中大曲率特征曲面的方法；然后，针对大曲率曲面组曲面，提出了运用最小二乘曲线曲面拟合的方法对大曲率组曲面进行拟合造型，生成面片面积较大，形状较匀整的自然二次曲面，提出了运用修正的Gauss-Newton法对非线性最小二乘问题进行求解，并给出了大曲率组曲面造型算法和整个复杂自由曲面的分片规划算法；最后，提出了运用自然二次曲面上的母线规划其上喷枪轨迹的方法。
在面向自然二次曲面的喷涂轨迹优化中，研究了提高自然二次曲面上涂层均匀度的喷涂轨迹优化方法。基于一种前人已有的喷枪模型，运用面积几何放大定理建立了自然二次曲面上的喷枪3D模型，基于该3D模型在指定的喷枪路径上建立了自然二次曲面上喷枪轨迹参数优化目标函数，并运用黄金分割法和可行方向法对特定的优化问题进行求解。基于PA-PA原则，提出了先优化喷涂半径变化范围，后优化喷枪轨迹参数的方法对不同组合面片交界处的喷枪轨迹进行优化，并建立了不同组合面片交界处的喷枪轨迹参数优化目标函数，并运用乘子法对该类优化问题进行求解。
在复杂曲面喷枪轨迹组合优化中，重点研究了提高整个复杂曲面上涂层均匀度和涂料利用率的方法。首先，针对喷枪路径规划方式和面片几何形状对喷涂效果的影响，提出了优化两种喷枪路径规划方式的全局路径规划算法。其次，针对影响涂层质量的面片之间的涂层分布干涉问题，运用直接修正轨迹间距法、修正喷枪喷射高度法和两者相结合的方法对交界线平行和近似平行时的涂层分布干涉问题进行论述，分别给出了优化目标函数，并运用非线性整数优化的蚁群算法对问题进行求解。再次，针对影响喷涂效果三要素中的涂料利用率问题，建立了喷涂路径规划时的涂料利用率近似表达式，在满足涂层质量要求的前提下，结合路径分段计算喷枪路径拐角处的涂层厚度法和扫描搜索算法优化了涂料利用率的影响因素，达到提高涂料利用率的目的。最后，基于优化喷涂效率和涂料利用率的矛盾，给出了最佳喷涂效果的评价函数。
本文对主要的设计方案进行了仿真研究。仿真结果表明，本文提出的数学模型以及各种喷枪轨迹优化方法均可以获得良好的效果。
Be aimed at the problem that spray tool trajectory optimization for large complexfree-form curved surface, separately from the spray tool modeling and its application, thepartition of large curvature complex free-form curved surface, the spray tool trajectoryoptimization for natural quadric surface and the combinatorial optimization of spray tooltrajectory for complex curved surface to study it. The key algorithms of spray tool3Dmodeling and improve the coating thickness uniformity of large curvature complex free-formcurved surface and the spray effect of complex free-form curved surface are investigated anddeveloped.
The main structure and technical route of off-line programming system for painting robotare introduced in this paper. The key research content is proposed that module of spray tooltrajectory optimization.
Based on a group of spray glaze experimental data, the method of spray tool modelingand its application are discussed. Quadratic spline is used to describe coating growth on aplane and the coating thickness expressions are developed within unit time when spray on aplane and on an arc surface. The inconsistent reason of coating thickness is analysed on planeand arc surface, the consistent optimization method of coating thickness is given. Because theapplied complexity of this tool model, the least-square curve fitting method is used togenerate a β distributed model which improves its practicability, the fitting algorithm isdeveloped and the spray tool model is used to tool trajectory optimization on a plane.
The partition of large curvature free-form curved surface and the method of tooltrajectory generation are studied. First, combination with spray radius and topological method,the extraction of large curvature features surface from free-form surface is developed. Than,the least square method is used to fit big curvature surfaces and natural quadric surface oflarge area, leveling shape is generated. The method is proposed that the amendatoryGauss-Newton is used to solve nonlinear least squares problem. The modeling algorithm oflarge curvature surfaces and the partition planning algorithm of a free-form surface are given.Finally, the generatrix of natural quadric surface is used to planning the tool trajectory on it.
The method of tool trajectory optimization that improves coating uniformity is studied.Based on a existing spray tool2D model, the geometry enlarge theorem is used to develop thespray tool3D model on natural quadric surface and use it to establish optimization objectivefunction of tool trajectory along designated path. The golden section method and feasibledirection method are used to solve optimization problems. Based on the PA-PA principle, themethod that combine optimze spray radius with optimize tool trajectory parameters isproposed to optimize the tool trajectory which at the junction of different combination patchesand optimization objective functions are established, the multiplier method is used to solveoptimization problems.
The methods that improve coating uniformity and coating utilization factor are studied. Frist, for tool path planning way and geometric shape of patch have an effect on spray effect,the global path planning algorithm is proposed that based on optimization of two pathplanning ways. Secondly, be aimed at the problem that coating distribution interference whichinfluence coating uniformity, the methods of adjust spacing distance, adjust spray height andcombine both are used to study coating distribution interference when border parallel andapproximate parallel, the optimization objective functions are given respectively and the antcolony optimization algorithm for nonlinear integer programming is used to solve them.Again, be aimed at the problem that coating utilization factor influence spray effect, theapproximate expression of coating utilizing factor is given when path planning, on conditionthat meet coating uniformity, The method is proposed that combine coating thicknessfunctions at corner of paths with search algorithm to optimize coating utilization factor.Finally, based on the contradiction between optimize spray efficiency and coating utilizationfactor.
In this paper, simulations are performed for main design schemes, simulations show thatmathematical model and a variety of tool trajectory optimization can obtain good results.
引文
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