  Path planning is an important component in any highly automated vehicle
system. In this report, the general problem of path planning is considered
first in partially known static environments where only static obstacles are
present but the layout of the environment is changing as the agent acquires new
information. Attention is then given to the problem of path planning in dynamic
environments where there are moving obstacles in addition to the static ones.
Specifically, a 2D car-like agent traversing in a 2D environment was
considered. It was found that the traditional configuration-time space approach
is unsuitable for producing trajectories consistent with the dynamic
constraints of a car. A novel scheme is then suggested where the state space is
4D consisting of position, speed and time but the search is done in the 3D
space composed by position and speed. Simulation tests shows that the new
scheme is capable of efficiently producing trajectories respecting the dynamic
constraint of a car-like agent with a bound on their optimality.
