Oriented Planetary Exploration Robotic Vision Binocular Camera Calibration

Introduction

The Mars Sample Return (MRS) mission plans to collect samples of Martian rocks, soil and gas for returning to Earth and carrying out scientific analysis (iMARS, 2008; National, 2011). In Mars rover missions ExoMars is the forthcoming ESA/Roscosmos 2016 and 2018 missions, which can be regarded as precursor missions to MSR. The first mission which is to carry a Trace Gas Orbiter and an Entry, Descent and Landing Demonstrator Module (EDM) will be launched and reach Mars in 2016. The second mission will carry a large capsule with a surface science platform and a rover to Mars in 2018. For achieving the purposes, it is of foremost importance that we find the targets having science interesting. Thus, camera calibration is essential to find the targets.

Robotic vision has very promising implications in both research and industry. Among the benefits derived from this technology is the ability to have a robot recognize objects and determine the objects’ relative locations (Faugeras, 1993). Depth perception can be especially useful in mobile robots and in robots requiring hand-eye coordination (see Figure 1). To facilitate the task of object detection, a pair of cameras can be used to implement stereo vision, in which triangulation between the two cameras and the object determines the location of the object relative to the cameras’ internal coordinate systems. A system capable of using vision much like that of humans, though perhaps even more precise, opens worlds of possibilities. However, the practical applications of robotic vision are still quite limited, due in part to imperfections in system design, process implementation, and analysis software. Two of the biggest flaws encountered are distortion in the lenses or other internal devices and errors in the system’s view of the location of these cameras in the workspace. Intrinsic parameters are used to model the imaging process, and extrinsic parameters are used to model the camera’s location in its environment (Wei & Ma, 1994). Camera calibration for stereo pairs of cameras determines values for both intrinsic and extrinsic parameters, and then uses software in the processor to internally correct the errors (Faugeras & Toscani, 1986). Without calibration, the image delivered to the robot may be inaccurate, and the robot’s response is likely to be proportionally skewed. Therefore, it is important to implement an accurate calibration method before stereo vision is used in robotic applications (Tsai et al., 1986).

Figure 1.

Our demonstration rover platform with stereo pairs of cameras (a wide-angle camera (WAC)) and a 3-DOF arm

In the paper we present a image rectification method that is an extension to the two-step procedure and is more accurate. The first subsection of the next section describes the closed-form solution to the problem using a direct linear transformation (DLT). The next subsection then briefly discuss the nonlinear parameter estimation. The section following that solves the image rectification problem. Image rectification is performed by using a new model that interpolates the correct image points based on the physical camera parameters derived in previous steps. A complete Matlab toolbox is performed for this calibration procedure, the results of which will be available through the experiments.

Explicit Camera Calibration

Physical camera parameters are commonly divided into extrinsic and intrinsic parameters. Extrinsic parameters are needed to transform object coordinates to a camera centered coordinate frame. In multi-camera systems, the extrinsic parameters also describe the relationship between the cameras. The pinhole camera model is based on the principle of collinearity, where each point in the object space is projected by a straight line through the projection center into the image plane. The origin of the camera coordinate system is in the projection center at the location (X₀,Y₀, Z₀) with respect to the object coordinate system, and the z-axis of the camera frame is perpendicular to the image plane. The rotation is represented using Euler angles , and . that define a sequence of three elementary rotations around x, y, z-axis respectively. The rotations are performed clockwise, first around the x-axis, then the y-axis that is already once rotated, and finally around the z-axis that is twice rotated during the previous stages.