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Egoistic MDS-based Rigid Body Localization

Niclas Führling, Giuseppe Abreu, David González G., Osvaldo Gonsa

TL;DR

A key point of the proposed method is that the translation vector between the two-bodies is modeled using the double-centering operator from multidimensional scaling (MDS) theory, enabling the method to be used between rigid bodies regardless of their shapes, in contrast to conventional approaches which require both bodies to have the same shape.

Abstract

We consider a novel anchorless rigid body localization (RBL) suitable for application in autonomous driving (AD), in so far as the algorithm enables a rigid body to egoistically detect the location (relative translation) and orientation (relative rotation) of another body, without knowledge of the shape of the latter, based only on a set of measurements of the distances between sensors of one vehicle to the other. A key point of the proposed method is that the translation vector between the two-bodies is modeled using the double-centering operator from multidimensional scaling (MDS) theory, enabling the method to be used between rigid bodies regardless of their shapes, in contrast to conventional approaches which require both bodies to have the same shape. Simulation results illustrate the good performance of the proposed technique in terms of root mean square error (RMSE) of the estimates in different setups.

Egoistic MDS-based Rigid Body Localization

TL;DR

A key point of the proposed method is that the translation vector between the two-bodies is modeled using the double-centering operator from multidimensional scaling (MDS) theory, enabling the method to be used between rigid bodies regardless of their shapes, in contrast to conventional approaches which require both bodies to have the same shape.

Abstract

We consider a novel anchorless rigid body localization (RBL) suitable for application in autonomous driving (AD), in so far as the algorithm enables a rigid body to egoistically detect the location (relative translation) and orientation (relative rotation) of another body, without knowledge of the shape of the latter, based only on a set of measurements of the distances between sensors of one vehicle to the other. A key point of the proposed method is that the translation vector between the two-bodies is modeled using the double-centering operator from multidimensional scaling (MDS) theory, enabling the method to be used between rigid bodies regardless of their shapes, in contrast to conventional approaches which require both bodies to have the same shape. Simulation results illustrate the good performance of the proposed technique in terms of root mean square error (RMSE) of the estimates in different setups.
Paper Structure (11 sections, 32 equations, 3 figures, 1 table)

This paper contains 11 sections, 32 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Rigid Body Localization System Model
  3. System Model
  4. Measurement Model
  5. Problem Statement
  6. A Note on Related SotA
  7. Proposed method
  8. Translation Estimation
  9. Rotation Matrix Estimation
  10. Performance Evaluation
  11. Conclusion

Figures (3)

  • Figure 1: Illustration of a rigid body at two distinct locations $\boldsymbol{S}^{(0)}$ and $\boldsymbol{S}^{(1)}$. Without loss of generality, we set the initial to be identical to the matrix $\boldsymbol{C}$, which defines the shape and orientation of the rigid body. The second location $\boldsymbol{S}^{(1)}$ of the body relative to its initial location $\boldsymbol{S}^{(0)}$ is then determined according to equation \ref{['eq:basic_model_one_body']}, and is obtained by the transformation of $\boldsymbol{S}^{(0)}$ via a rotation matrix $\bm{Q}$ and a translation vector $\boldsymbol{t}$.
  • Figure 3: RMSE of the translation estimate of the GA proposed method and the SotA, over the range error $\sigma$.
  • Figure 4: RMSE of the translation estimate of the proposed method compared to the GA variation, over the range error $\sigma$.