Verification of RISK 2 and RISK 3 on virtual data

The reliability of parameters RISK2 and RISK3 was evaluated on a number of simulations including swerving and braking maneuvers. More in detail, the full protocol of simulations is summed up in the following lists.

- Front braking: high decelerations leading to wheel locking (max braking torque 660 Nm, dry asphalt, max µ_x1.15). Target conditions (to perform a deeper investigation, in addition, also some rear braking maneuvers were considered)

• Initial speed, 50 km/h, 100 km/h, 150 km/h;

• Target roll angle, 0^◦, 10^◦, 20^◦, 30^◦.

- Swerving maneuver: fast cornering, e.g. fast lane change, with a roll rate below 60^◦/s.

• Initial speed, 50 km/h, 100 km/h, 150 km/h;

• Target roll angle, 30^◦.

- L_sw maneuver [15]: fast cornering, e.g. last-second collision avoidance, with a roll rate over 60^◦/s and below 110^◦/s.

• Initial speed, 50 km/h, 100 km/h, 150 km/h;

• Target roll angle, 30^◦.

Concerning the braking maneuvers the vehicle ran in steady state conditions for 6 s and then applied a braking force distributed over 0.5 s (with internal fluid delays 0.7 s, [41]). A similar time evolution has been adopted for the swerving maneuvers: 6 s is the time step at which the maneuver begins.

Despite the general application of RISK2 and RISK3 (braking, acceleration, swerving, steady cornering, curve entry, etc.) the dangerous maneuvers addressed in the simulations were only braking maneuvers, focusing only on the main purpose of the research activity. The applicability of the parameters in other scenarios, apart from braking, will be addressed in future activities.

The simulations reported above were performed for three different vehicles: a maxi scooter Piaggio Beverly300, a super sports motorcycle¹, and a sports touring motorbike². All the simulations were carried out in Bikesim ^R. Different vehicles were considered in order to have a preliminary evaluation of the versatility of the parameters application on different PTWs.

Due to the necessity to address mainly the instabilities related to the steering behavior and the mainframe oscillations (still connected to the steer oscillations), only the front braking and swerving maneuvers were simulated.

The swerving maneuvers (including Lsw) were simulated in order to address unsteady and fast maneuvers that an average rider can perform safely. It was expected that in such conditions the RISK2and RISK3 would not give any alert (exceeding the thresholds). The swerving maneuvers were simulated only at the largest roll angle, because it has been considered as the most critical swerving condition (compared to the cases with lower roll angles, 10^◦and 20^◦).

The parameters RISK2 and RISK3 and the corresponding thresholds were defined following literature basis, and motorcycle dynamics theory. The assumptions made for the thresholds properties (values of the constants) were made according to the state of the art, therefore the evaluation the aforementioned parameters on the listed simulations aimed to verify the assumptions made and not to perform a strict calibration.

Figure 5.3 shows the application of RISK₂and RISK₃to the L_swmaneuver at different speeds (ϕ target 30^◦), for the Beverly300. At each speed the parameters never exceed the thresholds. However it worth noting that the value of the parameters in RISK2are close to the limit, especially at 50 km/h; on the other side the Lsw represents the upper limit of the swerving maneuver, for a standard rider. It is correct to assume this as limit condition, expecting that it is almost impossible to perform faster swerving maneuvers, especially with a big scooter.

Regarding RISK3 no particular issues were detected, and the comparison, in the simulations addressed confirmed the reliability of RISK3 and RISK3T. It is interesting to notice that for increasing speeds the gap between RISK3 and RISK3T decreases. It is hypothesized that this aspect is partially related to the steering rate ˙δ: it was observed that at higher speeds ˙δ increases to achieve the target roll angle. That increases also the value of the front slip angle, thus the ∆α as well.

Also for the super sports motorbike and the touring motorcycle the verification of RISK₂ and RISK₃give good results as well. Figure 5.4 depicts the application of

1Default inertial, geometrical properties and mass distribution given by Bikesim ^Rsoftware (range of motorcycles such as the Yamaha YZF/FZ1, Honda CBR600RR, Kawasaki NINJA, and Suzuki GSX-R1000). Braking characteristics customized, similar to a Yamaha YZF/FZ1

2Default inertial, geometrical properties and mass distribution given by Bikesim ^Rsoftware (range of motorcycles such as BMW K1200 GT, Honda VFR1200, and Kawasaki 1400 GTR).

Braking characteristics customized, similar to a Honda VFR1200

0 2 4 6 8 10 Initial speed 50 km/h, Max roll angle 30^◦

0 2 4 6 8 10 Initial speed 100 km/h, Max roll angle 30^◦

0 2 4 6 8 10 Initial speed 150 km/h, Max roll angle 30^◦

Figure 5.3: Application of RISK2 and RISK3 to different Lsw

maneuvers. Vehicle: Piaggio Beverly300

4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 0

0.5 1 1.5 2

x 10⁻³

Time (s) RISK 2, RISK 2T

RISK2

RISK2T

4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

0 0.5

1x 10⁻³

Time (s) RISK 3, RISK 3T

RISK3

RISK3T

Figure 5.4: Application of RISK2 and RISK3 to a Lsw maneu-ver involving a super sports motorbike. Initial speed 50 km/h, Max roll angle 30^◦

the parameters to the super sports motorbike running at 150 km/h and performing a L_sw with the target roll angle of 30^◦.

It is possible to see, that differently from the Beverly300, the RISK₂ in this motorcycle is more distant from the threshold. The same is for the Touring motorbike. This small difference can be addressed focusing on the steering properties of the vehicle influenced by the mass distribution. In fact, the sports motorbikes have a distribution of masses more on the front wheel, while it is the opposite for the Beverly300, and other scooters. That can strongly influences the steering control, the vehicle maneuverability, and the risk parameters as well.

Considering the emergency braking maneuvers, at different roll angles and different initial speeds, the application of the risk parameters aims to detect the instant at which those maneuvers become unstable and not safe.

Figure 5.5 shows the results of the risk parameters application on the hard braking simulation, for different roll angles, at 50 km/h. In the cases depicted, the main parameter exceeds the threshold after 0.5-0.7 s the braking started (the time step increases for lower roll angles). At these time steps, the roll angle has not changed too much (within 2^◦) and the roll rate is below 10^◦/s (the max value is over 250^◦/s). That means that the potential critical event is detected in a time range sufficiently small to modify the vehicle dynamics to correct and recover the stability.

Comparing the behaviors of RISK2 and RISK3, it is possible to see that,

despite similar time steps in risk detection, the evolution with respect to the thresholds is different. Only RISK3stays constantly over the threshold during the maneuver, while RISK2moves across the threshold line. That shows that the use of only one parameter is not sufficient for the correct risk detection, both must be taken into consideration at the same time.

The same observations can be drawn also for the rear braking case. Figure 5.6 shows a hard rear braking, with wheel locking, at 20^◦and an initial speed of 50 km/h. For the rear braking case it is possible to see that RISK₃ anticipates the fall detection than RISK₂. During a hard rear braking while cornering the effect of front aligning torque on the steer, due longitudinal force on the front wheel is minimized, thus limiting the steering rate. Therefore the variation of the ∆α, caused by a fast change of αr, is faster than the variations oftan(δ), thus resulting˙ in a faster RISK3.

Also for the super sports motorcycle and the sports touring motorbike, the implementation of the risk parameters gives the same results. In Figure 5.7 the hard front braking in curve of a super sports motorcycle is depicted. Again, it is possible to notice the high number of fluctuations of RISK₂compared to RISK₃.

Finally, the reliability of RISK2 and RISK3 was tested in the racetrack introduced for the validation of the tire-road friction estimation (§4.2). In Figure 5.8 the run of the Bevely300 is shown. Hereafter only the run of Beverly300 is reported because, compared to the runs of the sports motorcycles, it is the only simulation where there has been one fall detection, due to an unexpected passing on the side curb at the end of the last curve (time 96.5 s). The event caused some skids (the corresponding δ and ˙δ are ±6^◦and ±6^◦/s), finally controlled by the rider when the vehicle went back to the track (Figure 5.9).

Due to the low level of danger and the low potentiality of fall, the detection of risk parameters is only for few time steps.