摘要
喷涂机器人系统是汽车制造中的关键设备之一,其结构设计与相关理论方法的研究具有重要的学术和应用价值。本文以研制喷涂机器人系统为目标,系统地研究了喷涂机器人机构运动学、动力学、机构性能评价及尺寸优化、几何参数标定等相关理论,开发了喷涂机器人相关单元技术,最后,建造了机器人样机系统一套,并完成了样机标定。取得了如下主要研究成果:
运用对偶四元数来描述机器人的空间运动及位姿,并建立起与传统的D-H参数表示法的映射关系。根据这种映射关系的特点及其内蕴的性质,将射影几何学的方法引入机器人的运动学分析,采用射影映射将表示机器人空间位姿及运动的固有刚体运动群SE(3)的元素,映射为7维射影空间中Study二次曲面上的点,从而建立起以几何学为基础的运动学分析方法。并利用两个3R子机构的约束流形与Study曲面相交,建立非球型手腕6R机器人的运动学逆解算法,该算法可作为空心非球型手腕喷涂机器人离线编程技术开发及轨迹规划的基础。
基于Kane方程建立机器人机构的动力学模型,为了解决传统Kane方程中偏速度求取困难的问题,引入基于旋量理论求得的机构物体Jacobian矩阵。并建立起物体Jacobian与偏速度的对等关系,证明二者在数学表达上的一致性。旋量形式的物体Jacobian使旋量理论描述刚体运动形式简洁、几何意义明确的特点体现在Kane方程中。同时基于Newton-Euler方程得到各杆件速度、加速度的递推公式,最终构建出机器人动力学模型。通过数值仿真与软件仿真的结果比较,证明了所建立动力学模型的正确性,在此基础上,基于机器人关节峰值扭矩及惯量匹配原则,计算出在加减速阶段作用在电机轴上的峰值扭矩,及折算到电机轴上的转动惯量,根据这两组参数选定所需的伺服电机型号。
为了对机器人机构的速度及加速度性能进行评价,根据一阶Jacobian矩阵和二阶Hessian矩阵的条件数,建立机器人机构的速度全域性能指标和加速度全域性能指标。在Hessian矩阵的求取过程中,深化旋量表示法的应用,推导出基于指数积公式的Hessian矩阵元素求解方程,使得求解过程简单易行且几何意义明确。进一步,以机构速度和加速度的全域性能指标为优化目标研究喷涂机器人连杆尺寸与速度及加速度性能之间的关系,在保证速度全域性能最优的情况下,求得主连杆尺寸组合为0.8m和1.5m,在保证加速度性能全域最优的情况下,求得主连杆尺寸组合为1.1m和1.2m。为了对具有相同功能的不同型号的机器人产品的综合性能进行评价,建立了机器人综合性能评价的指标体系。提出从系统演化的角度来分析研究产品性能形成的机理,并用自组织特征映射算法模拟系统演化过程,最终实现对其综合性能的评价,并以实例证明了这种评价方法的有效性。
根据此前的设计理论完成空心非球型手腕喷涂机器人的详细设计,完成零件加工及整机装配,利用YASKAWA伺服系统搭建了机器人控制系统。为了对机器人进行几何参数误差标定,建立基于MDH参数的运动学模型,并通过Jacobian矩阵扩展矩阵的奇异值分解得到几何参数误差中的冗余项,排除冗余后得到简化的几何参数误差标定模型。基于该模型进行计算机仿真,经过补偿使位置误差的最大值由标定前的4.978mm减小到0.056mm,补偿结果完全满足喷涂机器人工作的精度要求,证明了标定模型的有效性。进一步,进行了喷涂机器人的标定实验,使用激光跟踪仪对机器人工具端的空间位置进行了数据测量,计算出喷涂机器人机构的实际几何参数误差,并进行了参数误差补偿。标定后机器人工具端位置误差由14.46mm减小到0.12mm,实验结果验证了标定模型的准确性,机器人进行几何参数误差补偿后能够满足工作的精度要求。
Paint Robot is one of the key systems for automobile manufacturing, and therefore its structural design, related theories and methodologies have significant value in the academic researches and the industrial circles. Several key issues relevant to the development of a Paint Robot system are extensively investigated in this dissertation, such as the robot kinematics, dynamics, mechanism performance evaluation, dimension optimization, and geometry parameter calibration, et al. A prototype has been developed and calibrated. The following contributions have been made.
The space motion and pose of the robot are described using the dual quaternions. The mapping between the traditional D-H parameter method and the dual quaternions is established. According to the characteristics of this mapping, the projective geometry method is introduced for the kinematics analysis of the robot. The elements of the rigid motion group, which expresses the space pose and motion of the robot, can be mapped to a point of the Study quadratic surface in the seven-dimension projective space utilizing the projective mapping. Then, the kinematics analysis method is established via geometry frame. The inverse kinematics algorithm of the non-spherical wrist 6R robot is realized utilizing the intersection of the constraint manifolds of two 3R sub-mechanism with the Study quadratic surface. This algorithm serves as the basis of the offline programming and trajectory planning of the non-spherical wrist robot.
The dynamics model of the robot is established based on Kane Equation, and the body Jacobian matrix of the robot based on screw theory is introduced to solve the difficult problem of the partial rate in the traditional Kane Equation. The consistency in the mathematical expression of the body Jacobian matrix and the partial velocity is demonstrated. Utilizing screw theory, the body Jacobian matrix in screw form makes the Kane Equation simple and clear in geometric meaning. The velocity and acceleration of the links can be derived from the recursive formula based on Newton-Euler equation. The dynamic model of the robot is then established. The dynamic model is validated by comparing the computational analysis results with the software simulation. The peak torque and the moment of inertia on the motor shaft in the acceleration and deceleration phases are calculated based on the peak torque and the inertia matching principle. The servo motors are selected according to these two sets of parameters.
In order to evaluate the velocity and acceleration performances of the robot, the global performance index of the velocity and acceleration is established according to the condition number of Jacobian matrix and Hessian matrix. The solving equations for the elements of Hessian matrix are derived based on the exponential product formula. The solution process is simplified by the application of screw theory. Moreover, setting the global performance index of the velocity and acceleration as the optimization objective, the relationship between the size of the links and the performance index of the robot is investigated. The size combinations of the main links are: 0.8m and 1.5m under the optimal performance of global velocity; 1.1m and 1.2m under the optimal performance of global acceleration. The index system for the synthetical performance evaluation of different robots with the same functions is also established, where the formation of the performance level is derived from the system evolution’s perspective, and the self-organization feature map algorithm is utilized to simulate the process of evolution. The effectiveness of the proposed index system is validated through a specific case study.
The detailed design of the robot with non-spherical hollow wrist is completed according to the previous design theory. The manufacturing and assembly has been finished; and the control system is built upon YASKAWA servo system. The MDH kinematics model is established for the geometry error calibration of the robot. The redundant items of the geometry error are derived using singular value decomposition of the extended Jacobian matrix. And a simplified calibration model is obtained after excluding the redundant geometric parameters. Computational analysis is performed, where the maximum position error is reduced from 4.978mm to 0.056mm after the compensation. The results fully satisfy the accuracy requirements of the Paint Robot. Furthermore, the calibration experiment has been performed, where a laser tracker tool is utilized to measure the space position of the robot; and the real geometric error is calculated to compensate the parameter error. The maximum position error is reduced from 14.46mm to 0.12mm after the calibration. The experimental results validate the calibration model and further reveal the fact that the developed robot could meet the accuracy requirements of painting works after the error compensation.
引文
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