Scenario-dependant Optimality

The criterion of scenario-dependant optimality evaluates the planner’s ability to adapt to the requirements of different traffic scenarios. Such adaptations can be an adjustment of the parameters of the cost functions, an alteration in the layout of the state lattice, etc. Accordingly, a scenario reasoning module is necessary which can determine the type of adaptation in order to satisfy the scenario-based requirements. Although the scenario reasoning module is absent in the current implementation of the proposed planner, it can be easily embedded in the planning architecture (cf. Section 5.3). The evaluation here focuses on the flexibility of the planner in response to given scenario-based instructions which are manually issued in the experiments.

Figure 7.5(a)shows the experiment where a target speed and a target location are assigned to the planner. To follow the instruction, the vehicle has to reach the target speed at the target location. As the current planner is not able to incorporate arbitrary locations into its set of lattice nodes, it can only direct the vehicle to reach a speed that is close to the target speed at the location that is near to the required target location. By activating the cost functions related to achieving a target speed, the planner generates a plan as demonstrated in Figure 7.6. As is mentioned in previous discussions about the criterion of horizon optimality, scenario-based adaptations can have the same effect as the application of an extensive horizon from the perspective of increasing the global

(a)

(b)

(c)

Figure 7.4: The unsuccessful overtaking manoeuvre generated based on insuffi-cient knowledge about the vehicle obstacle which is provided by the simulated scanning sensors. The cyan box is the bounding box of the vehicle obstacle used for the construction of the cost maps.The cyan plan is older than the red one.

Note that the vehicle obstacle gives different shapes when the ego-vehicle looks at it from different points of view. The planner fails to generate a traversable trajectory in the last picture as the “looks” of the vehicle obstacle changes so much that the predicted position of the ego-vehicle for the current planning hori-zon is untraversable itself. The several layers of points are the spatial samples of the planning horizon where the red plan is generated.

optimality of the optimal plan. In the example of the lane change manoeuvre at high speed demonstrated in Figure 7.2, a timely deceleration designated by the scenario reasoning module can make it possible for the planner to generate a feasible lane change manoeuvre later, as is shown in Figure7.5(b).

It is noteworthy that it is the restriction of the maximum rate of change of curvature

˙

κ_max that makes all generated trajectories with high speed infeasible in the scenario shown in Figure 7.2(a). There is a relationship between the cubic spiral that represents the path edge and the rate of change of curvature along the trajectory edge, which is given as:

˙

κ= dκ(s)

dt = dκ(s) ds

ds

dt = dκ(s)

ds v (7.1)

where κ(s) refers to the expression of the curvature in terms of arc length (cf. Equa-tion3.7). Given a specific connectivity pattern and a straight road, the maximum ^dκ(s)_ds can be easily derived. With the knowledge of the mapping between the connectivity pat-tern and the maximum ^dκ(s)_ds corresponding to it, the planner can choose a connectivity pattern that can generate a trajectory with its maximum ^dκ(s)_ds below ^κ˙max_v . In this way,

(a) A target speed that is expected to be reached by the vehicle at a specific target location is issued by the “manual” scenario reasoning module. The target speed is 10m/s. The red point denotes the target location. The current speed of the vehicle is about 29m/s.

(b) The lane change manoeuvre at low speed.

Figure 7.5: Deceleration to reach the target speed designated by a manual scenario reasoning module. The several layers of points are the spatial samples of the planning horizon where the red plan is generated. The red plan is one planning cycle younger than the cyan plan.

(a) (b) (c)

Figure 7.6: The plan in terms of speed, acceleration and jerk during the deceler-ation. The green plan is younger than the blue one. The short red curves record the five-second tracking result of the vehicle. The end of the planning horizon based on which the blue plan is generated has not reached the target location.

The end of the planning horizon based on which the green plan is generated has passed the target location. The applied cost function for reaching a target speed only restricts the lattice nodes that have not passed the target location.

the planner is able to generate feasible trajectories as long as the required connectivity pattern can be realized in the lattice. Figure7.2(c)shows the plan made possible by the connectivity pattern that can introduce the trajectory edges that satisfy the restriction imposed on the rate of change of the curvature.

Another experiment where an adjustment of the weights of the cost functions is nec-essary is demonstrated in Figure7.7(a). The neighbouring lane of the current travelling lane of the vehicle has oncoming traffic. As the criterion of time efficiency has a higher priority than the requirement of avoiding driving onto oncoming lanes, the ego-vehicle implements a risky manoeuvre that is intended to overtake the slow-moving vehicle ob-stacle via the oncoming lane. Such manoeuvre results in an even riskier behaviour later when it is necessary for the vehicle to return back to the original lane, as is shown in Figure7.7(b)and Figure7.7(c). The scenario reasoning module can predict the necessity

(a) A trajectory that makes the ego-vehicle take over the slow-moving vehicle in front of it via an oncoming lane.

(b) The ego-vehicle makes a risky lane change.

(c) The critical situation resulting from the risky lane change.

Figure 7.7: Risky trajectories generated by the planner without any far-sighted instruction from the scenario reasoning module. The yellow and magenta patches belong to the first frame of the cost map of dynamic obstacles. The yellow area is the high cost area, while the magenta patch refers to the fatal area. The actual shape of the vehicle obstacle, rather than the simulated sensor data, is used in this experiment. The several layers of points are the spatial samples of the planning horizon where the red plan is generated. The red plan is one planning cycle younger than the cyan plan.

of the second lane change based on the given road model; it can thus increase the cost for the vehicle to drive onto the oncoming lane. In this way, the aggressive trajectory shown in Figure7.7(a) can be avoided.