基于双目视觉和扭摆法原理的刚体惯性张量测量技术研究
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浙江理工大学信息科学与工程学院杭州310018

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TH824

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国家自然科学基金项目(62271449)、浙江省大学生科技创新活动计划项目(2025R406A028)资助


Research on measurement technology of inertia tensor of rigid body based on binocular vision and torsion
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School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China

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    摘要:

    针对不规则刚体惯性张量测量问题,提出了一种融合双目视觉和扭摆法的惯性张量测量方案。首先通过参考至原子钟的时钟信号触发高分辨率工业相机采集单次测量扭摆运动序列图像,提取图像特征点后根据测量系统几何关系得到高精度摆角-时间曲线。基于该曲线,提取扭振运动的周期和阻尼比,利用线性阻尼条件下的扭振运动数学模型计算得到单次转动惯测量值。进一步,采用双目结构光三维重建技术获得被测物体和扭摆转盘点云,通过点云配准算法将物体实测点云与物体计算机辅助(CAD)模型点云精准对齐,求解齐次变换矩阵。再通过圆柱轴线拟合确定转轴方向,并利用上述齐次变换矩阵将其统一至CAD模型产品质心坐标系下,有效规避了传统测量方案存在的机械定位误差。计算得到物体质心坐标系各轴与扭摆转轴的夹角余弦值,结合转动惯量测量值建立1个惯性椭球方程。最终通过6个姿态的测量得到一个包含惯性张量全部参数的方程组,求解该方程组实现转动惯量与惯性积的高精度测量。对所提出的方法和系统开展了大量实验,实验结果验证了该方法的可行性和有效性。转动惯量测量绝对误差小于0.5×10-5 kg·m2,惯性主轴方位角最大偏差绝对值为0.99°。所提出的测量方案测量精度较高,不再依赖于机械定位,测量的效率和安全性显著提升,适用于多种产品的惯性参数测量。

    Abstract:

    To address the challenge of inertia tensor measurement for irregular rigid bodies, this article proposes a novel integrated method combining binocular vision and torsional pendulum techniques. First, high-resolution industrial cameras synchronized with an atomic clock are employed to capture sequential images of the torsional motion during a single measurement cycle. Feature points are extracted from the images, and a high-precision angular displacement-time curve is derived based on the geometric relationships within the measurement system. From this curve, the torsional vibration period and damping ratio are extracted. A linear damped torsional vibration model under linear damping conditions is subsequently applied to calculate the moment of inertia for a single measurement. Furthermore, binocular structured light 3D reconstruction technology is utilized to obtain the point cloud data of the measured object and the torsional pendulum. A point cloud registration algorithm is used to accurately align the real-measured point cloud of the object with the point cloud of the object′s computer-aided design (CAD) model, solving for the homogeneous transformation matrix. The axis direction is determined through cylindrical axis fitting, and the homogeneous transformation matrix is used to transform the data into the coordinate system of the CAD model′s product center of mass, effectively avoiding the mechanical positioning errors inherent in traditional measurement methods. The cosine values of the angles between the centroidal coordinate system axes and the torsional pendulum axis are computed. Combined with the measured moments of inertia, these values formulate an inertia ellipsoid equation. Ultimately, a system of equations encompassing all parameters of the inertia tensor is formulated through six rotational configurations and solved to achieve high-precision measurement of both the moments of inertia and inertia products. Extensive experiments are conducted on the proposed method and system. The experimental results evaluate the feasibility and effectiveness of the proposed method. The absolute error in the measurement of the moment of inertia is less than 0.5×10-5 kg·m2, and the maximum deviation in the principal axis orientation angle is 0.99°. The measurement proposed scheme proposed in this paper achieves high accuracy, no longer relying on mechanical positioning, significantly improving both measurement efficiency and safety. It is suitable for the measurement of inertial parameters of various products.

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韩小林,宋安玉,金志鹏,常頔,张烈山.基于双目视觉和扭摆法原理的刚体惯性张量测量技术研究[J].仪器仪表学报,2026,47(1):300-311

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  • 在线发布日期: 2026-03-30
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