从足球场上两点加引力方向确定Nao摄像头头部的位置与高度
Position and Altitude of the Nao Camera Head from Two Points on the Soccer Field plus the Gravitational Direction
AI总结：
本文提出利用地面上两个已知点与引力方向构成简化四面体，通过有理三角学快速解算Nao机器人摄像头在场上的二维坐标和高度，实现3-6厘米定位精度。
摘要：
为了能够踢足球，机器人需要对其在场上的当前位置有良好的估计。理想情况下，多个具有已知位置的特征是可见的。通过应用三角学，我们可以估计实际进行该观察的视点。鉴于标准平台联赛的Nao机器人视场相当有限，给定的摄像头帧通常只允许识别一个或两个点。在本文中，我们提出了一种方法，通过简化四面体的几何结构来确定场上的(x, y)坐标以及摄像头的高度h。该配置由地面上两个观测点加上引力方向构成。当两点之间的距离已知，并且测量到这些点的方向以及引力方向时，可以确定四面体的所有尺寸。通过使用有理三角学而不是经典三角学来执行这些计算，计算速度提高了28.7%，且数值精度相同。Nao头部的位置也可以通过OptiTrack系统进行外部测量。当我们从球门柱外边缘的消失点估计引力方向时，外部测量的位置与根据传感器数据内部预测的位置之间的差异给出了3-6厘米范围内的平均绝对误差。
英文摘要：
To be able to play soccer, a robot needs a good estimate of its current position on the field. Ideally, multiple features are visible that have known locations. By applying trigonometry we can estimate the viewpoint from where this observation was actually made. Given that the Nao robots of the Standard Platform League have quite a limited field of view, a given camera frame typically only allows for one or two points to be recognized. In this paper we propose a method for determining the (x, y) coordinates on the field and the height h of the camera from the geometry of a simplified tetrahedron. This configuration is formed by two observed points on the ground plane plus the gravitational direction. When the distance between the two points is known, and the directions to the points plus the gravitational direction are measured, all dimensions of the tetrahedron can be determined. By performing these calculations with rational trigonometry instead of classical trigonometry, the computations turn out to be 28.7% faster, with equal numerical accuracy. The position of the head of the Nao can also be externally measured with the OptiTrack system. The difference between externally measured and internally predicted position from sensor data gives us mean absolute errors in the 3-6 centimeters range, when we estimated the gravitational direction from the vanishing point of the outer edges of the goal posts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
