Semantics of Describing Scenes

In this section, we define the semantics of AVUnit(Scenario Description). Even though AVUnit only describes the motion task of the ego vehicle, the predefined motions of NPC vehicles and pedestrians, and other environment related information, such as time and weather, it describes a concrete scenario implicitly as the trajectory of the ego vehicle is determined by the ADS under testing according to AVUnit. Hence, we define the semantics of AVUnit as a trace, which is a sequence of scenes. Here a scene is a snapshot of the physical world, including the status of all objects defined in AVUnit(e.g.,the ego vehicle, NPC vehicles, pedestrians, and weather) and other traffic conditions (e.g., traffic signs), and the ADS world, including the perception results of NPC vehicles, pedestrians, obstacles, and traffic conditions.

Basic Defination of scene

Defination 1: A scene is a mapping θ such that:

  • θ(map) is the map (i.e., a map name);

  • θ(time) is the time;

  • θ(weather) is the weather.

  • θ(ego) is the status of the ego vehicle, including the position, orientation, velocity, and acceleration;

  • θ(npc,truth) maps each NPC vehicle npc to its status, including position, orientation, velocity, acceleration, andsize, in the real world;

  • θ(ped) maps each pedestrian ped to its status, i.e., its position, orientation, velocity, acceleration, and size, in the real world;

  • θ(obs) maps each static obstacle obs to its position andsize in the real world;

  • θ(traffic) returns the state of different traffic signs, suchas traffic lights, stop sign, and speed limit sign, in the real world.

  • θ(npc,perception) maps each NPC vehicle npc to itsstatus in the view of the ego vehicle;

  • θ(ped,perception) maps each pedestrian ped to its status in the view of the ego vehicle;

  • θ(obs,perception) maps each static obstacle obs to its status in the view of the ego vehicle;

  • θ(traffic,perception) returns the state of different traffic signs in the view of the ego vehicle.

Feasible Regions

At each scene, the objects, i.e., the ego vehicle, npc vehicles, pedestrians and static obstacles, should be on the feasible region of the map, which means their positions should not exceed the region of the defined map. Additionally, since vehicles should move along lanes, their positions should also be limited to roads. Note that pedestrians can move around the feasible region of the map. Moreover, a vehicle or pedestrianhas its own limit on the maximal speed. Specifically, for the initial scene \(\theta_0\), we should also guarantee the the objects are located at different positions. Note that during the execution of the scenario, we do not require and also cannot guarantee collision avoidance of the ego vehicle or other objects. Hence,the constraints for each scene can be defined as follows.

Defination 2: Let \(A(\theta(map))\) and \(L(\theta(map))\) be the whole feasible region and the lane region of the map, respectively, and \(OBJ\) be the set of the ego vehicle, all NPC vehicles, pedestrians and static obstacles in AVUnit. Let \(p(\theta(object))\) and \(vs(\theta(object))\), \(object \in OBJ\) denote the position and speed of an object at a scene. The maximal speed of an objectis denoted as \(vs_{\max}(object)\). Then, \(\forall \theta\), it should satisfy the following constraints:

\[\begin{split}p(\theta(object))\in A(\theta(map)) \label{c1}\\ vs(\theta(object)) \leq vs_{\max}(object)\label{c2}\\ p(\theta(npc)) \in L(\theta(map))\label{c3}\end{split}\]

The initial scene \(\theta_0\) should further satisfy:

\[\forall e_1, e_2\in OBJ, p(\theta_0(e_1)) \neq p(\theta_0(e_2)) \label{c4}.\]

Unchangeable Parameters

In AVUnit , we do not allow the change of maps during the execution of a scenario. A vehicle is also not allowed to move back during its motion on a road. Hence, we have the following constraints.

Defination 3: Given two successive scenes \(\theta_1\) and \(\theta_2\) of a trajectory, and let \(l(\theta(npc))\) be the lane where the vehicle \(npc\) is running along at scene \(\theta\). Then, we have:

\[\begin{split} \theta_1(map) = \theta_2(map); \label{c5}\\ l(\theta_1(npc)) \neq l(\theta_2(npc)) \vee \nonumber\\ d(p(\theta_1(npc)), l(\theta_1(npc))) \leq d(p(\theta_2(npc)), l(\theta_2(npc))) \label{c6}.\end{split}\]

Overall Defination

Defination 4: A trace of AVUnit is a sequence of scenes, denoted as \(T=\langle \theta_0, \theta_1, \ldots, \theta_n \rangle\), satisfying the constraints described in Equations above.