Horizon Optimality

With limited planning horizon, the proposed motion planner can only achieve horizon optimality rather than global optimality. That is, the construction of the trajectories and the selection of the optimal one are based solely on the information available within the current planning horizon. Worse still, even such limited information cannot be fully utilized by the planner due to the insufficient perception of the vehicle. The criterion of horizon optimality is thus intended to assess the extent to which the best constraint-abiding trajectory satisfies a long-term goal. Such long-term goals can be, for example, a specific expectation of the speed of the vehicle, which is calculated based on the

investigations into the future. They can also embody the requirement of taking into account the complete information available within the planning horizon.

Figure 7.2demonstrates a scenario where an extensive horizon can help the planner to recognize timely the necessity of deceleration for making a lane change within a short distance. Without any long-term information, the vehicle keeps running at high speed, which is an optimal behaviour from the perspective of the short planning horizon. By the time it realizes that it is necessary to make a lane change in order to drive onto the road that leads to the next checkpoint, there has been not enough room for the required manoeuvre. That is, the trajectories constructed in accordance with the limited connectivity pattern and the high speed are beyond the limited physical capability of the vehicle. The main constraint on the feasibility of the trajectory here is the maximum rate of change of curvature. As a result, the planner is left with no feasible plan, as is shown in Figure7.2(a).

In contrast, a more extensive planning horizon adopted in the experiment shown in Figure7.2(b)warns the planner of the necessity of a future lane change in time and thus makes it possible for the planner to plan a feasible trajectory with a timely deceleration.

However, an extensive planning horizon will definitely deteriorate the computational efficiency of the planning. In this sense, a lightweight scenario reasoning module that can assign a long-term goal to the planner is a better choice than an extensive planning horizon. The issues revolving around scenario reasoning will be discussed in the next subsection along with the evaluation of scenario-dependent optimality.

Now it is time to talk about the other kind of long-term goal, i.e., the requirement of considering the complete information within the planning horizon in the generation and selection of plans. Figure7.3and Figure7.4present different overtaking behaviours generated by the proposed planner in handling the same traffic scenario. In Figure7.3, the static costs of the paths in terms of obstacles are evaluated based on the actual shape of the vehicle obstacle, and the ego-vehicle circumnavigates the static vehicle obstacle smoothly. In contrast, the overtaking manoeuvre generated based on the information provided by the simulated sensors shown in Figure7.4is not satisfying. When the ego-vehicle looks at the ego-vehicle obstacle from behind, the perceived shape of the obstacle is much smaller compared to its actual shape. Consequently, the ego-vehicle takes a plan that is of high risk and even practically untraversable as demonstrated in Figure 7.4(a).

When the vehicle discovered the “larger shape” of the obstacle, as is shown in Fig-ure 7.4(b), it abandons the old plan (cyan) and generates a new trajectory (red) that is much safer. Finally, in Figure 7.4(c), the “looks” of the vehicle obstacle changes so drastically that all the trajectory edges from the ego-vehicle to the lattice turn out to be untraversable. Consequently, the planner fails to generate a plan. Such problems caused by insufficient perception can be mitigated by applying larger dilation around the obstacle and imposing heavier punishments when the ego-vehicle and the obstacle

(a) The planner fails to generate a feasible lane change manoeuvre at high speed. It has a short planning horizon of 100m. A spatial node in the lattice is connected to up to 2×9 other spatial nodes.

(b) The planner succeeds in generating a feasible lane change manoeuvre with the help of an extensive planning horizon of 150m. A spatial node in the lattice is connected to up to 2×9 other spatial nodes.

(c) The planner succeeds in generating a feasible lane change manoeuvre at high speed thanks to a richer connectivity pattern. Its planning horizon is 100m. A spatial node in the lattice is connected to up to 3×9 nodes.

Figure 7.2: The lane change behaviours generated by the proposed planner with different planning distances and connectivity patterns. The red plan is younger than the cyan one. The several layers of points are the spatial samples of the planning horizon where the red plan is generated.

get too close. Nonetheless, a sufficient perception is desired in order to generate safer, more flexible and more consistent trajectories. It is noteworthy that only IBEO LiDAR sensors are employed on the autonomous vehicle in the simulation experiments. These sensors are installed at relatively low positions around the vehicle (cf. Figure 1.1) and have a very small VFOV, which makes it easy to obstruct their sights by a part of the whole obstacle. Should the Velodyne LiDAR sensor be mounted on the top of the vehicle ( cf. Figure 1.1), the perception of the vehicle would be much better.

There are also cases where scanning sensors cannot play a role in capturing the information of the obstacles. An example of such scenario is when a pedestrian appears suddenly from behind the static vehicles parked at the roadsides. In this case, a collision might be unavoidable. The perception system of the autonomous vehicle should be improved so that the information of the hidden traffic participants can also be taken into account in planning trajectories.

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Figure 7.3: The overtaking manoeuvre generated based on sufficient information of the vehicle obstacle. The cyan box is the bounding box of the vehicle obstacle used for the construction of the cost maps. 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.