Parameter Discussion¶

The RSS papers uses a few constants required for the safety calculations. The values for these constants are not yet defined and open for discussion/regulation. Nevertheless, the implementation of the ad-rss-lib needs to define initial values for these functions.

In the following, the key parameters and the decision for possible initial values are discussed. The used parameters based on the RSS paper are:

• Response time $\rho$

  It is assumed that an AV vehicle has a shorter response time than a human driver. Therefore, there is a need to have two different parameters. As it might not be possible to determine whether another object is an AV vehicle or has a human driver, the ad-rss-lib will safely assume that all other objects are driven by humans. Hence, two parameters for the response time are used:

  • $\rho_{ego}$: for the ego vehicle
  • $\rho_{other}$: for all other objects

• Acceleration $\alpha$

  RSS proposes several different acceleration/deceleration values. One could argue that acceleration/deceleration differs with the type of vehicle. Also at least the acceleration is dependent on the current vehicle speed. As it cannot be assured that the individual acceleration of each and every car can be known and the specific car can be reliably detected, the ad-rss-lib will assume fixed constants for those values. These could be either the maximum physically possible values or restrictions that are imposed by regulation. Also there will not be different values for the ego vehicle and the other vehicles. It could be argued that for the ego vehicle e.g. desired acceleration might be known. Therefore, a shorter safety distance would be sufficient. But as all other vehicles do not know about the intention of the ego vehicle this would lead to a violation of their safe space. So the ad-rss-lib will need to calculate its checks with the globally defined accelerations values even if the vehicle does not intend to utilize them to its limits. The parameters used for acceleration are:

  • $\alpha_{accel,max}$ maximum possible acceleration
  • $\alpha_{brake,min}$ minimum allowed braking deceleration in longitudinal direction for most scenarios
  • $\alpha_{brake,max}$ maximum allowed deceleration in longitudinal direction
  • $\alpha_{brake,min,correct}$ minimum allowed deceleration in longitudinal direction for a car on its lane with another car approaching on the same lane in wrong driving direction
  • $\alpha^{lat}_{brake,min}$ minimum allowed braking deceleration in lateral direction
  • $\alpha^{lat}_{accel,max}$ maximum allowed acceleration in lateral direction
  • $\delta^{lat}_{min}$ fluctuation margin for that needs to be respected when calculating lateral safe distance

Decision on Selected Parameter Values¶

Response time¶

For the response times a common sense value for human drivers is about 2 seconds. For an AV vehicle the response time could be way lower. In order to be not too restrictive the initial value for the ego vehicle response time will be assumed as 1 second. Hence, $\rho_{other} = 2s$ and $\rho_{ego} = 1s$. If we assume a case of AD vehicles only, the response time may be reduced.

Longitudinal Acceleration¶

Finding meaningful acceleration values is more complicated. At the one hand the values should be as close as possible or even exceed the maximum physically possible values. The minimum deceleration values must also not exceed normal human driving behavior. So assuming a too high deceleration for other cars may lead to a false interpretation of the situation.

On the other hand a too big difference between the minimum and maximum acceleration values will lead to a very defensive driving style. As a result, participating in dense traffic, will not be possible (see figure below). A rule of thumb for deceleration in German driving schools is: $\alpha_{brake,min} = 4m/s^2$ and $\alpha_{brake,max} = 8m/s^2$.

But on the other hand, modern cars are able to decelerate with up to $12m/s^2$. Especially for deceleration, it is questionable whether it is possible and tolerable to restrict maximum braking below physically possible braking force.

For the maximum acceleration at low speeds a standard car will be in the range of $3.4m/s^2$ to $7m/s^2$. But there are also sport cars that can go faster than that. But for acceleration a regulation to a maximum value seems to be more likely than for deceleration.

Restricting velocity to the current speed limit¶

Required safety distance for cars driving at 50 km/h (city speed) in same direction with $\alpha_{brake,min} = 4m/s^2$ and $\alpha_{brake,max} = 8m/s^2$ and $\rho_{ego} = \rho_{other} = 2s$

The assumption that a car can always accelerate at $\alpha_{accel,max}$ during the reponse time, leads to a significant increase of the required safety distance. The figure above shows the required safety distance for different acceleration values. So acceleration about $4m/s^2$ doubles the required safety distance from $40m$ to about $80m$ at city speeds.

Therefore, it might be advisable to add a restriction that a car is only allowed to accelerate up to the allowed speed limit. In addition, the common behavior (in Germany) is to respect a safety distance of speed/2, e.g. in a city with a speed limit of $50km/h$ the safety distance shall be $25m$. Hence, it is obvious that the parameters may require some adjustments to allow reasonable driving.

Further possible restrictions¶

Another possibility to decrease the required safety distance to the leading vehicle would be to take the intention of the ego vehicle into account. E.g. if the ego vehicle is following another vehicle and is not intending to accelerate, then there is no need to assume that the ego vehicle is accelerating during its response time. Nevertheless, there are several issues with that approach:

1. It needs to be assured that all intended and unintended accelerations (e.g. driving down a slope) are known to RSS.
2. If RSS formulas are regarded as regulations, the safety distance must be kept regardless to the intent of the vehicle.

Therefore, in the current implementation this approach will not be applied.

Lateral Acceleration¶

When defining the parameters for lateral acceleration and deceleration, it is import to keep in mind that the definition must allow bypassing of vehicles. Physically high lateral accelerations are possible. In order to be able to bypass a vehicle that is driving on a parallel lane, the safe lateral distance needs to be safe during the complete response time of the other vehicle.

Let us consider two identical vehicles driving on the centerline of two adjacent lanes with zero lateral velocity. There is no lateral conflict, if the distance between the border of the car and the adjacent lane is bigger than the distance that the vehicle will cover when accelerating laterally at maximum during its response time and then decelerating to zero lateral velocity.

Distance a vehicle will cover when applying the "Stated Braking Pattern" with $\rho_{vehicle} = 2s$

The figure above shows the required safety distance, without considering the fluctuation margin, each car needs to keep to the lane border so the vehicles can pass without lateral conflict. With an assumed minimal lane width of 3 meters and an assumed vehicle width of 2 meters, the distance from vehicle edge to lane border is 0.5 meter, if the car is driving exactly in the middle of the lane.

Hence, the required safety distance must be at most 0.5 meter. When using the same values for acceleration and deceleration this will lead to $\alpha^{lat}_{accel,max} < 0.1m/s^2$. But when restricting the acceleration to that value a lane change will take almost 8 seconds.

As a result it is advisable, to use a higher deceleration than acceleration to keep the required safety margin and allow for faster lane changes. E.g. $\alpha^{lat}_{brake,min} = 0.8m/s^2$ and $\alpha^{lat}_{accel,max} = 0.2m/s^2$ will fulfill the given safety distance requirement. An increase to higher acceleration values is for the given constraints not possible, as the distance covered during response time is already 0.4 meters.

It is obvious that given the lateral safety definition a lane change will at least have a duration of two times the response time.

The lateral distance requirement is very strict, therefore it is required to also come up with a desirably small value for the required lateral safety margin $\delta^{lat}_{min}$. As this should only cover for fluctuations, there is also no need for a huge margin. Thus initially this value will be set to $\delta^{lat}_{min} = 10 cm$. This value should be able to cover small fluctuations, but will not have a big impact on the safety distance.