# Modular Approach for Odometry Localization Method for Vehicles with Increased Maneuverability

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. State of the Art

## 2. Odometry Localization Method

#### 2.1. Functionality of a State Estimator

#### 2.2. Sensors

#### 2.3. Vehicle Models

#### 2.3.1. Motion Model

#### 2.3.2. Complementary Models

**Model-1:**Model for wheel velocity ${v}_{i}$

**Model-2:**Model for side slip angle $\beta $

**Model-3:**Model for wheel velocity angle ${\epsilon}_{i}$

#### 2.4. Design of Odometry Localization Method Using Modular Approach

**Step 0:**In this step, the resources for a state estimator will be prepared. The resources here include, on the one hand, the models, which may be used as the state transition model or the observation model, and on the other hand the available signals on board, which may be used as inputs of the models or as observations to take part in the correction step in Figure 3.

**Round****1**

**Step 1:**In this step, the unknown variables will be defined as state variables. Usually, the unknown variables in Round 1 are the variables to be estimated.

**Step 2.1:**After defining the first state variables, state transition models will be selected among the prepared models in step 0 to describe the state variables. Models with outputs of the defined state variables can be used. These models are often differential equations. If there is no suitable one among the prepared models, users have to design a suitable model or use a random walk model instead. A random walk model means that the state variable will inherit its value from the last time step.

**Step 2.2:**The second part of step 2 is to select or design observation models. Observation models transform the state variables into a form of sensor measurements. The output of the observation models must be a variable, which can be measured by a sensor. This sensor measurement will be defined as an observation. In addition, observation models cannot be differential equations.

**Round****2**

**Step 1:**Similar to step 1 in the first round, the unknown variables in the state transition models and the observation models, which have not had their sources identified in Round 1, will be defined as new state variables.

**Step 2:**It is same as step 2 in Round 1.

#### 2.4.1. Odometry Basic Version

**Step 0:**The models and the available signals have already been introduced in Section 2.2 and Section 2.3.

**Round 1:**

**Step 1:**In the case of odometry localization, the variables to be estimated are the vehicle position and orientation. The first state variables are $X={\left[\begin{array}{ccc}x& y& \theta \end{array}\right]}^{T}$.

**Step 2.1:**After defining the first state variables, state transition models have to be designed to describe the state variables. Equation (1)’s motion model can be used to describe the vehicle position and orientation. The motion model is divided into two blocks, respectively, for the position and orientation. The blocks of the motion model and the state variables are connected by a double arrow line, because the motion model is a discrete differential equation and needs the value from the last time step to determine the actual time step. There are three unknown variables, $v$,$\beta $ and $\omega $, in Equation (1)’s motion model, in which the variable $\omega $ can use the yaw rate sensor signal. Therefore, the yaw rate sensor signal is defined as an input ${\omega}_{I}$ (the subscript I stands for the input). However, there are no accessible sensors to measure vehicle velocity $v$ and side slip angle $\beta $ directly. These two variables remain temporarily unknown.

**Step 2.2:**The goal of this step is to design the observation models to describe the sensor signals through at least one state variable. However, this step can be skipped if no suitable model exists. Because GPS data are not planned to be used, there is no model to describe the sensor signals by the defined state variables ${\left[\begin{array}{ccc}x& y& \theta \end{array}\right]}^{T}$.

**Round 2:**

**Step 1:**Two remaining unknown variables $v$ und $\beta $ from the last round are defined as new state variables. The state variable vector becomes $X={\left[\begin{array}{ccccc}x& y& \theta & v& \beta \end{array}\right]}^{T}.$

**Step 2.1:**After defining the new state variable, the existing motion model can be completed by the newly defined $v$ and $\beta $, which means the unknown variables in the motion model use the newly defined state variables $v$ and $\beta $ as sources. After that, state transition models for $v$ and $\beta $ will be designed. If the users do not want to have a complex system, it is recommended in this round to use the defined state variables and the available sensor signals as inputs for the state transition models, so there will not be too many new state variables. If it is difficult to find a suitable model, a random walk model can be used instead of a model with physical meaning. In Figure 7, the random walk model is represented by a diamond with the letter “R”. The connection between the random walk model and the state variable is also a double arrow line.

**Step 2.2:**According to model-1 (Equation (3)), wheel velocities can be expressed by the state variables $v$ and $\beta $. Thus, the wheel speed sensor signals are defined as an observation ${v}_{O,i}$ (the subscript O stands for observation). Model-1 also requires the yaw rate and wheel velocity angle as inputs. Assuming that the tire side slip angle can be ignored here, then the wheel velocity angles are equal to the wheel steering angles. Just like the yaw rate signal that has been already defined as an input ${\omega}_{I}$ in Round 1, the wheel steering angle signals are also defined as inputs ${\delta}_{I,i}$.

#### 2.4.2. Odometry Version 111

#### 2.4.3. Odometry Version 212

#### 2.4.4. Odometry Version 232

#### 2.4.5. Odometry Version 213

#### 2.4.6. Odometry Version 233

#### 2.4.7. Comparison of Odometry Versions

## 3. Validation

#### 3.1. Test Vehicle

#### 3.2. Driving Maneuvers

#### 3.3. Validation Environments

#### 3.4. Robustness Analysis

#### 3.5. Evaluation Criteria (EC)

**EC-1:**End position and orientation error in global coordinate system (with superscript “E”):$${e}_{pos,end}^{E}={e}_{pos,t}^{E}=\sqrt{{\left({x}_{t}^{E}-{\widehat{x}}_{t}^{E}\right)}^{2}+{\left({y}_{t}^{E}-{\widehat{y}}_{t}^{E}\right)}^{2}}$$$${e}_{ang,end}^{E}={e}_{ang,t}^{E}={\theta}_{t}^{E}-{\widehat{\theta}}_{t}^{E}$$**EC-2:**Maximum position and orientation error in global coordinate system while driving:$${e}_{pos,max}^{E}=\mathrm{max}\left({e}_{pos,n}^{E}\right)=\mathrm{max}\left(\sqrt{{\left({x}_{n}^{E}-{\widehat{x}}_{n}^{E}\right)}^{2}+{\left({y}_{n}^{E}-{\widehat{y}}_{n}^{E}\right)}^{2}}\right)$$$${e}_{ang,max}^{E}=\mathrm{max}\left({\theta}_{n}^{E}-{\widehat{\theta}}_{n}^{E}\right)$$**EC-3:**Average error of position change and orientation change:$${\overline{e}}_{\mathrm{d}p}=\frac{{{\displaystyle \sum}}_{n=1}^{t}\left|\mathrm{d}{p}_{n}-\mathrm{d}{\widehat{p}}_{n}\right|}{{{\displaystyle \sum}}_{n=1}^{t}\mathrm{d}{p}_{n}}$$$${\overline{e}}_{\mathrm{d}\theta}=\frac{{{\displaystyle \sum}}_{n=1}^{t}\left|\mathrm{d}{\theta}_{n}-\mathrm{d}{\widehat{\theta}}_{n}\right|}{{{\displaystyle \sum}}_{n=1}^{t}\mathrm{d}{\theta}_{n}}$$

## 4. Results and Discussion

#### 4.1. Simulation Results

#### 4.2. Real Driving Results

## 5. Conclusions

- The greater the number of models used to constrain state variables, the higher the estimation accuracy, theoretically. In reality, it also depends on the quality and effective range of a model. Sensor quality is also a factor;
- The use of the state variables ${\epsilon}_{i}$ or the sensor signals ${\delta}_{i}$ as inputs in model-1 and model-2 plays no role in the estimation accuracy. If the state variables ${\epsilon}_{i}$ have state transition model-3, the robustness of the odometry will be ensured if the sensors are defective;
- The versions with model-1 and 2, model-1 and 3 and model-1, 2 and 3 have almost the same accuracy. Versions 213 and 233 are the two most robust versions.

- It simplified the process of designing a state estimator. The elements for a state estimator can be easily derived from the diagram of this method;
- The contribution of a certain model to accuracy and robustness can be predicted using this approach;
- New models or new sensors can be easily implemented, and possible effects can be analyzed;
- It provides a clear overview of all used models and sensors. It helps users to manage different estimators.

## 6. Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Reference Position of Real Driving Tests

## Appendix B. Nomenclature

Symbol | Description |
---|---|

$(x,y)$ | Vehicle position in world coordinate system |

$\theta $ | Yaw angle of vehicle |

$v$ | Vehicle velocity |

${v}_{i}$ | Wheel velocity |

${v}_{i,x}$ | Wheel velocity along vehicle longitudinal axis |

${v}_{i,y}$ | Wheel velocity along vehicle lateral direction |

${v}_{i,y}$ | Wheel velocity along vehicle lateral direction |

$\beta $ | Side slip angle |

$\omega $ | Yaw rate |

${\delta}_{i}$ | Wheel steering angle |

${\epsilon}_{i}$ | Wheel velocity angle |

${r}_{i,x}$ | Distance between tire–road contact point and vehicle center of gravity in vehicle longitudinal direction |

${r}_{i,y}$ | Distance between tire–road contact point and vehicle center of gravity in vehicle lateral direction |

$\Delta t$ | Sample time |

Subscript | Description |
---|---|

$k-1$ | Last time step |

$k$ | Actual time step |

$i$ | $\mathrm{Position}\text{}\mathrm{of}\text{}\mathrm{wheel},\text{}i=fl,fr,rl,rr$ |

$O$ | Sensor signal used as observation |

$I$ | Sensor signal used as input value |

## References

- Verordnung des Bundesministers für Verkehr, Innovation und Technologie, Mit der die Automatisiertes Fahren Verordnung Geändert Wird (1.Novelle zur AutomatFahrV). Available online: https://rdb.manz.at/document/ris.c.BGBl__II_Nr__66_2019 (accessed on 23 December 2020).
- Klein, M.; Mihailescu, A.; Hesse, L.; Eckstein, L. Einzelradlenkung des Forschungsfahrzeugs Speed E. ATZ Automob. Z.
**2013**, 115, 782–787. [Google Scholar] [CrossRef] - Bünte, T.; Ho, L.M.; Satzger, C.; Brembeck, J. Zentrale Fahrdynamikregelung der Robotischen Forschungsplattform RoboMobil. ATZ Elektron.
**2014**, 9, 72–79. [Google Scholar] [CrossRef] - Nees, D.; Altherr, J.; Mayer, M.P.; Frey, M.; Buchwald, S.; Kautzmann, P. OmniSteer—Multidirectional chassis system based on wheel-individual steering. In 10th International Munich Chassis Symposium 2019: Chassis. Tech Plus; Pfeffer, P.E., Ed.; Springer: Wiesbaden, Germany, 2020; pp. 531–547. ISBN 978-3-658-26434-5. [Google Scholar]
- Zekavat, R.; Buehrer, R.M. Handbook of Position Location. Theory, Practice, and Advances, 2nd ed.; John Wiley & Sons Incorporated: Newark, MJ, USA, 2018; ISBN 9781119434580. [Google Scholar]
- Winner, H.; Hakuli, S.; Lotz, F.; Singer, C. Handbuch Fahrerassistenzsysteme; Springer Fachmedien Wiesbaden: Wiesbaden, Germany, 2015; ISBN 978-3-658-05733-6. [Google Scholar]
- Scherzinger, B. Precise robust positioning with inertially aided RTK. Navigation
**2006**, 53, 73–83. [Google Scholar] [CrossRef] - Vivacqua, R.; Vassallo, R.; Martins, F. A Low Cost Sensors Approach for Accurate Vehicle Localization and Autonomous Driving Application. Sensors
**2017**, 17, 2359. [Google Scholar] [CrossRef] [PubMed] - Aqel, M.O.A.; Marhaban, M.H.; Saripan, M.I.; Ismail, N.B. Review of visual odometry: Types, approaches, challenges, and applications. SpringerPlus
**2016**, 5, 1897. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hertzberg, J.; Lingemann, K.; Nüchter, A. Mobile Roboter. In Eine Einführung aus Sicht der Informatik; Springer: Berlin/Heidelberg, Germany, 2012; ISBN 978-3-642-01726-1. [Google Scholar]
- Noureldin, A.; Karamat, T.B.; Georgy, J. Fundamentals of Inertial Navigation, Satellite-based Positioning and their Integration; Springer: Berlin/Heidelberg, Germany, 2013; ISBN 978-3-642-30466-8. [Google Scholar]
- Groves, P.D. Principles of GNSS, inertial, and multisensor integrated navigation systems, 2nd edition [Book review]. IEEE Aerosp. Electron. Syst. Mag.
**2015**, 30, 26–27. [Google Scholar] [CrossRef] - Borenstein, J.; Everett, H.R.; Feng, L.; Wehe, D. Mobile robot positioning: Sensors and techniques. J. Robot. Syst.
**1997**, 14, 231–249. [Google Scholar] [CrossRef] - Berntorp, K. Particle filter for combined wheel-slip and vehicle-motion estimation. In Proceedings of the American Control Conference (ACC), Chicago, IL, USA, 1–3 July 2015; IEEE: Piscataway, NJ, USA, 2015; pp. 5414–5419, ISBN 978-1-4799-8684-2. [Google Scholar]
- Brunker, A.; Wohlgemuth, T.; Frey, M.; Gauterin, F. GNSS-shortages-resistant and self-adaptive rear axle kinematic parameter estimator (SA-RAKPE). In Proceedings of the 28th IEEE Intelligent Vehicles Symposium, Redondo Beach, CA, USA, 11–14 June 2017; IEEE: Piscataway, NJ, USA, 2017; pp. 456–461, ISBN 978-1-5090-4804-5. [Google Scholar]
- Brunker, A.; Wohlgemuth, T.; Frey, M.; Gauterin, F. Dual-Bayes Localization Filter Extension for Safeguarding in the Case of Uncertain Direction Signals. Sensors
**2018**, 18, 3539. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Larsen, T.D.; Hansen, K.L.; Andersen, N.A.; Ravn, O. Design of Kalman filters for mobile robots; evaluation of the kinematic and odometric approach. In Proceedings of the 1999 IEEE International Conference on Control Applications Held Together with IEEE International Symposium on Computer Aided Control System Design, Kohala Coast, HI, USA, 22–27 August 1999; IEEE: Piscataway, NJ, USA, 1999; pp. 1021–1026, ISBN 0-7803-5446-X. [Google Scholar]
- Lee, K.; Chung, W. Calibration of kinematic parameters of a Car-Like Mobile Robot to improve odometry accuracy. In Proceedings of the 2008 IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, USA, 19–23 May 2008; pp. 2546–2551, ISBN 978-1-4244-1646-2. [Google Scholar]
- Kochem, M.; Neddenriep, R.; Isermann, R.; Wagner, N.; Hamann, C.D. Accurate local vehicle dead-reckoning for a parking assistance system. In Proceedings of the 2002 American Control Conference, Anchorage, AK, USA, 8–10 May 2002; Hilton Anchorage and Egan Convention Center: Anchorage, AK, USA; IEEE: Piscataway, NJ, USA, 2002; Volume 5, pp. 4297–4302, ISBN 0-7803-7298-0. [Google Scholar]
- Tham, Y.K.; Wang, H.; Teoh, E.K. Adaptive state estimation for 4-wheel steerable industrial vehicles. In Proceedings of the 1998 37th IEEE Conference on Decision and Control, Tampa, FL, USA, 16–18 December 1998; IEEE: Piscataway, NJ, USA, 1998; pp. 4509–4514, ISBN 0-7803-4394-8. [Google Scholar]
- Brunker, A.; Wohlgemuth, T.; Frey, M.; Gauterin, F. Odometry 2.0: A Slip-Adaptive EIF-Based Four-Wheel-Odometry Model for Parking. IEEE Trans. Intell. Veh.
**2019**, 4, 114–126. [Google Scholar] [CrossRef] - Chung, H.; Ojeda, L.; Borenstein, J. Accurate mobile robot dead-reckoning with a precision-calibrated fiber-optic gyroscope. IEEE Trans. Robot. Automat.
**2001**, 17, 80–84. [Google Scholar] [CrossRef] - Marco, V.R.; Kalkkuhl, J.; Seel, T. Nonlinear observer with observability-based parameter adaptation for vehicle motion estimation. IFAC-PapersOnLine
**2018**, 51, 60–65. [Google Scholar] [CrossRef] - Rhudy, M.; Gu, Y. Understanding nonlinear Kalman filters part 1: Selection of EKF or UKF. Interact. Robot. Lett.
**2013**. Available online: https://yugu.faculty.wvu.edu/research/interactive-robotics-letters/understanding-nonlinear-kalman-filters-part-i (accessed on 23 December 2020). - Julier, S.J.; Uhlmann, J.K. New extension of the Kalman filter to nonlinear systems. In Proceedings of the Signal Processing Sensor Fusion, and Target Recognition VI, Orlando, FL, USA, 28 July 1997; pp. 182–193. [Google Scholar]
- Welch, G.; Bishop, G. An Introduction to the Kalman Filter. In Proceedings of the ACM SIGGRAPH, Los Angeles, CA, USA, 12–17 August 2001; ACM Press, Addison-Wesley: New York, NY, USA, 2001. [Google Scholar]
- Mitschke, M.; Wallentowitz, H. Dynamik der Kraftfahrzeuge, Vierte, Neubearbeitete Auflage; Springer: Berlin/Heidelberg, Germany, 2004; ISBN 978-3-662-06802-1. [Google Scholar]
- Frey, M.; Han, C.; Rügamer, D.; Schneider, D. Automatisiertes Mehrdirektionales Fahrwerksystem auf Basis Radselektiver Radantriebe (OmniSteer). Schlussbericht zum Forschungsvorhaben: Projektlaufzeit: 01.01.2016-31.03.2019. Available online: https://www.tib.eu/suchen/id/TIBKAT:1687318824/ (accessed on 23 December 2020).

**Figure 1.**(

**a**) Possible driving modes using novel suspensions; (

**b**) possible continuously driven parking maneuver using novel suspensions.

**Figure 2.**Classification of localization methods according to Ref. [5].

**Figure 4.**Position of the sensors (blue points: wheel steering angle sensors; red points: wheel speed sensors; yellow point: yaw rate sensor).

**Figure 5.**(

**a**) Movement of a vehicle from time step $k-1$ to $k$; (

**b**) kinematic relationship between wheel velocity and vehicle velocity.

**Figure 7.**Modular approach to designing a state estimator for odometry localization (basic version).

**Figure 8.**Modular approach to designing a state estimator for odometry localization (Version 111 based on basic version, changes marked with dashed lines or dashed blocks and blue letters, respectively).

**Figure 10.**Modular approach to designing a state estimator for odometry localization (Version 212 based on Version 111, changes marked with dashed lines or dashed blocks and blue letters, respectively).

**Figure 11.**Modular approach to designing a state estimator for odometry localization (Version 232 based on Version 212, changes marked with dashed lines or dashed blocks and blue letters, respectively).

**Figure 12.**Modular approach to designing a state estimator for odometry localization (Version 213 based on Version 212, changes marked with dashed lines or dashed blocks and blue letters, respectively).

**Figure 13.**Modular approach to designing a state estimator for odometry localization (Version 233 based on Version 212, changes marked with dashed lines or dashed blocks and blue letters, respectively).

**Figure 14.**(

**a**) Demonstration vehicle of project “OmniSteer”; (

**b**) novel chassis system at increased steering angle 90°; (

**c**) novel chassis system at increased steering angle −90°.

**Figure 15.**Driving maneuvers considered. (

**a**) DM1: Vehicle parks in the parking lot without turning or stopping, 90° steering angle on each wheel can be realized; (

**b**) DM2: Vehicle moves forward into the parking lot and the rear part of the vehicle is then pulled out. (

**c**) DM3: Vehicle parks directly on the opposite side of the street without stopover; (

**d**) DM4: Conventional reversing parking method; (

**e**) DM5: Vehicle parks in a parking lot by steering the rear wheels in opposite directions to the front wheels; (

**f**) DM6: Similar to DM5, but with correction at the end position; (

**g**) DM7: Vehicle moves forward into the parking lot and the rear part of the vehicle is then pulled out, to avoid the obstacle; (

**h**) DM8: Vehicle turns on its own vertical axis.

**Figure 16.**(

**a**) Validation process in simulation environment; (

**b**) virtualization of omnidirectional parking maneuver in simulation environment.

**Figure 18.**Simulation results of different odometry versions: (

**a**) Trajectories in DM1; (

**b**) Trajectories in DM3; (

**c**) Legend.

**Figure 19.**Simulations results of different odometry versions: (

**a**) Maximum position errors; (

**b**) Maximum orientation errors; (

**c**) Average errors of position change; (

**d**) Average errors of orientation change.

**Figure 20.**(

**a**) Version 111: Correction paths for $\omega $ (blue), $v$ and $\beta $ (red). (

**b**) Version 232: Correction paths for $\omega $ (blue), $v$ (red) and $\beta $(green). (

**c**) Version 213: Correction paths for $\omega $ (blue), $v$ and $\beta $(red).

**Figure 21.**Simulation results of different odometry versions under sensor failures: (

**a**) Maximum position errors; (

**b**) Maximum orientation errors; (

**c**) Maximum position errors; (

**d**) Maximum orientation errors.

**Figure 22.**Simulation results of four odometry versions under sensor failures: (

**a**) Maximum position errors; (

**b**) Maximum orientation errors; (

**c**) Average position errors; (

**d**) Average orientation errors.

**Figure 23.**Real driving results of different odometry versions: (

**a**) Trajectories in DM1; (

**b**) Trajectories in DM3; (

**c**) Legend.

**Figure 24.**Real driving results of different odometry versions using a yaw rate sensor with a resolution of 0.1°/s: (

**a**) End position errors; (

**b**) End orientation errors.

**Figure 25.**Real driving results of different odometry versions using a yaw rate sensor with a resolution of 0.01°/s: (

**a**) End position errors; (

**b**) End orientation errors.

**Figure 26.**Real driving results of different odometry versions under sensor failures: (

**a**) End position errors; (

**b**) End orientation errors.

**Figure 27.**Real driving results of four odometry versions under sensor failures: (

**a**) End position errors; (

**b**) End orientation errors.

Position | Sensor | Price/Unit |
---|---|---|

Wheel steering angle sensors | Bosch LWS 5.6.3 | 80 EUR |

Wheel speed sensors | Integrated Speed Sensor of Traction Motor ^{1} | - |

Yaw rate sensor | UM7 IMU | 150 EUR |

^{1}Heinzmann PMS 080.

Version | Model-1 | Model-2 | Model-3 | ||
---|---|---|---|---|---|

${\mathit{\epsilon}}_{\mathit{i}}$ or ${\mathit{\delta}}_{\mathit{I},\mathit{i}}$ Used? | Model-2 Used? | ${\mathit{\epsilon}}_{\mathit{i}}$ or ${\mathit{\delta}}_{\mathit{I},\mathit{i}}$ Used? | Model-3 Used? | ||

111 | ${\delta}_{I,i}$ | No | - | - | Model 1 |

112 | ${\delta}_{I,i}$ | No | - | No | |

212 | ${\epsilon}_{i}$ | No | - | No | |

121 | ${\delta}_{I,i}$ | Yes | ${\delta}_{I,i}$ | - | Model 1 and 2 |

122 | ${\delta}_{I,i}$ | Yes | ${\delta}_{I,i}$ | No | |

132 | ${\delta}_{I,i}$ | Yes | ${\epsilon}_{i}$ | No | |

222 | ${\epsilon}_{i}$ | Yes | ${\delta}_{I,i}$ | No | |

232 | ${\epsilon}_{i}$ | Yes | ${\epsilon}_{i}$ | No | |

113 | ${\delta}_{I,i}$ | No | - | Yes | Model 1 and 3 |

213 | ${\epsilon}_{i}$ | No | - | Yes | |

123 | ${\delta}_{I,i}$ | Yes | ${\delta}_{I,i}$ | Yes | Model 1, 2 and 3 |

133 | ${\delta}_{I,i}$ | Yes | ${\epsilon}_{i}$ | Yes | |

223 | ${\epsilon}_{i}$ | Yes | ${\delta}_{I,i}$ | Yes | |

233 | ${\epsilon}_{i}$ | Yes | ${\epsilon}_{i}$ | Yes |

Case No. | Failed Sensors |
---|---|

1 | No sensor failed |

2 | Wheel speed sensor FL |

3 | Wheel speed sensor FR |

4 | Wheel speed sensor RL |

5 | Wheel speed sensor RR |

6 | Yaw rate sensor |

7 | Wheel steering sensor FL |

8 | Wheel steering sensor FR |

9 | Wheel steering sensor RL |

10 | Wheel steering sensor RR |

11 | Wheel speed sensor FL + Wheel steering sensor FL |

12 | Wheel speed sensor FR + Wheel steering sensor FR |

13 | Wheel speed sensor RL + Wheel steering sensor RL |

14 | Wheel speed sensor RR + Wheel steering sensor RR |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Han, C.; Frey, M.; Gauterin, F.
Modular Approach for Odometry Localization Method for Vehicles with Increased Maneuverability. *Sensors* **2021**, *21*, 79.
https://doi.org/10.3390/s21010079

**AMA Style**

Han C, Frey M, Gauterin F.
Modular Approach for Odometry Localization Method for Vehicles with Increased Maneuverability. *Sensors*. 2021; 21(1):79.
https://doi.org/10.3390/s21010079

**Chicago/Turabian Style**

Han, Chenlei, Michael Frey, and Frank Gauterin.
2021. "Modular Approach for Odometry Localization Method for Vehicles with Increased Maneuverability" *Sensors* 21, no. 1: 79.
https://doi.org/10.3390/s21010079