Flexible planar spacecraft, such as solar sails, phased antenna arrays and space solar power satellites vary their shape in flight and also may not have a known shape after deployment. To allow applications where spacecraft shapes are measured to allow the closed-loop correction of flight or payload parameters, this paper presents a method for measuring shapes with miniature sun sensors embedded within the structure. Two algorithms to reconstruct the shape of the structure from the two local angles to the sun are presented; the first one is geometry-based, whereas the second one uses a finite element model of the structure. Both algorithms are validated on a 1.3 m $\times$ 0.25 m structure with 14 novel miniature sun sensors with an accuracy of $0.5^{\circ }$, developed for the present research. The structure was reconstructed to an accuracy better than one millimeter by both algorithms, after undergoing bending and torsional deformations. While the geometrically based algorithm is fast and accurate for small deformations, the finite element based algorithm performs better overall, especially for larger deformations.

柔性平面航天器，例如太阳帆，相控天线阵和太空太阳能卫星，在飞行中会改变其形状，并且在部署后也可能没有已知的形状。为了允许测量航天器形状以允许对飞行或有效载荷参数进行闭环校正的应用，本文提出了一种在结构中嵌入微型太阳传感器的形状测量方法。提出了两种从两个局部角度到太阳重构结构形状的算法；第一个基于几何，而第二个使用结构的有限元模型。两种算法均在1.3 m上进行了验证$\times$ 0.25 m结构，带有14个新颖的微型阳光传感器，精度为 $0。5^{\circ }$，是为当前研究而开发的。在经历弯曲和扭转变形后，通过两种算法将结构重建的精度都优于1毫米。虽然基于几何的算法对于较小的变形是快速且准确的，但是基于有限元的算法在总体上表现更好，尤其是对于较大的变形。