针对大型装备智能制造中的机器人在线位姿激光跟踪测量与实时引导需求,提出了一种机器人坐标系与激光测量坐标系标定转换和解算方法。设计了基于距离原则的机器人末端光学工具中心点TCP(Tool Center Point)位置标定算法。通过运用空间...针对大型装备智能制造中的机器人在线位姿激光跟踪测量与实时引导需求,提出了一种机器人坐标系与激光测量坐标系标定转换和解算方法。设计了基于距离原则的机器人末端光学工具中心点TCP(Tool Center Point)位置标定算法。通过运用空间点坐标重心化配置算法和基于罗德里格矩阵变换的最小二乘优化算法解算出了具有单位正交性的位姿变换旋转矩阵。进行了机器人坐标系位姿变换激光测量标定和优化对比实验,旋转矩阵初值和正交优化值进行点坐标转换后的综合RMSE分别为0.579 0mm和0.501 5mm。结果表明该方法能够有效改进姿态旋转矩阵正交性,并提高位姿变换解算精度。展开更多
We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute t...We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.展开更多
The orthogonal Latin hypercube design and its relaxation,and column-orthogonal design,are two kinds of orthogonal designs for computer experiments.However,they usually do not achieve maximum stratifications in multi-d...The orthogonal Latin hypercube design and its relaxation,and column-orthogonal design,are two kinds of orthogonal designs for computer experiments.However,they usually do not achieve maximum stratifications in multi-dimensional margins.In this paper,we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal arrays.The newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects(quadratic effects and bilinear effects)when the rotated orthogonal arrays have strength larger than two.Besides orthogonality,the resulting designs also preserve better space-filling properties than those constructed by using the existing methods.In addition,we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial designs.Some newly constructed orthogonal Latin hypercube designs are tabulated for practical use.展开更多
文摘针对大型装备智能制造中的机器人在线位姿激光跟踪测量与实时引导需求,提出了一种机器人坐标系与激光测量坐标系标定转换和解算方法。设计了基于距离原则的机器人末端光学工具中心点TCP(Tool Center Point)位置标定算法。通过运用空间点坐标重心化配置算法和基于罗德里格矩阵变换的最小二乘优化算法解算出了具有单位正交性的位姿变换旋转矩阵。进行了机器人坐标系位姿变换激光测量标定和优化对比实验,旋转矩阵初值和正交优化值进行点坐标转换后的综合RMSE分别为0.579 0mm和0.501 5mm。结果表明该方法能够有效改进姿态旋转矩阵正交性,并提高位姿变换解算精度。
文摘We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.
基金supported by National Natural Science Foundation of China(Grant Nos.11871033,11771220,11671386,11771219 and 11971345)National Ten Thousand Talents Program+2 种基金Tianjin Development Program for Innovation and EntrepreneurshipTianjin“131”Talents Programthe Postdoctoral Science Foundation Funded Project of China(Grant No.2017M611147)。
文摘The orthogonal Latin hypercube design and its relaxation,and column-orthogonal design,are two kinds of orthogonal designs for computer experiments.However,they usually do not achieve maximum stratifications in multi-dimensional margins.In this paper,we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal arrays.The newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects(quadratic effects and bilinear effects)when the rotated orthogonal arrays have strength larger than two.Besides orthogonality,the resulting designs also preserve better space-filling properties than those constructed by using the existing methods.In addition,we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial designs.Some newly constructed orthogonal Latin hypercube designs are tabulated for practical use.
