A* search algorithm with an added time dimension to deal with dynamic obstacles.

astar-algorithm, obstacle-avoidance, time-dimension, 3d
pip install space-time-astar==0.7.1


Space-Time A*

Space-Time A* (STA*) Search Algorithm with an Additional Time Dimension to Deal with Dynamic Obstacles.


The package is named space-time-astar and listed on PyPI. You can use the pip to install:

pip3 install space-time-astar

For multiple agents, you might be interested in the cbs-mapf package which uses this package as the low-level planner, also on GitHub and PyPI.


Import Planner

from stastar.planner import Planner

Constructor Parameters

Planner(grid_size: int, robot_radius: int, static_obstacles: List[Tuple[int, int]])
  • grid_size: int - each grid will be square with side length grid_size.
  • robot_radius: int - agents are assumed to be circles with radius being robot_radius.
  • static_obstacles: List[Tuple[int, int]] - A list of coordinates specifying the static obstacles in the map.

It is important that grid_size is not too small and static_obstacles does not contain too many coordinates, otherwise the performance will severely deteriorate. What is 'too many' you might ask? It depends on your requirements.

Find Path

Use Planner's plan() method:

plan(start: Tuple[int, int],
     goal: Tuple[int, int],
     dynamic_obstacles: Dict[int, Set[Tuple[int, int]]],
     semi_dynamic_obstacles:Dict[int, Set[Tuple[int, int]]] = dict(),
     max_iter:int = 500,
     debug:bool = False) -> np.ndarray:


  • start: Tuple[int, int] - A start coordinate.
  • goal: Tuple[int, int] - A goal coordinate.
  • dynamic_obstacles: Dict[int, Set[Tuple[int, int]]] - Dynamic obstacles are really other agents reservation in space-time, more details below.
  • semi_dynamic_obstacles: Dict[int, Set[Tuple[int, int]]], optional - This parameter exist because we have to take the agents that have reached their destinations into account, they are essentially static obstacles from specific times.
  • max_iter: int, optional - Max iterations of the search. Default to 500.
  • debug: bool, optional - Prints some debug message. Default to False.

The keys for dynamic_obstacles are integers representing time and the values are sets of coordinates. It tells the planner what coordinates we need to avoid at each time step. Currently, it is assumed that dynamic obstacles are other agents (with the same robot_radius) and are treated differently to static obstacles.


A numpy.ndaarray with shape (L, 2) with L being the length of the path.

Theoretical Background

Here is a good document about Space-Time A* (STA*) written by David Silver.

In a nutshell, STA* is normal A* plus a time dimension. See the illustration below.

On the left block, the first agent plans its path and reserve its path through time (with no regard to the second agent).

On the right block, the second agent plans its path while avoiding the path reserved by the first agent (i.e. the dynamic_obstacles argument).

Implementation decisions in space-time-astar package

  • The Manhattan distance, an admissible and consistent heuristic, is used in this implementation. You can change this by changing the h() function in planner.py.

  • The agents can be bigger than the grid.

  • The dynamic obstacles are assumed to be other agents of the same size. This can be changed in the safe_dynamic() inner function in plan().


Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.