Relevancia de las variables

To validate the theoretical results, the proposed adaptive approach has been implemented in PLEXE [172], a high-fidelity simulator that allows the platoon investigation by coupling realistic vehicle dynamics (such

4.4 Numerical Analysis  75

Figure 4.1: Keyframe of the simulation scenario. The vehicles platoon moves on a reserved lane (the right-most lane). Initial conditions are reported in Table 4.2.

as engine and brake limitations, air drag, friction, etc....) with realistic wireless network simulations. Indeed, PLEXE exploits, in an integrated simulation environment, the network simulator OMNeT++/MiXiM, the road traffic simulator SUMO and detailed vehicle dynamic models. OM- NET++/MiXiM is used to simulate V2V communication based on the IEEE 802.11p standard, while the extended version of SUMO, that in- cludes realistic car models, can simulate the vehicle dynamics under the action of the collaborative strategy. We remark that, in agreement with our theoretical framework we have configured the PLEXE simulator so that our collaborative algorithm only exploits neighbor information coming from V2V communications. Moreover, in this simulation envi- ronment, the different communication delays values are not parameters to be set during simulations (e.g., as well as they result from a random distribution) since their realistic presence, originated by the actual con- ditions of the communication channel, is accurately emulated by PLEXE [170]. To show the effectiveness of the proposed strategy for cooperative tracking, here we consider a 10 [km], 3 lanes, stretch of freeway. Here an automated platoon of 7 vehicles plus a leader travels in a reserved lane (the right-most lane) and each vehicle, driven by its on-board control, has no possibility to overtake the vehicle ahead (Fig. 4.1 shows a keyframe of the simulation scenario).

The traking performances have been evaluated considering two repre- sentative leader maneuvers, namely: (i) a trapezoidal speed profile (see Fig. 4.2a); (ii) a realistic driving profile used to test the performance of connected vehicles during the Grand Cooperative Driving Challenge (GCDC) [106] (see Fig. 4.2b).

Note that the trapezoidal profiles are usually used to mimic the effect of traffic jam, when a sudden deceleration is required due to the presence of a forward obstacle (e.g. a vehicle not belonging to platoon or not

60 80 100 120 140 160 180 200 0 10 20 30 40 50 v0 (t ) time [s] (a) 100 120 140 160 180 200 0 10 20 30 40 50 v0 (t ) time [s] (b)

Figure 4.2: Leader maneuvers: (a) Trapezoidal speed profile; (b) Realistic driving profile.

connected) then followed by an acceleration for the repositioning of the platoon to the target velocity as soon as it is possible [59]. Furthermore, to disclose the flexibility of the approach with respect to information flows, the investigation is conducted for different exemplar communi- cation topologies used in the platoon literature [59] and depicted in Fig. 3.5:

1. Predecessor-Follower (P-F): each vehicle can exchange information only with its preceding vehicle;

2. Leader-Predecessor-Follower (L-P-F): each vehicle can communi- cate with its preceding vehicle and the leading vehicle;

3. Bidirectional-Leader-Follower (B-L-F): each vehicle can exchange information with its preceding vehicle, its follower vehicle and the leading vehicle;

4. All-to-All (Broadcast, BR): each vehicle exchange information with all the other vehicles in platoon.

The parameters for both network and traffic simulation are reported in Tab. 4.1 and Tab. 4.2. Note that the value of the theoretical delay margin computed as in (4.53) and reported in Tab. 4.2, τ? _{= 0.21 [s],}

is within the average end-to-end communication delay, typical of IEEE 802.11p vehicular networks, which is of the order of hundredths of a second (i.e., 10−2 _{[s]) [6].}

To further evaluate the safety in all the different driving and com- munication scenarios, we have also quantitatively analyzed the possible

4.4 Numerical Analysis  77

Table 4.1: NETWORK SIMULATION PARAMETERS.

Communication system model setting

Communication protocol IEEE802.11p

Channel data rate 6 [M bps]

Beacon frequency 10 [Hz]

Beacon size 200 [bytes]

Bernoullian channel

PER p 0.6

Gilbert-Elliott channel

PER p (GOOD) 0.3

PER p (BAD) 0.7

state duration exp(0.5 [s−1]) (E[X] = 2 [s])

Table 4.2: TRAFFIC SIMULATION PARAMETERS.

Freeway length 10 [km]

Lanes 3 (two-way)

Platoon size 8 cars

Platooning car max acceleration 3.5 [ms-2_]

Drivetrain constant T 0.5 [s]

Platooning car mass 1460 [kg]

Platooning car length li 4 [m]

Initial position [r0(0), · · · , r7(0)]> [40, 60, 80, 100, 120, 140, 160, 180]>[m]

Initial speed [v0(0), · · · , v7(0)]> [27, 25, 22, 26, 25, 24, 28, 21]>[ms-1]

Initial acceleration ai(0) 0 [ms-2] ∀i = 0, 1, · · · , 7

Control gains ζij,1 ζij,1 = 0.01

Control gains ζij,2 ζij,2 = 10

Control gains ζij,3 ζij,3 = 0.1

Initial condition ρij(0) ρ10(0) = 5.9, ρ10(0) = 2.35 ρi,i−1(0) = 0.6 (i = 1, · · · , N ) Initial condition βij(0) β10(0) = 6.8, βi0(0) = 0.68 βi,i−1(0) = 0.68 (i = 1, · · · , N ) Initial condition γij(0) γ10(0) = 0.68, γi0(0) = 0.68 γi,i−1(0) = 0.68 (i = 1, · · · , N ) Spacing policy dij 15 [m]

Theoretical delay margin τ? 0.21 [s]

emergence of critical driving situations for all the maneuvers under in- vestigation by exploiting a non-dimensional warning index (or collision index CI) that is well known in the automotive literature [138]. This index represents the occurrence of a possible physical collision in the

current driving situation and it is defined for each vehicle i (i = 1, · · · , 7) as follows: CIi= ci− dbr,i dw,i− dbr,i , (4.54)

where ci is the actual spacing between vehicle i and vehicle i − 1; dw,i

and dbr,i are the braking-critical and warning-critical distances between

vehicle i and vehicle i − 1, respectively. (See [138] for the definition of all these quantities and for details on how they can be computed according to a given trajectory.) From (4.54) it follows that, if the actual distance ci exceeds dw,i and dbr,i, then the warning index CIi assumes a positive

value and indicates that the current driving situation is in a safe region. If ci is below dbr,i, then the warning index assumes a negative value

denoting a dangerous driving situation. Therefore, the distance of the index from zero can be interpreted as a safety margin.

Finally, the robustness with respect to packet losses/hard delay has been also evaluated by implementing the well-known Bernoulli and Gilbert- Elliot channel models [169]. In particular, we first use a Bernoullian channel with independent random losses Packet Error Rates (PERs), and then we employ a Gilbert-Elliott channel driven by a two-state Markov chain.