# Voting algorithm approach for autonomous vehicle safe driving

Mohamed Ryad Boukhari, Ahmed Chaibet, Moussa Boukhnifer, Sebastien Glaser

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Mohamed Ryad Boukhari, Ahmed Chaibet, Moussa Boukhnifer, Sebastien Glaser. Voting algorithm approach for autonomous vehicle safe driving. 2018 IEEE International Conference on Industrial Technology (ICIT), Feb 2018, Lyon, France. pp.327-332, 10.1109/icit.2018.8352198. hal-04446575

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This may be the author's version of a work that was submitted/accepted for publication in the following source:

Boukhari, Mohamed, Chaibet, Ahmed, Boukhnifer, Moussa, & Glaser, Sebastien (2018)

Voting algorithm approach for autonomous vehicle safe driving.

In Gomes, L, Venet, P, Monmasson, E, & Spagnuolo, G (Eds.) *Proceedings of the 2018 IEEE International Conference on Industrial Technology (ICIT 2018)*.

Institute of Electrical and Electronics Engineers Inc., United States of America, pp. 327-332.

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https://doi.org/10.1109/ICIT.2018.8352198
# Voting Algorithm Approach for Autonomous
Vehicle Safe Driving

Mohamed Ryad Boukhari

Institut VEDECOM

Versailles, France

ryad.boukhari@vedecom.fr

Ahmed Chaibet

ESTACA

Montigny-le-Bretonneux, France

ahmed.chaibet@estaca.fr

Moussa Boukhnifer

ESTACA

Montigny-le-Bretonneux, France

moussa.boukhnifer@estaca.fr

Sébastien Glaser

Institut VEDECOM

Versailles, France

sebastien.glaser@vedecom.fr

***Abstract***—The aim of this paper is to assess three voting algorithms ensuring fault tolerance for an autonomous vehicle. Thus, by using a vehicle longitudinal dynamic model and a SHERPA/VEDECOM sensors model, the emphasis is to ensure a reliable inter-distance measurement to the controller in both faultless and faulty scenarios. The simulation results show the effectiveness of the designed algorithms to provide fault tolerance; nonetheless, some disparities are noticed between the voting algorithms in terms of performance.

***Index Terms***—Voting Algorithms, Fault Tolerant Control, Vehicle Perception, Sensors.

## I. INTRODUCTION

Driverless cars have attracted considerable attention nowadays, where the scientific community tries to perform more and more efficient intelligent transportation and autonomous systems. Thus, self-driving cars must have the ability to operate interactively with their surroundings without human intervention. In this perspective, the autonomous driving relies on the development of dedicated functions, where each one has a defined task [1]. The vehicles environment perception consists in sensing the vehicles neighborhood and providing information about obstacles positioning (positions and velocities). The perception is of high importance, since it is needed in the path planning and the feedback control tasks. Furthermore, the whole accurate vehicle operation is based on the reliability of the perception. However, the latter appears to be harsh to perform in view of the complexity and the unpredictability of the vehicle’s environment.

This paper focuses on the vehicle’s longitudinal spacing control obeying a given inter-distance policy. Consequently, the distance between the leader and the controlled vehicle has to be harnessed. Nevertheless, the real issue of measuring the vehicular inter-distance is the lack of the present state of the art sensors technology to perform in all operating modes. Thus, the use of several sensors technologies is to overcome each ones issues by fusing their data [2]. Furthermore, the sensors data fusion can be affected if the sensors have either hardware or software failures, leading to information inaccuracies. Hence, the aim is to handle these unreliable measurements and thus ensure a fault tolerance that guarantees safer operation and autonomous driving.

The problem was dealt in [3], where authors proposed a switching strategy to choose between three feedback control systems, each one consisting of: a given sensor (radar, lidar and sensor vision), a state observer, and a controller. The switching paradigm selects the feedback control that minimizes a quadratic criterion, from those which the tracking errors performances lie in a faultless robust invariant set. Evaluating vehicular inter-distance can be very difficult to perform in practice due to the unpredictable environment, and even Kalman filtering techniques faults, because of the difficulty to determine the process noise matrix.

In [4], [5], a sensor fusion architecture minimizing the sensors faults influence is presented. This technique is based on a federated fusion structure weighted by *Support Vector Machine (SVM) Fault Detection and Diagnosis* module. The latter compares discrepancies between two local fusion structures, using each a Velodyne sensor and vision sensor, and the master fusion structure. The Velodyne sensor is considered as sensor reference in the two local fusion structures. Then, the weighting logic configures the sensors’ influence (either low or high). This technique seeks to ensure if the obstacle is detected. Then, one can subsequently measure the distance between the obstacle and the autonomous vehicle. This method’s drawback is due to the use of cascaded detectors, which can increase the computing time.

In that context, the purpose of our work is to propose a voting algorithm approach to reduce the impact of the fault and ensure a safe autonomous driving. This method has been widely used to deal with the fault tolerance issues. Indeed, this technique is mainly used in engineering areas, for the ease of design and implementation. Examples include many spheres, sentiment analysis [6], medical monitoring [7], electric vehicle application [8]–[10] and aeronautics [11].

The paper under consideration deals with comparative study with the *Maximum Likelihood Voting (MLV)*, the *Weighting Average (WA)* and the *History Based Weighting Average (HBWA)* algorithms. It is structured as follows: The general context and fault tolerant scheme are viewed in section 2, the voting algorithms are presented in the section 3. Simulation results are dealt with in section 4, and concluding remarks are supplied in section 5.
## II. FAULT TOLERANT SCHEME

The VEDECOM demonstrator vehicle is equipped with two frontal (Ibeo Lux) Lidars up to 200m: range operating at low frequency of 50Hz (the two Lidars are mounted in the front left and front right vehicle). Thus, the fusion box processing software fuses the information); a 200m long-range Radar RS300 of an operating frequency up to 77GHz and a monovision camera using an EyeQ2 Chip Mobileye image processing hardware. The map of sensors' regions is depicted in Fig. 1.

<figure><img src="image_4.png" /><figcaption>Fig. 1: The multi-sensor regions</figcaption></figure>

Each of the cited sensors has a specific limitation leading that does not operate properly in certain conditions. Indeed, the use by Lidar of light spectrum wavelengths, can lead to failures proportionally when there are increasing conditions of snow, fog, rain or dust particles in the air. Furthermore, the Lidar cannot detect color or contrast, and cannot provide optical character recognition capabilities [12]. Furthermore, the Radar may fail to detect the front vehicle due to the speed difference between the leader and the following vehicle. Radar can also be incapable to detect motorcycle, or front vehicles outside the center of the lane [13]. Besides, the Mobileye may not completely work if the camera is partially or totally blocked. Moreover, it does not guarantee a 100% detection rate of the front vehicle. In addition, weather conditions influence considerably Mobileye recognition and response capabilities.

As aforementioned, each sensor has its limitation, mainly because of the technology used, resulting in such a way to specific operating field of each sensor. Moreover, each sensor is liable to a fault its ideal operating area due to either a software or hardware failure, which leads to faulty distance measurement. To counteract this dysfunction, the fault tolerant scheme must handle all the possible scenarios, and keep a stable and safe autonomous driving. For that purpose, we propose the output fault tolerant paradigm as it can be seen in Fig. 2 which ensuring a safe range measurement. Indeed, from each sensor/signal processing bloc, the voting algorithm provides a reliable and a fault tolerant distance signal to the

speed reference bloc, then, the controller reduces the faulty impact on the safety autonomous vehicle driving.

<figure><img src="image_5.png" /><figcaption>Fig. 2: The Fault Tolerant paradigm</figcaption></figure>

The setpoint speed is generated by the speed reference block. It is based on the safe distance criterion [14]. Then, from the given distance, one can deduce the speed which ensuring this safe distance:

$$V_{ref} = \frac{d_{FTC} - d_{stop}}{h} \qquad (1)$$

Where $d_{stop}$ is the distance at the stop, and h a time constant.

The proposed control scheme is designed by taking into account the following assumptions:

* Only one fault by sensor is considered;

* The road is assumed to be plane (no slope, no inclination)

* Vehicle lateral dynamic is not considered.

* Yaw, Pitch and roll dynamics are not considered

## III. THE VOTING ALGORITHMS

As depicted in Fig. 2, the voting algorithm is capable of extract a safe distance measurement, only by using the sensors signal. This ability is allowed by the comparison of the input signals, and then the voting logic switches to the reliable signal. The voting techniques used in this work are:

### A. Maximum Likelihood Voting (MLV)

The first works on the MLV are found in [15]. The main idea of this approach is to choose one of the input signals, ensuring the highest reliable probability. Thus, the dynamic reliability of each sensor $f_i$, a conditional probabilities $\Delta_i$ are computed as follows [9], [16], [17]:

$$\Delta_i = \begin{cases} f_i, & \text{if } |x_k - x_i| \le D_{max} \\ \frac{1 - f_i}{N - 1}, & \text{otherwise} \end{cases} \qquad (2)$$

Where N is the input sensors number (in our study N= 3), $D_{max}$ is a real constant corresponding to the threshold (it is set to 10% of the reference range to apprehend the noise effect), and $x_k$ is the reference range. The likelihood of each input sensor is then calculated:
$$ \chi_i = \frac{\prod_{i=1}^{N} \Delta_i}{\sum_{i=1}^{N} \prod_{i=1}^{N} \Delta_i} \quad (3) $$

The output signal is then chosen, obeying to the maximum likelihood:

$$ y = \underset{\text{st.argmax}}{\chi_i} x_i \quad (4) $$

## B. Weighting Average (WA)

Based upon weighting coefficients, the WA algorithm calculates the average of the input signals. Besides, The output signal is determined as a continuous smooth function of the redundant inputs using the weighted average. Indeed, this technique aims to reduce the transient effect, such that no switching is permitted, but the faulty sensor is isolated through a continuous numerical weighting [18]. Hence, given an input signals $x_i$ such that $i = 1, ..., N$, and $N$ is the number of sensors, the output signal $y$ is determined as follows:

$$ y = \sum_{i=1}^{N} w_i x_i / \sum_{i=1}^{N} w_i \quad (5) $$

Where $w_i$, $i = 1, ..., N$ are the weighting coefficients. These coefficients correspond to the sum of the inverse distance of each input signal from other signals, in such a way that, more the signal is close to the others implies a high weighting. Further, the weighting are obtained as follows:

$$ w_p = \sum_{i=1}^{p} \sum_{i<j}^{N} k_{ij}, \quad p = 1, ..., N \quad (6) $$

$k_{ij}$ are the inverse of the distance between the input signals, they are given by:

$$ k_{ij, i \neq j} = \begin{cases} 10^{-5} & \text{if } |x_i - x_j| = 0 \\ \frac{1}{|x_i - x_j|} & \text{otherwise} \end{cases} \quad (7) $$

## C. History-Based Weighting Average (HBWA)

The use of a history informing on the health of the input signals is the main idea of this technique. Indeed, through the time, reliability indices of each sensor is accumulated helping, in such a way, in weightings computation. In [19], authors have presented two philosophies of this technique. The first one, called **Agreement State Indicator Weighted Average**, which uses a dynamic weighting functions based upon the state indicators. Hence, the weightings are proportionally linked with the indicators history. Furthermore, the second one called **Module Elimination Weighted Average**, calculates an average of the indicators history, then, each input with indicator history lower than this average, is considered as unreliable, and its weight is set to zero. Based upon this approach, recent works on the HBWA are found in the literature. Thus, authors in [20] presented a modified HBWA algorithm using a harsh dynamic threshold. Nevertheless, the proposed methodology presents a drawback of ambiguities associated to the input

signals. In [21], a hybrid HBWA algorithm is presented. The considered methodology provides high reliability; safety and availability performances compared to the existing history based weighted average voting algorithms. This technique relies on the following algorithm:

1) Given input signals $x_i$ and $x_j$ the distance is calculated:

$$ k_{ij} = |x_i - x_j| \quad (8) $$

Where $i, j = 1, 2, ..., N$ and $i \neq j$.

2) Using tunable threshold parameters $a$ and $q$, the level of agreement of each input is computed as follows:

$$ s_{ij} = \begin{cases} 1 & \text{if } k_{ij} \le a \\ \left(\frac{q}{q-1}\right)\left(1 - \frac{k_{ij}}{q \cdot a}\right) & \text{if } a < k_{ij} < q \cdot a \\ 0 & \text{if } q \cdot a \le k_{ij} \end{cases} \quad (9) $$

3) The level of consensus $S_i$ of the input $i$, is then calculated:

$$ S_i = \sum_{j=1, i \neq j}^{N} s_{ij} / N - 1 \quad (10) $$

4) The weight $w_i$, of each input $i$, is calculated as follows:

$$ w_i = \begin{cases} 0 & \text{if } S_i = 0 \text{ or } P_i(n) < P_{\text{avg}}(n) \\ \frac{S_i}{N-1} & \text{otherwise} \end{cases} \quad (11) $$

$P_i(n)$ and $P_{\text{avg}}(n)$ are the state indicators of the $i^{th}$ sensor at the $n^{th}$ cycle, and the average of the state indicators at the $n^{th}$ cycle, respectively and they will be then discussed later.

5) An initial output, noted $\bar{y}$, is then calculated using the sensor signal inputs $x_i$ and the weightings $w_i$:

$$ \bar{y} = \frac{\sum_{i=1}^{N} w_i x_i}{w_i} \quad (12) $$

Where $i = 1, ..., N$.

6) The distances between the initial output and each input signal of the sensor are calculated in order to determine the appropriate final output:

$$ k_{\bar{y}i} = |\bar{y} - x_i| \quad (13) $$

And $i = 1, ..., N$.

7) The final output signal, $y$, is then chosen:

$$ y = \underset{\text{st.argmin}}{k_{\bar{y}i}} x_i \quad (14) $$
8) The history $H(n)$ of the $i^{th}$ sensor is recorded at the $n^{th}$ voting cycle, by calculating the level of consensus $h(n)$ of the current cycle, based upon the distance of each sensor $x_i$ input with the final output $y$:

$$h(n) = \begin{cases} 1 & \text{if } k_{yi} \le a \\ \left(\frac{q}{q-1}\right)\left(1 - \frac{k_{yi}}{q \cdot a}\right) & \text{if } a < k_{yi} < q \cdot a \\ 0 & \text{if } q \cdot a \le k_{yi} \end{cases} \quad (15)$$

Subsequently, the history record is given by:

$$H_i(n) = \sum_{n=1}^{N} h_i(n) \quad (16)$$

9) The state indicator $P_i(n)$ of the $i^{th}$ input at the $n^{th}$ voting cycle is calculated by the following equation:

$$P_i(n) = \frac{H_i(n)}{n} \quad (17)$$

<figure><img src="image_6.png" /><figcaption>Fig. 3: Sensor measurements with faults emulation</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 5: The interdistance resulting from MLV algorithm</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7: The interdistance resulting from WA algorithm</figcaption></figure>

10) Finally, the average state indicator $P_{avg}(n)$, at the $n^{th}$ voting cycle is determined as follows:

$$P_{avg}(n) = \frac{\sum_{i=1}^{N} P_{i}(n)}{N} \quad (18)$$

## IV. SIMULATION RESULTS

The simulation results of our proposed fault tolerant scheme are presented in this section. The first step consists in determining the threshold parameters of the MLV and HBWA. For this purpose, an iterative method based on extensive simulation is used. The threshold values are given as follows: $a = 0.007$, $q = 700$ and $D_{max} = 1.37$. Each sensor has its reliability regarding its operating range. Furthermore, we assume that the Lidar reliability is $f_{Lidar} = 99\%$, the Radar is much reliable in long range obeying the following reliability relation $f_{Radar} = 0.00067 \cdot d + 0.95$, while the Mobileye presents a better accuracy in the nearest distances with a reliability expression $f_{Mobileye} = -0.0013 \cdot d + 0.97$.

<figure><img src="image_9.png" /><figcaption>Fig. 4: Comparison of faults effects on vehicle speed</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6: The sensors transition of MLV algorithm</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8: The WA algorithm weightings</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 9: The interdistance resulting from HBWA algorithm</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10: The sensors state indicators evolution</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11: Distance comparison</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12: Speed reference comparison</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 13: Speed comparison</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 14: Acceleration comparison</figcaption></figure>

As aforementioned, this simulation uses a SHERPA/VEDECOM ground reality based on sensors model, allowing us to measure the vehicular range. Indeed, we emulate the sensor faults at specific moments, by setting the measurement back to zero as depicted in Fig. 3. The autonomous vehicle must keep a safe inter-distance regarding the leader vehicle speed profile. In Fig. 4, we can see that faulty sensors influence the autonomous vehicle behavior, and lead to unsafe driving. The first voting algorithm tested is the MLV. As input, we have the three faulty sensor signals of Fig. 3, and the output of the algorithm is depicted in Fig. 5, where the inter-distance of the MLV algorithm in red line and the real inter-distance in green line. From this figure, we may notice that the MLV algorithm ensures a safe inter-distance despite the emulating faults on the: Lidar at

$t = [35.5s, 45.5s] \cup [129s, 170s]$, the Radar at $t = [7s, 14.4s]$ and the Mobileye at $t = [63.6s, 74.4s]$. Fig. 6 gives an overview of sensors' transitions of the MLV algorithm. Indeed, when the Lidar has a good performance, it is always chosen; otherwise, the algorithm chooses the reliable sensor regarding its reliability. Hence, we can also notice regarding near distances, the MLV algorithm switches on the Mobileye, while in the long range, it selects the Radar.

The WA algorithm was also tested using the same scenario as above, Fig. 7 shows the inter-distance of the WA algorithm in blue while comparing it with the real inter-distance in green. Hence, the weightings of the WA algorithm are depicted in Fig. 8. This algorithm is capable of managing the faulty behavior. The third algorithm HBWA is subjected to the same test conditions - where the output of this algorithm in black
and the real inter-distance in green are given in Fig. 9. Through this figure, we can notice that the faults are rejected by this algorithm. In Fig. 10 the state indicators of each sensor are given. We remark that the reliability of each sensor decreases from high level probability to lower one. In addition, when we emulate the faults, we see a slow decrease of the state indicators and an instant increase when the sensor recovers (at the end of the fault emulation). The comparison between the three voting algorithms in terms of distance and reference speed generated is depicted in Fig. 11 and Fig. 12, respectively, while, the speed and acceleration of the autonomous vehicle comparison are shown in Fig. 13 and Fig. 14, respectively. As we can notice from these figures, the dynamic performances of the autonomous vehicle are affected by the three voting algorithms.

## V. CONCLUSION

To counteract the issue of external sensor faults in the case of longitudinal autonomous driving, a comparative study of three voting algorithms is performed. Indeed, this approach demonstrated its ability and effectiveness in faults' management. Furthermore, the History-Based Weighting Average shows better performances than the two other algorithms. Since it selects one sensor as an output, as well as the Maximum Likelihood Voting, it is a complex task to compute thresholds that can undertake the *Chattering Phenomenon* for a large operating window. Even if it tolerates the faults, the Weighting Average has poor performances compared to the above-mentioned algorithms. In fact, the output signal is degraded by using the corrupted inputs as well. Furthermore, one of the main drawbacks of this technique is inherent to the choice of the signals which are close to each other. If the signals were far from each other, this would be safer even if they were corrupted.

Future works include the validation of the proposed algorithms in a real demonstrator vehicle.

## ACKNOWLEDGEMENT

Thanks goes to the "Institut VEDECOM", the donor of this work.

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