Pioneering SE(2)-Equivariant Trajectory Planning for Automated Driving

Planning the trajectory of the controlled ego
vehicle is a key challenge in automated driving. As for human
drivers, predicting the motions of surrounding vehicles is
important to plan the own actions. Recent motion prediction
methods utilize equivariant neural networks to exploit geo-
metric symmetries in the scene. However, no existing method
combines motion prediction and trajectory planning in a joint
step while guaranteeing equivariance under roto-translations of
the input space. We address this gap by proposing a lightweight
equivariant planning model that generates multi-modal joint
predictions for all vehicles and selects one mode as the ego plan.
The equivariant network design improves sample efficiency,
guarantees output stability, and reduces model parameters.
We further propose equivariant route attraction to guide the
ego vehicle along a high-level route provided by an off-the-
shelf GPS navigation system. This module creates a momentum
from embedded vehicle positions toward the route in latent
space while keeping the equivariance property. Route attraction
enables goal-oriented behavior without forcing the vehicle to
stick to the exact route. We conduct experiments on the
challenging nuScenes dataset to investigate the capability of our
planner. The results show that the planned trajectory is stable
under roto-translations of the input scene which demonstrates
the equivariance of our model. Despite using only a small split
of the dataset for training, our method improves L2 distance
at 3 s by 20.6 % and surpasses the state of the art.