Abstract Augmented Lazy Theta*: Applying Graph Abstractions to Trajectory Planning with Speed-Limit Constraints

Trajectory planning is a generalisation of path planning in
which velocity is also taken into consideration. Considering
velocity, in the context of a real-world system such as a
robotic vehicle, means considering physical constraints such
as the speed limit constraints when steering the vehicle. One
of the recent algorithms for solving this type of planning
problem is Augmented Lazy Theta*.
In this work we introduce the trajectory planner Abstract
Augmented Lazy Theta*. This planner uses a combination
of abstraction and relaxation to reduce the search space of
Augmented Lazy Theta*. We demonstrate that Abstract Augmented
Lazy Theta* significantly improves the time performance
of Augmented Lazy Theta* whilst retaining the same
overall solution quality. Additionally, we show that Abstract
Augmented Lazy Theta* performs competitively with another
state-of-the-art trajectory planning algorithm, the RRT*
algorithm, by demonstrating significantly better