# LiDAR-Based GNSS Denied Localization for Autonomous Racing Cars

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## Abstract

**:**

## 1. Introduction

- While facing a tight turn or passing through narrow corridors, the optimal trajectory is close to the internal edge of the turn or, more in general, the track border;
- The optimal speed profile is at the limit of friction, thus, small localization errors can lead to divergent behaviors.

## 2. Problem Formulation

## 3. Sensors Setup

**OxTS Inertial Navigation System (INS):**this commercial module consists of a dual-antenna GNSS and an IMU , which are pre-fused to obtain a high frequency (250 Hz) pose, velocity, and accelerations estimates;**Ibeo LiDAR range finders**: four LiDAR sensors are placed on the corners of the vehicle, each with 4 vertically stacked layers at 0.8 degrees spacing. The aggregate point cloud resulting from all the sensors is provided with a rate of 25 Hz.**Optical Speed Sensor (OSS):**this sensor provides direct longitudinal and lateral speed measurements through a Controller Area Network (CAN) interface at 500 Hz, and it is not affected by wheel drift.

## 4. Mapping Procedure

#### Map Quality Assessment

## 5. State Estimation Algorithm

- Computational burden: the NVIDIA Drive PX2 has a high number of CUDA cores, while CPU is rather limited; in this paper we propose a CPU implementation for simplicity and because the available computing power was enough for the particular experimental task;
- Flexibility: the particular race format affects not only strategy but also which sensors are available and what other modules must concurrently run on the board (e.g., interfaces with V2X race control infrastructure, planning software);
- Real-time requirements: the DevBot motion control module runs in real-time on a dedicated SpeedGoat board at 250 Hz. No patch was allowed to the standard Ubuntu kernel to make it real-time compliant. Thus, it needs to receive a pose estimate signal with high frequency.

#### 5.1. Odometry (EKF1)

#### 5.2. Lidar Scan Matching (IAMCL)

- The filter automatic initialization provided in the AMCL ROS package [17] takes too much time to converge; in the racing context, however, the initialization must be accurate and should be performed before the car starts driving;
- During the race, many particles are generated outside of the racing track boundaries or with opposite orientation (with respect to the race fixed direction), which is inefficient;
- Due to unavoidable, even small, map imperfections (mainly false positives in the occupancy grid), the algorithm exhibits a kidnapping problem pretty often.

#### 5.2.1. Automatic Initialization Procedure

Algorithm 1: Automatic initialization algorithm (init). |

#### 5.2.2. Informed Prediction

#### 5.3. Smoothing Filter (EKF2)

## 6. Results

#### 6.1. Comparison With State-of-the-Art

#### 6.2. Experimental Tests

- 1.
- A run in autonomous mode at ${v}_{max}=60$ km/h;
- 2.
- A run driven by a professional human driver at ${v}_{max}=100$ km/h, the maximum speed allowed by the track;
- 3.
- A run in autonomous mode at ${v}_{max}=200$ km/h on the simulator.

#### 6.3. Dataset 1: Autonomous Mode (Experimental)

#### 6.4. Dataset 2: Manual Drive Mode (Experimental)

#### 6.5. Dataset 3: Autonomous Mode (Simulation)

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Roborace DevBot 2.0 in the Zala Zone Circuit. Localization challenges were performed in this circuit, and the presented localization framework was used.

**Figure 2.**Overview of the DevBot sensors. Light Detection and Ranging (LiDARs) are mounted in the front, side and back of the car. Global Navigation Satellite Systems (GNSS) and Inertial Measurement Unit (IMU) sensors come from the OxTS system and the Optical Speed Sensor (OSS) measures longitudinal and lateral car velocities. The Real-Time Kinematic (RTK) base station is an optional system that allows extremely high positioning precision to the OxTS system.

**Figure 3.**The adopted sensor measurement reference frame. u and v are the longitudinal and lateral velocities; x and y are the vehicle coordinates with respect to the map origin.

**Figure 4.**The map built for the race. The circuit track borders are represented by the two green lines, white areas are the obstacle free spaces, while the red line represents the racing line, to be followed during the run.

**Figure 5.**(

**a**) Computation of the mapping error ${e}_{map}\left({\xi}^{*}\left(k\right)\right)$. Given a LiDAR reading place on a GNSS pose, each laser scan point (${p}_{i}$ in red) is compared with its closest map occupied point (${m}_{{p}_{i}}$ in green); (

**b**) Result of the map quality assessment procedure on the Zala Zone track map. The circular markers are placed on GNSS positions; the colors, from green to red, represent the values of ${e}_{map}$ (green markers correspond to lower values of ${e}_{map}$).

**Figure 6.**Localization pipeline overview. OSS and IMU data feed the Extended Kalman Filters (EKFs); EKF1 produces an odometry estimate which is sent to the Informed Adaptive Monte Carlo Localization (IAMCL) module. By comparing LiDAR data with the pre-built map, IAMCL outputs a pose estimate that is then sent to EKF2, a smoothing filter with a high-frequency output. The green arrows indicate the initialization procedure described in Section 5.2.1.

**Figure 7.**Representation of the automatic initialization procedure: a number of particles is generated with a Gaussian distribution around the track center line within the admissible state space (the inner area of the racing track), while limiting the particles orientation along the race direction. Each particle is represented by a red arrow; we rotate and translate the LiDAR point cloud around each red arrow, and compute the best matching particle, whose resulting match is shown in green.

**Figure 8.**Illustrative schema of the IAMCL algorithm. The particles are first drawn with a distribution around an initial pose, then the ones with states that violate the track boundaries are eliminated and redrawn in the admissible state space.

**Figure 9.**Longitudinal and lateral errors. These are computed as the distance error components along the GNSS defined car orientation direction.

**Figure 10.**Satellite view of Zala Zone proving ground. Track boundaries and the racing line are shown in red. Gates are shown in white and the starting point in green.

**Figure 11.**Top view of the Roborace DevBot 2.0 in Zala Zone Circuit. Narrow corridors (gates) were distributed along the track, the car is 2 meters wide, while the gates were $2.5$ meters wide.

**Figure 12.**Comparison of the longitudinal, lateral and heading errors of two variants of IAMCL (with and without the extrapolation defined in Equation (7)) and the Adaptive Monte Carlo Localization (AMCL) algorithm during the second lap of the dataset.

**Figure 13.**Comparison of the longitudinal, lateral and heading errors of two variants of IAMCL (with and without the extrapolation defined in Equation (7)) and AMCL during the third lap of the dataset, with focus on an AMCL failure (due to robot kidnapping). Note that IAMCL does not suffer from such situation even if they share the same underlying scan matching algorithm.

**Figure 14.**Autonomous lap at ${v}_{max}=60$ km/h. Signals are plotted together with standard deviation (light blue), mean (red) and maximum error (yellow). The measurement of such metrics starts when the car actually starts driving after initialization.

**Figure 15.**Manually driven lap at ${v}_{max}=100$ km/h. Signals are plotted together with standard deviation (light blue), mean (red) and maximum error (yellow).

**Figure 16.**Autonomous lap in simulation at ${v}_{max}=200$ km/h. Signals are plotted together with standard deviation (light blue), mean (red) and maximum error (yellow). The measurement of such metrics starts when the car actually starts driving after initialization.

Case | H | $\mathit{h}\left(\mathit{q}\right(\mathit{k}\left)\right)$ |
---|---|---|

velocity not available | $\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\end{array}\right]$ | $\left[\begin{array}{c}x\\ y\\ \phi \end{array}\right]$ |

pose estimate not available | $\left[\begin{array}{cccc}0& 0& 0& 1\end{array}\right]$ | $\left[\begin{array}{c}u\end{array}\right]$ |

all measurements available | ${\mathbb{I}}_{4x4}$ | $\left[\begin{array}{c}x\\ y\\ \phi \\ u\end{array}\right]$ |

**Table 2.**Comparison between the average longitudinal, lateral and heading average errors of the localization stack using IAMCL (with and without extrapolation) or AMCL.

IAMCL (w/ extr.) | IAMCL (w/o extr.) | AMCL | |
---|---|---|---|

Long. error (avg/max) | 0.47/1.78 m | 1.10/2.69 m | 0.68/1.63 m |

Lat. error (avg/max) | 0.21/0.81 m | 0.20/0.72 m | 0.23/0.81 m |

Heading error (avg/max) | 0.51/1.39 deg | 0.57/1.81 deg | 0.29/1.29 deg |

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## Share and Cite

**MDPI and ACS Style**

Massa, F.; Bonamini, L.; Settimi, A.; Pallottino, L.; Caporale, D. LiDAR-Based GNSS Denied Localization for Autonomous Racing Cars. *Sensors* **2020**, *20*, 3992.
https://doi.org/10.3390/s20143992

**AMA Style**

Massa F, Bonamini L, Settimi A, Pallottino L, Caporale D. LiDAR-Based GNSS Denied Localization for Autonomous Racing Cars. *Sensors*. 2020; 20(14):3992.
https://doi.org/10.3390/s20143992

**Chicago/Turabian Style**

Massa, Federico, Luca Bonamini, Alessandro Settimi, Lucia Pallottino, and Danilo Caporale. 2020. "LiDAR-Based GNSS Denied Localization for Autonomous Racing Cars" *Sensors* 20, no. 14: 3992.
https://doi.org/10.3390/s20143992