SOLVING THE 5-Bespeak RELATIVE POSE PROBLEM FOR VISION-BASED Estimation AND CONTROL

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Introduction

Given 2 images of an unknown object taken from 2 unlike views, tin nosotros recover the rotation and translation betwixt the 2 views?

The reply is yeah! If we can find and match v feature points in ii images, the rotation can be recovered. Even so translation tin only exist recovered up to a calibration factor. This is because the depth data is lost during the projection. In other words, it is non possible to find how far an object is from the camera from the object's epitome.

Furthermore, there are generally 10 solutions to the problem using 5 feature points. To uniquely recover the pose a 3rd view of the object or more than feature points is required. Why 5 feature points? Information technology is the minimum number of points required to recover the pose (i.e. rotation and scaled translation) between ii arbitrary images.  This riduces the likelihood of fake matches that can cause the algorihtm to fail.

Using Quaternions to Represent the Pose Interpretation Problem

It is known that 8 signal matches admit a linear solution using the famous Essential Matrix.  The existing 5-signal algorithms too rely on the Essential matrix to recover the pose. However the Essential matrix has central weaknesses, and introduces these weaknesses into 5-betoken algorithms that apply it. We suggest a new and applied method that eschews the essential matrix by representing the pose estimation problem in the quaternion space and has several advantages:

  • When relative translation between two photographic camera views is zero, the Essential matrix is undefined. Since our proposed algorithm does non apply the Essential matrix, this problem is avoided.
  • If the 3D feature points are coplanar, at that place are by and large ii solutions for the essential matrix. Since our proposed algorithm does not rely on the Essential matrix, planar structure degeneracy is avoided.
  • Our approach has no secondary decomposition of the Essential matrix into rotation and translation terms; rotation and translation are direct estimated. Furthermore, the depth of the points with respect to both photographic camera frames are simultaneously recovered.
  • The rotation is estimated in the quaternion grade. In applications such equally computer graphics and controls, quaternions are frequently the preferred representation of rotation.
  • The algorithm tin be easily extended to more than than five points. When there are more than six feature points available, the algorithm can be used to uniquely determine the pose difference between two photographic camera views.
  • In simulations, our proposed algorithm shows a practiced resilience to noise and fault in camera calibration.

Applications and Experimental Results

The v-point pose estimation problem has applications in vision based robot control, also known as visual servoing. Feature points obtained from a vision sensor mounted on a robot are used in the pose estimation algorithm to estimate consecutive robot motions and provide movement feedback to control the robot.

For instance in the experiment bellow, given an epitome taken from a desired view, the pose estimation algorithm recovers the pose difference betwixt the camera'due south current view and the desired view from 5 feature points. The recovered pose is used in the control algorithm as feedback to motility the camera to the desired view:

Publications

  • K. Fathian, J. Jin, South.-G. Wee, D.-H. Lee, Y.-G. Kim, N. R. Gans, Camera relative pose interpretation for visual servoing using  quaternions,Robotics and Autonomous Systems, vol. 107, Pages 45-62, June, 2018
  • K. Fathian, J. P. Ramirez-Paredes, E. A. Doucette, J. W. Curtis, N. R. Gans. "QuEst: A Quaternion-Based Approach for Camera Motion Interpretation from Minimal Feature Points",IEEE Robotics and Automation Letters,vol. 3, no. 2, pp. 857-864, April, 2018
  • Thousand. Fathian, J. Jin and N. R. Gans, "A New Arroyo for Solving the Five-Point Relative Pose Problem for Vision-Based estimation and Control,"Proc. American Control Conference, 2014