# Multicriteria Autonomous Vehicle Control at Non-Signalized Intersections
## 4 Simulation Results
### Complex Simulation Example  
The proposed method is also validated with a more complex example in CarSim environment. Here, four different type of autonomous vehicles arrive at the intersection, while a fifth vehicle also approaches the intersection entering zone and joins the proposed optimization as the preceding vehicle leaves the intersection. The initial positions and velocities of the autonomous vehicles along with their masses are shown in Figure 8. As illustrated, the intention of Vehicle 1 and Vehicle 3 is to continue heading straight, while Vehicle 2, Vehicle 4 and Vehicle 5 are intending to turn left.  
Simulations with the above detailed initial conditions were run with differently calibrated centralized controllers: first optimizing traveling time, secondly energy consumption.  
The velocity and acceleration profiles of the vehicles running with the two different performance criteria are shown in Figure 9. In the case of the time optimal control law, Vehicle 4 crosses the intersection first, followed by Vehicle 3, Vehicle 1 and Vehicle 5, while Vehicle 2 finally leaves the intersection at 10.2 s. As shown in Figure 9a the velocities of each vehicles increase at some point and Vehicle 1 and Vehicle 3 uses the maximal possible acceleration for a short period of time, see Figure 9b. Note, that Vehicle 4 having a big initial velocity decelerates heavily before entering the intersection conflict zone, and as all other vehicles, keeps an even velocity after entering.  
On the other hand, with the energy optimal intersection control the vehicle ordering is changed significantly. Similarly to the time-optimal case, Vehicle 4 having big initial velocity and mass as well, leaves the intersection first. Next, Vehicle 1 also having bigger mass enters the intersection, followed by Vehicle 3 and Vehicle 2, while Vehicle 5 leaves the intersection finally at 12 s. Thus, in case of the energy optimal intersection control, the total traveling time of the vehicles increase by almost 2 s. Note, that in  
Figure 8: Intersection scenario with five vehicles.  
order to save energy, all vehicles only decelerate as shown in Figure 9d, decreasing their velocity before entering the conflict zone, see Figure 9c.  
In Figure 10, the control energies (both driving and braking) of each vehicles are depicted along with the total control energy of all vehicles. It is well demonstrated, that the time-optimal solution shown in Figure 10a requires more than 2500 kJ of total control energy in contrast with the approximately 1700 kJ required by the energy-optimal centralized controller. Thus, for the given scenario, more than 800 kJ of total control energy can be saved in the intersection for the price of approximately 2 s in total traveling time.  
Note, that above simulation scenarios where repeated with several different initial conditions. The proposed algorithm proved to be reliable, computationally efficient and fast enough for the simulation environment, hence it can be tested in real-time implementations.  
Figure 9: Velocities and accelerations of autonomous vehicles.