光电望远镜次镜精调Stewart机构优化标定方法
|
摘要
针对光电望远镜次镜精调Stewart机构的参数标定问题,在以往标定方法的基础上,首先,提出了在逆运动学模型基础上推导Stewart机构标定模型的方法,避免了正运动学求解析解困难、数值求解效率低且存在误差的问题;其次,对推导出的标定模型求解问题进行了分析,求解了其雅克比矩阵,针对模型系数矩阵不可逆的情况,提出了一种改进的高斯牛顿迭代法及具体的实验步骤;最后,分析了最小二乘原理导致的测量误差对精度影响大的现象,在Matlab中对设计的Stewart机构进行了标定仿真实验,在测量误差为0.1μm以下、标定精度平均提高56倍时,平均精度仅提高7.8倍。对样机进行标定后,位置精度平均提高了30.77倍,姿态精度平均提高了20.73倍。结果表明:该优化标定方法可以得到Stewart机构较精确的结构参数,从而有效提高其位姿调整精度。
Aiming at the parameters calibration of the fine tuning Stewart mechanism for the secondary mirror of the optoelectronic telescope,based on the previous calibration method,first of all,a method for calibrating model of Stewart mechanism is proposed based on the inverse kinematics model,which avoids the problem of the difficulty of solving the forward kinematics,the low efficiency of numerical solution and the error of the numerical solution.Secondly,the problem of solving the calibration model is analyzed,and the Jacobian matrix is solved and an improved Gauss-Newton iteration method and a specific experimental procedure are presented for the case that the model coefficient matrix is not reversible.Finally,the effect of measurement error caused by the least square principle is analyzed,the calibration simulation experiment on the designed Stewart mechanism is carried out by using the Matlab.The results show that the calibration accuracy is increased by 56 times when the measurement error is less than 0.1μm,the average precision is only increase by 7.8times when the measurement error is less than 1μm.After the calibration of the prototype,the average position precision is increased by 30.77 times,and the attitude accuracy is increased by 20.73 times.The more accurate structure parameters of Stewart mechanism can be obtained by using the optimization proposed calibration method,which can effectively improve the accuracy of position and attitude.
Aiming at the parameters calibration of the fine tuning Stewart mechanism for the secondary mirror of the optoelectronic telescope,based on the previous calibration method,first of all,a method for calibrating model of Stewart mechanism is proposed based on the inverse kinematics model,which avoids the problem of the difficulty of solving the forward kinematics,the low efficiency of numerical solution and the error of the numerical solution.Secondly,the problem of solving the calibration model is analyzed,and the Jacobian matrix is solved and an improved Gauss-Newton iteration method and a specific experimental procedure are presented for the case that the model coefficient matrix is not reversible.Finally,the effect of measurement error caused by the least square principle is analyzed,the calibration simulation experiment on the designed Stewart mechanism is carried out by using the Matlab.The results show that the calibration accuracy is increased by 56 times when the measurement error is less than 0.1μm,the average precision is only increase by 7.8times when the measurement error is less than 1μm.After the calibration of the prototype,the average position precision is increased by 30.77 times,and the attitude accuracy is increased by 20.73 times.The more accurate structure parameters of Stewart mechanism can be obtained by using the optimization proposed calibration method,which can effectively improve the accuracy of position and attitude.
引文
[1]安源,许晖,金光,等.动载体光电平台角振动隔振设计[J].半导体光电,2006,27(5):614-617.An Yuan,Xu Hui,Jin Guang,et al.Design of angular vibration isolation for optoelectronic platform on moving vehicle[J].Semiconductor Optoelectronics,2006,27(5):614-617.
[2]许晖,安源,金光,等.光电平台无角位移减振机构运动分析[J].半导体光电,2006,27(5):611-613.Xu Hui,An Yuan,Jin Guang,et al.Kinetic of irrotational displacement isolator for optoelectronic platform[J].Semiconductor Optoelectronics,2006,27(5):614-617.
[3]王书新,李景林,刘磊,等.大尺寸焦平面空间相机调焦机构的精度分析[J].光学精密工程,2010,18(10):2239-2243.Wang Shuxin,Li Jinglin,Liu Lei,et al.Accuracy analysis of focusing mechanism in space camera with long-focal-plane[J].Opt.and Precision Engin.,2010,18(10):2239-2243.
[4]徐刚,杨世模,龚雨兵.大型光学望远镜副镜位姿精调机构的优化设计[J].光学精密工程,2008,16(7):1181-1189.Xu Gang,Yang Shimo,Gong Yubing.Optimal design of pose and position fine tuning apparatus for secondary mirror in large optical telescope[J].Opt.and Precision Engin.,2008,16(7):1181-1189.
[5]Eckhart P,Ralf-Rainer R,Stefan H,et al.Five-axis secondary system for UKIRT[J].Proc.of SPIE,1994,2199:516-522.
[6]Robert G,Scott R,Andre A.A six degree-of-freedom positioner for optical components[J].Proc.of SPIE,2003,4841:540-551.
[7]杨剑锋,徐振邦,吴清文,等.空间光学载荷六维隔振系统的设计[J].光学精密工程,2015,23(5):143-153.Yang J F,Xu Zh B,Wu Q W,et al.Design of six dimensional vibration isolation system for space optical payload[J].Opt.Precision Eng.,2015,23(5):143-153.
[8]贾学志,王栋,张雷,等.轻型空间相机调焦机构的优化设计与精度试验[J].光学精密工程,2011,19(8):1824-1831.Jia X Zh,Wang D,Zhang L,et al.Optimizing desingn and precision experiment of focusing mechanism in lightweight space camera[J].Opt.Precision Eng.,2011,19(8):1824-1831.
[9]Majarena A C,Santolaria J,Samper D,et al.An overview of kinematic and calibration models using internal/external sensors or constraints to improve the behavior of spatial parallel mechanisms[J].Sensors,2010,10(11):10256-10297.
[10]Crocker J H.Fixing the hubble space telescope[J].Space Astronomical Telescopes and Instruments,1991,1494:2-8.
[11]Allen J,Bronowicki,John W.A family of full spacecraft-topay load isolators[J].Technol.Rev.J.,2005:21-41.
[12]Geijo E M,Casalta J M,Can Cha Dom,et al.VISTA secondary mirror drive performance and test results[C]//Astronomical Telescopes and Instrumentation.Inter.Society for Opt.and Photon.,2006:627338-627338-10.
[13]Neill D R,Sneed R,Dawson J,et al.Baseline design of the LSST hexapods and rotator[J].Proc.of SPIE,2014,9151:91512B-1-16
[14]Sebring T A,Dunham E W,Millis R L.The discovery channel telescope:awide-field telescope in northern arizona[J].Ground-based Telescopes,2004,338:71-79.
[15]Casalta J M,Geijo E M,Zago L.The performances of GTC secondary mirror drive unit[J].Proc.of SPIE,2004,5495:507-517.
[16]马立,于瀛洁,程维明,等.BP神经网络补偿并联机构定位误差[J].光学精密工程,2008,16(5):878-883.Ma L,Yu Y J,Cheng W M,et al.Position error compensation for a parallel robot based on BP neural networks[J].Opt.Precision Eng.,2008,16(5):878-883.
[17]Besnard S,Khalil W.Calibration of parallel robots using two inclinometers[C]//Proc.of Inter.Conf.on Robotics and Automation,Michigan,1999:1758-1763.
[18]Rauf A,Ryu J.Fully autonomous calibration of parallel manipulators by imposing calibration[C]//Proc.of IEEE Inter.Conf.on Robotics and Automation,Seoul,2001:2389-2394.
[19]Ren X D,Feng Z R,Su C P.A new calibration method for parallel kinematics machine tools using orientation constraint[J].Int.J.Mach Tools Manuf.,2009,49(9):708-729.
[20]Williams I,Hovland G,Brogardh T.Kinematic error calibration of the Gantry-Tau parallel manipulator[C]//Proc.of IEEE Inter.Conf.on Robotics and Automation,Florida,2006:4199-4204.
[2]许晖,安源,金光,等.光电平台无角位移减振机构运动分析[J].半导体光电,2006,27(5):611-613.Xu Hui,An Yuan,Jin Guang,et al.Kinetic of irrotational displacement isolator for optoelectronic platform[J].Semiconductor Optoelectronics,2006,27(5):614-617.
[3]王书新,李景林,刘磊,等.大尺寸焦平面空间相机调焦机构的精度分析[J].光学精密工程,2010,18(10):2239-2243.Wang Shuxin,Li Jinglin,Liu Lei,et al.Accuracy analysis of focusing mechanism in space camera with long-focal-plane[J].Opt.and Precision Engin.,2010,18(10):2239-2243.
[4]徐刚,杨世模,龚雨兵.大型光学望远镜副镜位姿精调机构的优化设计[J].光学精密工程,2008,16(7):1181-1189.Xu Gang,Yang Shimo,Gong Yubing.Optimal design of pose and position fine tuning apparatus for secondary mirror in large optical telescope[J].Opt.and Precision Engin.,2008,16(7):1181-1189.
[5]Eckhart P,Ralf-Rainer R,Stefan H,et al.Five-axis secondary system for UKIRT[J].Proc.of SPIE,1994,2199:516-522.
[6]Robert G,Scott R,Andre A.A six degree-of-freedom positioner for optical components[J].Proc.of SPIE,2003,4841:540-551.
[7]杨剑锋,徐振邦,吴清文,等.空间光学载荷六维隔振系统的设计[J].光学精密工程,2015,23(5):143-153.Yang J F,Xu Zh B,Wu Q W,et al.Design of six dimensional vibration isolation system for space optical payload[J].Opt.Precision Eng.,2015,23(5):143-153.
[8]贾学志,王栋,张雷,等.轻型空间相机调焦机构的优化设计与精度试验[J].光学精密工程,2011,19(8):1824-1831.Jia X Zh,Wang D,Zhang L,et al.Optimizing desingn and precision experiment of focusing mechanism in lightweight space camera[J].Opt.Precision Eng.,2011,19(8):1824-1831.
[9]Majarena A C,Santolaria J,Samper D,et al.An overview of kinematic and calibration models using internal/external sensors or constraints to improve the behavior of spatial parallel mechanisms[J].Sensors,2010,10(11):10256-10297.
[10]Crocker J H.Fixing the hubble space telescope[J].Space Astronomical Telescopes and Instruments,1991,1494:2-8.
[11]Allen J,Bronowicki,John W.A family of full spacecraft-topay load isolators[J].Technol.Rev.J.,2005:21-41.
[12]Geijo E M,Casalta J M,Can Cha Dom,et al.VISTA secondary mirror drive performance and test results[C]//Astronomical Telescopes and Instrumentation.Inter.Society for Opt.and Photon.,2006:627338-627338-10.
[13]Neill D R,Sneed R,Dawson J,et al.Baseline design of the LSST hexapods and rotator[J].Proc.of SPIE,2014,9151:91512B-1-16
[14]Sebring T A,Dunham E W,Millis R L.The discovery channel telescope:awide-field telescope in northern arizona[J].Ground-based Telescopes,2004,338:71-79.
[15]Casalta J M,Geijo E M,Zago L.The performances of GTC secondary mirror drive unit[J].Proc.of SPIE,2004,5495:507-517.
[16]马立,于瀛洁,程维明,等.BP神经网络补偿并联机构定位误差[J].光学精密工程,2008,16(5):878-883.Ma L,Yu Y J,Cheng W M,et al.Position error compensation for a parallel robot based on BP neural networks[J].Opt.Precision Eng.,2008,16(5):878-883.
[17]Besnard S,Khalil W.Calibration of parallel robots using two inclinometers[C]//Proc.of Inter.Conf.on Robotics and Automation,Michigan,1999:1758-1763.
[18]Rauf A,Ryu J.Fully autonomous calibration of parallel manipulators by imposing calibration[C]//Proc.of IEEE Inter.Conf.on Robotics and Automation,Seoul,2001:2389-2394.
[19]Ren X D,Feng Z R,Su C P.A new calibration method for parallel kinematics machine tools using orientation constraint[J].Int.J.Mach Tools Manuf.,2009,49(9):708-729.
[20]Williams I,Hovland G,Brogardh T.Kinematic error calibration of the Gantry-Tau parallel manipulator[C]//Proc.of IEEE Inter.Conf.on Robotics and Automation,Florida,2006:4199-4204.