Advances in Applied Clifford Algebras

, Volume 27, Issue 3, pp 2035–2049 | Cite as

Motor Estimation using Heterogeneous Sets of Objects in Conformal Geometric Algebra

  • Lars TingelstadEmail author
  • Olav Egeland
Open Access


In this paper we present a novel method for nonlinear rigid body motion estimation from noisy data using heterogeneous sets of objects of the conformal model in geometric algebra. The rigid body motions are represented by motors. We employ state-of-the-art nonlinear optimization tools and compute gradients and Jacobian matrices using forward-mode automatic differentiation based on dual numbers. The use of automatic differentiation enables us to employ a wide range of cost functions in the estimation process. This includes cost functions for motor estimation using points, lines and planes. Moreover, we explain how these cost functions make it possible to use other geometric objects in the conformal model in the motor estimation process, e.g., spheres, circles and tangent vectors. Experimental results show that we are able to successfully estimate rigid body motions from synthetic datasets of heterogeneous sets of conformal objects including a combination of points, lines and planes.


Rigid body motion estimation Geometric algebra Automatic differentiation Optimization 

Mathematics Subject Classification

Primary 15A66 Secondary 00A00 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Production and Quality Engineering, Faculty of Engineering Science and TechnologyNTNU, Norwegian University of Science and TechnologyTrondheimNorway

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