Motor Estimation using Heterogeneous Sets of Objects in Conformal Geometric Algebra

Motor Estimation using Heterogeneous Sets of Objects in Conformal Geometric Algebra 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. Advances in Applied Clifford Algebras Springer Journals

Motor Estimation using Heterogeneous Sets of Objects in Conformal Geometric Algebra

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Springer International Publishing
Copyright © 2016 by The Author(s)
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
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