  Motion planning in dynamically changing environments is one of the most
complex challenges in autonomous driving. Safety is a crucial requirement,
along with driving comfort and speed limits. While classical sampling-based,
lattice-based, and optimization-based planning methods can generate smooth and
short paths, they often do not consider the dynamics of the environment. Some
techniques do consider it, but they rely on updating the environment on-the-go
rather than explicitly accounting for the dynamics, which is not suitable for
self-driving. To address this, we propose a novel method based on the Neural
Field Optimal Motion Planner (NFOMP), which outperforms state-of-the-art
approaches in terms of normalized curvature and the number of cusps. Our
approach embeds previously known moving obstacles into the neural field
collision model to account for the dynamics of the environment. We also
introduce time profiling of the trajectory and non-linear velocity constraints
by adding Lagrange multipliers to the trajectory loss function. We applied our
method to solve the optimal motion planning problem in an urban environment
using the BeamNG.tech driving simulator. An autonomous car drove the generated
trajectories in three city scenarios while sharing the road with the obstacle
vehicle. Our evaluation shows that the maximum acceleration the passenger can
experience instantly is -7.5 m/s^2 and that 89.6% of the driving time is
devoted to normal driving with accelerations below 3.5 m/s^2. The driving style
is characterized by 46.0% and 31.4% of the driving time being devoted to the
light rail transit style and the moderate driving style, respectively.
