Angle Invariance for Distance Measurements Using a Single Camera

Various types of sensors are available to implement distance measurement for mobile robots. Scene recognition and path planning point to the use of optical imaging systems and machine vision approaches. For middle size robots, such as those used in robotic football league, reduced weight and volume are mandatory, and a single camera fixed on the robot is the usual choice. 3D localization of objects with such a simple system is impossible, unless some knowledge of the environment and/or objects is available. Localization in 3D space needs three coordinates. The common central projection used in linear image produces a 2D image, from which only two coordinates can be extracted. For the central projection system, any point in a straight line to the lens optical centre of the lens has the same image pixel representation. The distance from the object to the optical centre is the unknown coordinate to be obtained by processing other information. In the case of mobile robots, the movement is usually on a plane surface, meaning that height and camera orientation remain constant. If the object is also at a fixed height, its possible positions define a horizontal plane, and its particular location can be obtained by intersecting this plane with the straight line defined by the corresponding image point on the sensor and the lens optical centre. This work presents both a calculation method and also a calibration procedure for this setup. This paper concerns the use of linear optical systems, where angles to the optical axis are maintained for both image and object sides. For optical systems with radial distortions, such as barrel and pincushion types, a one-dimensional function relating object and image side angles can be used to compensate the non linearity and allow this approach to be used. Also in vision systems, where mirrors are combined with normal lens to allow 360deg viewing, similar image-object angular relationships can be used to compute target positions