Closed-Form Solution for Lost-In-Space Visual Navigation Problem

The paper describes a new closed-form solution for the lost-in-space visual navigation problem. Focal plane images of several known beacons are used to determine both position and attitude of a sensor equipped with position-sensing diodes. A preliminary set of possible solutions is obtained without any initial guesses using any three beacons. These solutions employ a closed-form method for finding sensor-to-beacon distances based on their lines of sight. Instead of providing these solutions in terms of polynomial roots, the paper for the first time derives these solutions explicitly and includes a complete error analysis. Using additional beacons, the possible three-beacon solutions are refined, extraneous solutions are discarded, and the best solution is identified via the Gauss–Newton method. The paper also includes numerical examples and a statistical validation of the proposed method.

[1]  Robert M. Haralick,et al.  Review and analysis of solutions of the three point perspective pose estimation problem , 1994, International Journal of Computer Vision.

[2]  P. Schönemann,et al.  A generalized solution of the orthogonal procrustes problem , 1966 .

[3]  E. H. Thompson.  An exact linear solution of the problem of absolute orientation , 1958 .

[4]  S. Kearsley.  On the orthogonal transformation used for structural comparisons , 1989 .

[5]  F. Sansò.  An exact solution of the roto-translation problem , 1973 .

[6]  Soren W. Henriksen,et al.  Manual of photogrammetry , 1980 .

[7]  G. Schut.  On exact linear equations for the computation of the rotational elements of absolute orientation , 1960 .

[8]  J. Keat.  Analysis of Least-Squares Attitude Determination Routine DOAO , 1977 .

[9]  Malcolm D. Shuster.  Survey of attitude representations , 1993 .

[10]  Pu Liu,et al.  Fast determination of the optimal rotational matrix for macromolecular superpositions , 2009, J. Comput. Chem..

[11]  Phillip C. Calhoun,et al.  Solution to the problem of determining the relative 6 DOF state for spacecraft automated rendezvous and docking , 1995, Defense, Security, and Sensing.

[12]  K. Dill,et al.  Using quaternions to calculate RMSD , 2004, J. Comput. Chem..

[13]  R. Diamond.  A note on the rotational superposition problem , 1988 .

[14]  John L. Crassidis,et al.  VISION-BASED RELATIVE NAVIGATION FOR FORMATION FLYING OF SPACECRAFT , 2000 .

[15]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using unit quaternions , 1987 .

[16]  Xinhua Zhuang,et al.  Pose estimation from corresponding point data , 1989, IEEE Trans. Syst. Man Cybern..

[17]  F. Markley.  Attitude determination using vector observations and the singular value decomposition , 1988 .

[18]  Sidney Spital,et al.  A Third Order Differential Equation (Donald E. Amos) , 1966 .

[19]  W. Kabsch.  A solution for the best rotation to relate two sets of vectors , 1976 .

[20]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

[21]  Monish D. Tandale,et al.  Vision-Based Sensor and Navigation System for Autonomous Air Refueling , 2005 .

[22]  P R Wolf,et al.  Elements of Photogrammetry , 1983 .

[23]  B. Green.  THE ORTHOGONAL APPROXIMATION OF AN OBLIQUE STRUCTURE IN FACTOR ANALYSIS , 1952 .

[24]  F. Markley,et al.  Optimal Linear Attitude Estimator , 2007 .

[25]  J. Stuelpnagel,et al.  A Least Squares Estimate of Satellite Attitude (Grace Wahba) , 1966 .

[26]  Daniele Mortari,et al.  How to Estimate Attitude from Vector Observations , 1999 .

[27]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using orthonormal matrices , 1988 .

[28]  W. Kabsch.  A discussion of the solution for the best rotation to relate two sets of vectors , 1978 .

[29]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[30]  M. Shuster.  A survey of attitude representation , 1993 .

[31]  Nasser Kehtarnavaz,et al.  A vision-based DSP embedded navigation sensor , 2002 .

[32]  Sergei Tanygin.  Closed-Form Position Triangulation for Lost-In-Space Attitude and Position Determination , 2004 .

[33]  D. Theobald.  short communications Acta Crystallographica Section A Foundations of , 2005 .