免Z轴旋转洗出的6-RSPS模拟器平台若干关键技术研究
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摘要
本文在分析国内外驾驶模拟器发展现状的基础之上,针对传统Stewart平台不能围绕Z轴3600旋转的特点,当车辆连续加速回转时,由于没有足够的转角,而不能提供持续的偏航角速度,降低了驾驶的逼真度。对此,本文提出了免Z轴旋转洗出的6-RSPS (revolute-spherical-prismatic-spherical)模拟器平台,并系统地研究了该平台机构的运动学、精度、动力学、工作空间、洗出算法等相关关键技术,并通过仿真验证了相关理论的有效性及可行性。具体研究内容如下：
提出了免Z轴旋转洗出的6-RSPS模拟器平台,确定了机构的实施方案；计算了机构的自由度；根据杆长矢量关系,得到了平台位置、姿态与伸缩支杆的长度和旋转支杆的旋转角度之间的关系,进而推导出机构的一组逆解,与经典的Stewart机构反解唯一的特点对比,6-RSPS结构的反解存在多个解；并确定相关参数的约束及优化条件,根据约束及优化条件得到了最优逆解；提出用BFS(Broyden-Fletcher-Shanmo)算法求解并联机构的运动学正解,取得良好的效果。
分析了影响6-RSPS模拟器平台位姿精度的因素,然后根据误差独立作用原理建立总体误差模型,并利用微分法通过对运动学方程求导建立各个环节的独立误差模型,探讨了旋转角度误差、杆长误差、静平台铰链误差及动平台铰链误差等各个误差对动平台的精度产生的影响,并通过仿真验证各个环节对动平台误差产生的影响；基于此模型可对6-RSPS机构的位姿精度进行评估,为进一步提高该机构的位姿精度提供了理论依据。
利用虚位移方法进行了机构的静力学分析,建立了静力学模型,得到了机构在静止或低速时多个位姿下伸缩支杆的驱动力以及旋转支杆的驱动力矩；然后利用凯恩方法进行了机构的逆动力学分析,建立了适用于6-RSPS机构的动力学模型,得到了机构在运动时伸缩支杆的驱动力以及旋转支杆的驱动力矩；并分别通过仿真验证了建模方法的正确性,为动力学优化、控制及仿真提供了良好的理论基础。
分析了对6-RSPS模拟器平台工作空间产生影响的因素,以及各因素对平台位姿的限制；并针对本机构的特点,提出了先搜索YOZ面上Y轴正半轴截面上的工作空间,然后将截面旋转360°求解三维工作空间的方法,使得搜索量大大减少,提高了搜索效率；并应用此搜索方法求得多个位姿状态下的工作空间。
在Stewart平台经典洗出算法的基础之上,根据6-RSPS模拟器平台的特点,提出了适用于本机构的免于Z轴旋转方向的洗出算法；并对算法中的相关参数选择进行了研究,然后进行了仿真实验,仿真结果表明：免于Z轴旋转方向的洗出算法对于6-RSPS模拟器平台是切实可行并合适的,可以避免Z轴旋转方向上的洗出算法,从而能够更精确地模拟车辆转弯时的感觉,可有效提高驾驶的逼真度。
In this paper, based on the analysis of the research status of the driving simulator, regarding the shortcomings of the traditional Stewart platform which can't rotate around the Z-axis within360°range, for this reason, the feeling of the driving simulator simulating vehicle turning continuously was limited. The6-RSPS platform which can rotate360°around the Z-axis was proposed. Some key technologies such as the kinematics, dynamics, accuracy analysis, workspace and washout algorithm of6-RSPS were studied systematically. The effective and feasibility of the theory proposed was verified by simulation. Specific research contents are as follows:
6-RSPS platform for simulator was proposed, the design scheme of the mechanism was determined, and the degree of freedom of the mechanism was calculated. According to the vector relationship of the link-length, the relationship between the position and orientation of the platform and the length of the telescopic link and rotation angle of link was obtained, then, a group of inverse solution was deduced. Compare to the classic Stewart platform which has only one inverse solution, the6-RSPS platform has more than one inverse solution. So the conditions of the constraints and optimization of the relevant parameters was proposed, and the optimal inverse solution of the mechanism was obtained according to the conditions. In order to get the forward kinematics of the6-RSPS parallel mechanism, BFS algorithm was proposed and great results was achieved.
The factors that influence the accuracy of the6-RSPS platform were analyzed, the overall error model was established in accordance with the principle of independent role of the error, the independent error model of all factors was established by using the differential method for kinematic equations. The impact on the accuracy of the moving platform generated by the error of rotate-angle, the error of link-length, the error of joint on static platform and the error of joint on moving platform and so forth were discussed, and verified the correctness by simulation. Based on this model, the accuracy of position and orientation of6-RSPS platform can be assessed, providing a theoretical basis for improving the accuracy of position and orientation further.
Statics of the6-RSPS mechanism was analysis by the principle of virtual work, and the model of statics was established. The driving force of stretching-link and driving torque of rotating-link under different position and orientation was obtained. Inverse dynamics of the6-RSPS mechanism was analyzed by Kane principle, and the model of inverse dynamics was established. The driving force of stretching-link and driving torque of rotating-link under moving was obtained. The correctness of the modeling was verified according to simulation, providing a theoretical basis for dynamic optimization, control and simulation.
The factors that influence the workspace of the6-RSPS platform were analyzed, and how these factors restrict the position and orientation of the platform was studied. Regarding the characteristics of the mechanism, proposing the method of search the workspace on the surface of YOZ on the positive of Y-axis cross-section, and then rotate360°, the3-D workspace was obtained. The efficiency of searching process was improved, and several workspaces under multiple position and orientation state were obtained using this method.
Based on the classical washout algorithm on the Stewart platform, regarding the characteristics of6-RSPS, a new washout algorithm suitable for the mechanism was proposed, and related parameters of the algorithm were researched. The results of simulation experiment show:the washout algorithm that without washouting the rotation on the direction of the Z-axis for6-RSPS platform is feasible and appropriate. It proved that it can be able to simulate the feeling of simulator simulating vehicle turning continuously more accurately and effectively.
提出了免Z轴旋转洗出的6-RSPS模拟器平台,确定了机构的实施方案；计算了机构的自由度；根据杆长矢量关系,得到了平台位置、姿态与伸缩支杆的长度和旋转支杆的旋转角度之间的关系,进而推导出机构的一组逆解,与经典的Stewart机构反解唯一的特点对比,6-RSPS结构的反解存在多个解；并确定相关参数的约束及优化条件,根据约束及优化条件得到了最优逆解；提出用BFS(Broyden-Fletcher-Shanmo)算法求解并联机构的运动学正解,取得良好的效果。
分析了影响6-RSPS模拟器平台位姿精度的因素,然后根据误差独立作用原理建立总体误差模型,并利用微分法通过对运动学方程求导建立各个环节的独立误差模型,探讨了旋转角度误差、杆长误差、静平台铰链误差及动平台铰链误差等各个误差对动平台的精度产生的影响,并通过仿真验证各个环节对动平台误差产生的影响；基于此模型可对6-RSPS机构的位姿精度进行评估,为进一步提高该机构的位姿精度提供了理论依据。
利用虚位移方法进行了机构的静力学分析,建立了静力学模型,得到了机构在静止或低速时多个位姿下伸缩支杆的驱动力以及旋转支杆的驱动力矩；然后利用凯恩方法进行了机构的逆动力学分析,建立了适用于6-RSPS机构的动力学模型,得到了机构在运动时伸缩支杆的驱动力以及旋转支杆的驱动力矩；并分别通过仿真验证了建模方法的正确性,为动力学优化、控制及仿真提供了良好的理论基础。
分析了对6-RSPS模拟器平台工作空间产生影响的因素,以及各因素对平台位姿的限制；并针对本机构的特点,提出了先搜索YOZ面上Y轴正半轴截面上的工作空间,然后将截面旋转360°求解三维工作空间的方法,使得搜索量大大减少,提高了搜索效率；并应用此搜索方法求得多个位姿状态下的工作空间。
在Stewart平台经典洗出算法的基础之上,根据6-RSPS模拟器平台的特点,提出了适用于本机构的免于Z轴旋转方向的洗出算法；并对算法中的相关参数选择进行了研究,然后进行了仿真实验,仿真结果表明：免于Z轴旋转方向的洗出算法对于6-RSPS模拟器平台是切实可行并合适的,可以避免Z轴旋转方向上的洗出算法,从而能够更精确地模拟车辆转弯时的感觉,可有效提高驾驶的逼真度。
In this paper, based on the analysis of the research status of the driving simulator, regarding the shortcomings of the traditional Stewart platform which can't rotate around the Z-axis within360°range, for this reason, the feeling of the driving simulator simulating vehicle turning continuously was limited. The6-RSPS platform which can rotate360°around the Z-axis was proposed. Some key technologies such as the kinematics, dynamics, accuracy analysis, workspace and washout algorithm of6-RSPS were studied systematically. The effective and feasibility of the theory proposed was verified by simulation. Specific research contents are as follows:
6-RSPS platform for simulator was proposed, the design scheme of the mechanism was determined, and the degree of freedom of the mechanism was calculated. According to the vector relationship of the link-length, the relationship between the position and orientation of the platform and the length of the telescopic link and rotation angle of link was obtained, then, a group of inverse solution was deduced. Compare to the classic Stewart platform which has only one inverse solution, the6-RSPS platform has more than one inverse solution. So the conditions of the constraints and optimization of the relevant parameters was proposed, and the optimal inverse solution of the mechanism was obtained according to the conditions. In order to get the forward kinematics of the6-RSPS parallel mechanism, BFS algorithm was proposed and great results was achieved.
The factors that influence the accuracy of the6-RSPS platform were analyzed, the overall error model was established in accordance with the principle of independent role of the error, the independent error model of all factors was established by using the differential method for kinematic equations. The impact on the accuracy of the moving platform generated by the error of rotate-angle, the error of link-length, the error of joint on static platform and the error of joint on moving platform and so forth were discussed, and verified the correctness by simulation. Based on this model, the accuracy of position and orientation of6-RSPS platform can be assessed, providing a theoretical basis for improving the accuracy of position and orientation further.
Statics of the6-RSPS mechanism was analysis by the principle of virtual work, and the model of statics was established. The driving force of stretching-link and driving torque of rotating-link under different position and orientation was obtained. Inverse dynamics of the6-RSPS mechanism was analyzed by Kane principle, and the model of inverse dynamics was established. The driving force of stretching-link and driving torque of rotating-link under moving was obtained. The correctness of the modeling was verified according to simulation, providing a theoretical basis for dynamic optimization, control and simulation.
The factors that influence the workspace of the6-RSPS platform were analyzed, and how these factors restrict the position and orientation of the platform was studied. Regarding the characteristics of the mechanism, proposing the method of search the workspace on the surface of YOZ on the positive of Y-axis cross-section, and then rotate360°, the3-D workspace was obtained. The efficiency of searching process was improved, and several workspaces under multiple position and orientation state were obtained using this method.
Based on the classical washout algorithm on the Stewart platform, regarding the characteristics of6-RSPS, a new washout algorithm suitable for the mechanism was proposed, and related parameters of the algorithm were researched. The results of simulation experiment show:the washout algorithm that without washouting the rotation on the direction of the Z-axis for6-RSPS platform is feasible and appropriate. It proved that it can be able to simulate the feeling of simulator simulating vehicle turning continuously more accurately and effectively.
引文
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