Abstract
This paper presents Multiple Traffic Light Advisor (MTLA), a novel Green Light Optimal Speed Advisory (GLOSA) system that leverages 5G communication technology. GLOSA systems are emerging as a key component in intelligent transportation systems, thanks to the development of effective communication technologies. At its core, MTLA serves as a guidance system for drivers, providing real-time instructions to adjust vehicle speed to optimize the utilization of current and future states of traffic lights along their route.The work addresses several limitations in the current state-of-the-art approaches, including the use of an overly simplified velocity profile, the omission of potential grip and jerk in problem formulation, and the absence of a detailed description of the algorithm’s implementation aspects. Initially, we comprehensively present an optimization-free implementation of the overall control architecture based on an unconventional speed profile. Subsequently, MTLA is improved within a non-linear Model Predictive Control (MPC) framework which uses the latter nonoptimal solution as an initial guess and considers potential grip and jerk in the problem formulation. The developed systems are numerically tested and compared within a high-fidelity simulation environment using the IPG CarMaker simulator. The results demonstrate promising performance in terms of energy savings, with a significant reduction of 37% in energy usage, as well as improved overall comfort with respect to the case where no guidance is given to the driver. These findings suggest a high potential for future developments in this domain.
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Acknowledgements
The authors would like to thank all their partners in the Vodafone 5G Trial in Milan: Vodafone Automotive, Marelli, Pirelli, and Stellantis. A special acknowledgment is extended to IPG for their generous provision of student licenses that were necessary for the development and testing of the developed algorithms.
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All authors contributed equally to the development and testing of algorithms in the manuscript. The manuscript was written and revised by Michael Khayyat, Alberto Gabriele, Francesca Mancini, and Stefano Arrigoni and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Appendix A In-depth Explanation of Flowcharts
Appendix A In-depth Explanation of Flowcharts
1.1 A.1 Flowchart in Fig. 7a
The algorithm for the nonoptimal MTLA system is explained in detail. Its working principle is shown in the flowchart of Fig. 7a, the Green Check and Red Check blocks are further illustrated in Figs. 7b and c respectively. Index i represents the number of the traffic light in analysis, meaning that if \(i=2\) the second TL in front of the vehicle is considered. On the other hand, index j refers to the green phase analyzed, \(j=1\) is relative to the first green phase and \(j=2\) refers to the second green phase. The maximum value of j has been set to 2 in order not to perform to many iterations each time the algorithm is run. Moreover, if \(j=3\) it would mean to pass the third green phase, in case the actual phase is green, or the second green, in case it is red, and to do so such a low speed would be required that it would result annoying for the driver.
The first two blocks are the “Localization” and the “Activation Check”. ”Localization” block consists of the localization of the vehicle on a map by means of its abscissa. Moreover, all traffic light positions are reported on the same map.
“Activation” block defines if further calculations (and output warning for the driver) are required or not. It is based on the geometrical distance and speed evaluation between vehicle and TLs.
In the case of multiple traffic lights, once the algorithm finds the first of the four traffic lights within the horizon, the system should always be active until the last traffic light is passed. If the distance between two subsequent TLs is greater than the horizon, the following situation may occur: after passing the first traffic light, the system is deactivated as it does not find a TL within the horizon until the vehicle gets close enough to the second TL.
Once the algorithm is activated, an iterative cycle that analyzes the four traffic lights ahead of the vehicle starts. The first thing that is checked is the actual phase (“Phase” block) of the TL considered, if green the “Green Check” block is executed, otherwise the ”Red Check” one. Inside these blocks, the feasibility to get a green phase is examined and whenever a feasible maneuver to reach the \(i^{th}\) traffic light is found, the following variables are stored inside the algorithm:
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reference velocity \(v_{\text {ref}}\) that the driver should reach to get the green traffic light under analysis;
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reference acceleration \(a_{\text {ref}}\) that the driver should perform to get the green traffic light under analysis;
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the warning to be issued to the driver;
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the interval of admissible velocities \(v_{\text {adm},i}=[v_{\min ,i},v_{\max ,i}]\) to get the green traffic light under analysis.
If it is not possible to pass the traffic light under examination during a green phase, the algorithm stops and the last stored warning is issued.
1.2 A.2 Flowcharts in Figs. 7b and c
Once the “Green Check” block is activated, a whole cycle starts. It iterates according to the index j and analyzes the possibility to get either the first (\(j=1\)) or second (\(j=2\)) green phase of the \(i^{th}\) traffic light. If neither can be reached, the algorithm stops and a warning is issued to the driver. More details on the “Exit” block are given in A.2.3. The first step of the “Green Check” is the Velocity Range Definition, this step computes the required velocity range to get the green phase \(v_{\text {req},i}\). Concerning the \(j=1\) case, Eqs. 2 and 3 are used if \(i=1\), else Eqs. 9 and 10 are adopted. Otherwise, when \(j=2\), Eqs. 4 and 5 are used if \(i=1\) and Eqs. 11 and 12 if \(i>1\). The second step is the Intersection Check. In this block, the required velocity range to get the \(i^{th}\) green with the one needed to get the \(i-1^{th}\) green are intersected as in Eq. 15. The aim is to find a velocity range that allows passing both the \(i^{th}\) and \(i-1^{th}\) traffic lights.
If the first traffic light is studied (\(i=1\)), the admissible velocity range is the road admissible one as in Eq. A1
where \(v_{\text {max,road}}\) is equal to the road maximum limit speed \(v_{\text {lim,road}}\), which is \(50~\text {km}\text {h}^{-1}\) in urban environment, and \(v_{\text {min,road}}\) is an arbitrary value set to \(20~\text {km}\text {h}^{-1}\) so to avoid travelling at too low speed. On the other hand, when \(i>1\) the admissible interval is already defined from the \(i-1^{th}\) iteration. As a matter of fact, whenever there is the possibility to get the green of the \(i^{th}\) TL, an admissible velocity interval is defined. This will become the \(i-1\) interval used in the Intersection Check for the next traffic light. Furthermore, it is noteworthy that, once a velocity range to pass the first traffic light is defined, the road limits are respected. For instance, if an intersection between \(v_{\text {req},2}\) and \(v_{\text {adm},1}\) exists, this respects the road limits too. Now, if Eq. 15 results in an empty interval, it is not possible to reach the \(i^{th}\) traffic light when its \(j^{th}\) green phase is on, so the possibility to get the next one is then analyzed (\(j=j+1\)). Contrary if the interval is non-empty, \(v_{\text {adm},i}\) is defined as in Eq. A2:
Then, the “Actual Velocity Check” (AVC) block is executed, it analyzes the possibility for the driver to keep the current speed rather than performing an acceleration or deceleration maneuver. Further explanation is given in the following section, A.2.1. If the last check is satisfied, the next traffic light is analyzed (\(i=i+1\)), if not, the “Acceleration/Deceleration Maneuver Check” (AMC) is performed. Given that the diver cannot keep the current speed constant, the safeness of the acceleration or deceleration maneuver is checked. A more comprehensive analysis of this block is in A.2.2. If the “AMC” block result is positive the driver can get the \(j^{th}\) green of the \(i^{th}\) traffic light through an acceleration or deceleration maneuver. The index i is increased by one unit (\(i=i+1\)) and the next traffic light is studied. If the result is negative, the next green phase is analyzed (\(j=j+1\)).
1.2.1 A.2.1 Actual Velocity Check
The “Actual Velocity Check” analyzes the possibility for the driver to keep its actual speed constant and to get the green phase under analysis. In this way, a useless acceleration/deceleration maneuver is avoided. If the actual speed belongs to the admissible velocity range (\(v_{\text {adm},i}\)), it will allow the driver to get the green. Therefore, there is no necessity to either accelerate or decelerate and the driver can keep its speed constant. This condition occurs when Eq. A3 is satisfied:
When Eq. A3 is satisfied, the following variables are stored:
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\(v_{\text {ref}} = v\)
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\(a_{\text {ref}} = 0\)
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No warning
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\(v_{\text {adm},i}=[v_{\min ,i},v_{\max ,i}]\)
1.2.2 A.2.2 Acceleration/Deceleration Maneuver Check
The “Acceleration/Deceleration Maneuver Check” analyzes the possibility to perform an acceleration/deceleration maneuver to get the green phase of the \(i^{th}\) TL. In order to reach the traffic light as fast as possible, the target velocity \(v_{t,i}\) is set equal to the maximum velocity of the admissible interval. The corresponding target acceleration \(a_{t,i}\) is computed considering a UAM up to the first traffic light as in Eq. A4.
When \(a_{t,i}>0\), an acceleration maneuver is required, otherwise, if \(a_{t,i}<0\), a deceleration maneuver has to be performed. Now, it is verified if such acceleration/deceleration maneuver is safe for the driver. To this aim, safety acceleration and deceleration parameters are defined. The safety acceleration value \(a_{\text {safety}}\) is set to \(3~\text {m}\text {s}^{-2}\), while the safety deceleration value \(d_{\text {safety}}\) is set to \(1~\text {m}\text {s}^{-2}\). The latter has been chosen so to have soft braking maneuvers, indeed \(d_{\text {safety}}\) is the \(25\%\) of the harsh braking limit of \(4~\text {m}\text {s}^{-2}\).
The acceleration maneuver feasibility analysis is hereby described. The required acceleration to get the green of the \(i^{th}\) TL is compared with the safety one, as in Eq. A5:
When the target acceleration is smaller than the safety one, the maneuver can be performed by the driver without risks. Then, the following variables are defined and stored:
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\(v_{\text {ref}} = v_{t,i} \)
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\(a_{\text {ref}} = a_{t,i}\)
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Green Warning
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\(v_{\text {adm},i}=[v_{\min ,i},v_{\max ,i}]\)
If the safety acceleration check result is negative, an alternative way to reach the traffic light is analyzed. Instead of trying to reach the green with the acceleration corresponding to the maximum velocity of \(v_{\text {adm},i}\) (A4), the acceleration value is \(a_{\text {safety}}\). Then the feasibility of this acceleration is checked, if the speed that the vehicle reaches at the end of the acceleration phase is within the admissible velocity range \(v_{\text {adm},i}\), this maneuver can be performed. If not, the \(a_{\text {safety}}\) acceleration will not allow the driver to reach the traffic light when the green phase is on, meaning that the result of the “Acceleration/Deceleration Maneuver Check” block is negative. The velocity reached by the vehicle at the end of the acceleration phase is computed starting from Eq. 1, where the acceleration distance d is the distance to the first traffic light \(l_1\) and acceleration a is equal to \(a_{\text {safety}}\). Then, acceleration time \(t_{\text {acc}}\) and target velocity \(v_{t,i}\) are computed as in Eq. A6:
If the target velocity belongs to the interval of admissible speeds, the following variables are stored:
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\(v_{\text {ref}} = V_{t,i} \)
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\(a_{\text {ref}} = a_{\text {safety}}\)
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Green Warning
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\(v_{\text {adm},i}=[v_{\min ,i},v_{t,i}]\)
The deceleration maneuver feasibility analysis is now explained. The required deceleration to get the green of the \(i^{th}\) TL is compared with the safety one, as in Eq. A7:
When the absolute value of the target acceleration is smaller than the safety one, the maneuver can be performed by the driver without risks. The following variables are stored:
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\(v_{\text {ref}} = v_{t,i} \)
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\(a_{\text {ref}} = a_{t,i}\)
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Red Warning
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\(v_{\text {adm},i}=[v_{\min ,i},v_{\max ,i}]\)
If Eq. A7 is not satisfied, the deceleration maneuver to get the green phase of the \(i^{th}\) TL is not acceptable. Moreover, it is not possible to restrict the deceleration range, as done for the acceleration case. Indeed, the acceleration corresponding to the maximum velocity of the interval of admissible speeds \(v_{\text {adm},i}\) is the smallest in absolute value among all the admissible accelerations. Hence, by imposing the value of deceleration equal to the safety one, the respective speed is not within the interval \(v_{\text {adm},i}\).
1.2.3 A.2.3 Exit
The “Exit” block is performed whenever a traffic light cannot be passed during one of its green phases. Therefore, an analysis of the following ones is deemed useless. The warning stored during the previous iteration (\(i-1\)) is issued to the driver. When \(i=1\) and the Exit block is executed, the vehicle needs to be stopped. In fact, it is not feasible to reach the first traffic light when its green phase is on, so the vehicle needs to stop. The deceleration is computed as in Eq. A8:
If such deceleration is smaller than the harsh braking limit value of \(4~\text {m}\text {s}^{-2}\), the Red Warning is issued to the driver. On the contrary, if a hard deceleration is required the visual and acoustic warning (Red \(+\)Sound Warning) is issued.
It is noteworthy that the deceleration required to stop the vehicle at the \(i_{th}\) traffic light is calculated only once the TL has become the first one ahead of the vehicle (the vehicle passed the traffic light \(i-1\)). It can be objected that suggesting a stop in this way could make the deceleration maneuver dangerous or even not feasible. However, traffic lights are designed so to always make a safe arrest maneuver feasible if the speed limit is respected.
1.3 A.3 Flowcharts in Fig. 9b, Fig. 9c
In order to calculate the admissible region in Fig. 9a, the algorithm represented by the flowchart in Fig. 9b is used. The algorithm analyzes the first two traffic lights ahead of the vehicle (conditional block of the flowchart in Fig. 9b) and for each one the state constraints are defined (\(i^{th}\) TL State Constraints block of Fig. 9b). The state constraints are representative of the limited time-space region the vehicle can occupy so to pass the \(i^{th}\) traffic light only during green phases and they depend on the actual phase of the traffic light under analysis, as explained next.
The algorithm of the \(i^{th}\) TL State Constraint block is represented in the flowchart of Fig. 9c, where according to the actual phase the “Green Check” block or “Red Check” block is executed. The output of these blocks is the \(i^{th}\) TL State Constraints”. Lastly, the state constraints identified for each traffic light are intersected (Range Intersection block of Fig. 9b) to get the final range of admissible positions (State Constraints block of Fig. 9b).
1.4 A.4 Flowcharts in Figs. 10a and b
The flowchart of the “Red Check” block is shown in Fig. 10a. If the time of the phase shift is larger or equal to the prediction horizon, the vehicle should be ahead of the TL for the whole horizon. Otherwise, it can be beyond the TL only after the phase shift. The flowchart of the “Green Check” block is illustrated in Fig. 10b. If the time of the phase shift is larger than the prediction horizon, the vehicle can be ahead or beyond the TL. Contrary, if the time is lower or equal, a further analysis is performed on the possibility to pass the traffic light during the actual green phase. This is done by checking if the MTLA algorithm in Fig. 7a calculates that it is not possible to pass the \(i^{th}\) traffic light (\(N_{\text {green}}<i\)) or to pass it during the second green phase (\(N_{\text {pass}}>1\)). If one of these two conditions is verified the vehicle should be ahead of the traffic light after the phase shift, otherwise it should be beyond it.
Once the admissible regions are obtained for the two TLs, the “Range Intersection” Block is executed. It consists of making the intersection of the state constraints of the single traffic lights as in Eq. 16. Finally, the position state constraint can be formalized as in Eq. A9:
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Khayyat, M., Gabriele, A., Mancini, F. et al. Enhanced Traffic Light Guidance for Safe and Energy-Efficient Driving: A Study on Multiple Traffic Light Advisor (MTLA) and 5G Integration. J Intell Robot Syst 110, 73 (2024). https://doi.org/10.1007/s10846-024-02110-6
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DOI: https://doi.org/10.1007/s10846-024-02110-6