update docs

Author: SchwartzCode

docs/modules/5_path_planning/time_based_grid_search/time_based_grid_search_main.rst

@@ -87,102 +87,16 @@ Multi-Agent Path Planning
 Priority Based Planning
 ~~~~~~~~~~~~~~~~~~~~
 
-TODO: explain the algorithm
+The planner generates an order to plan in, and generates plans for the robots in that order. Each planned path is reserved in the grid, and all future plans must avoid that path. The robots are planned for in descending order of distance from start to goal.
 
-TODO: explain why spacetime a* is so much slower
+This is a sub-optimal algorithm because no replanning happens once paths are found. It does not guarantee the shortest path is found for any particular robot, nor that the final set of paths found contains the lowest possible amount of time or movement.
 
-Using SpaceTimeAstar for the single agent planner::
-    Using planner: <class 'PathPlanning.TimeBasedPathPlanning.SpaceTimeAStar.SpaceTimeAStar'>
-
-    Planning for agent:  StartAndGoal(index=1, start=Position(x=1, y=1), goal=Position(x=19, y=18))
-    Found path to goal after 300 expansions
-
-    Planning for agent:  StartAndGoal(index=2, start=Position(x=1, y=2), goal=Position(x=19, y=17))
-    Found path to goal after 645 expansions
-
-    Planning for agent:  StartAndGoal(index=3, start=Position(x=1, y=3), goal=Position(x=19, y=16))
-    Found path to goal after 273 expansions
-
-    Planning for agent:  StartAndGoal(index=4, start=Position(x=1, y=4), goal=Position(x=19, y=15))
-    Found path to goal after 7798 expansions
-
-    Planning for agent:  StartAndGoal(index=5, start=Position(x=1, y=5), goal=Position(x=19, y=14))
-    Found path to goal after 186 expansions
-
-    Planning for agent:  StartAndGoal(index=6, start=Position(x=1, y=6), goal=Position(x=19, y=13))
-    Found path to goal after 216790 expansions
-
-    Planning for agent:  StartAndGoal(index=7, start=Position(x=1, y=7), goal=Position(x=19, y=12))
-    Found path to goal after 472128 expansions
-
-    Planning for agent:  StartAndGoal(index=8, start=Position(x=1, y=8), goal=Position(x=19, y=11))
-    Found path to goal after 916485 expansions
-
-    Planning for agent:  StartAndGoal(index=9, start=Position(x=1, y=9), goal=Position(x=19, y=10))
-    Found path to goal after 2098980 expansions
-
-    Planning for agent:  StartAndGoal(index=10, start=Position(x=1, y=10), goal=Position(x=19, y=9))
-    Found path to goal after 50 expansions
-
-    Planning for agent:  StartAndGoal(index=11, start=Position(x=1, y=11), goal=Position(x=19, y=8))
-    Found path to goal after 62 expansions
-
-    Planning for agent:  StartAndGoal(index=12, start=Position(x=1, y=12), goal=Position(x=19, y=7))
-    ...
-    (timed out)
-
-Using the safe interval path planner::
-
-    Planning for agent:  StartAndGoal(index=1, start=Position(x=1, y=1), goal=Position(x=19, y=18))
-    Found path to goal after 256 expansions
-
-    Planning for agent:  StartAndGoal(index=2, start=Position(x=1, y=2), goal=Position(x=19, y=17))
-    Found path to goal after 336 expansions
-
-    Planning for agent:  StartAndGoal(index=3, start=Position(x=1, y=3), goal=Position(x=19, y=16))
-    Found path to goal after 526 expansions
-
-    Planning for agent:  StartAndGoal(index=4, start=Position(x=1, y=4), goal=Position(x=19, y=15))
-    Found path to goal after 619 expansions
-
-    Planning for agent:  StartAndGoal(index=5, start=Position(x=1, y=5), goal=Position(x=19, y=14))
-    Found path to goal after 534 expansions
-
-    Planning for agent:  StartAndGoal(index=6, start=Position(x=1, y=6), goal=Position(x=19, y=13))
-    Found path to goal after 596 expansions
-
-    Planning for agent:  StartAndGoal(index=7, start=Position(x=1, y=7), goal=Position(x=19, y=12))
-    Found path to goal after 149 expansions
-
-    Planning for agent:  StartAndGoal(index=8, start=Position(x=1, y=8), goal=Position(x=19, y=11))
-    Found path to goal after 551 expansions
-
-    Planning for agent:  StartAndGoal(index=9, start=Position(x=1, y=9), goal=Position(x=19, y=10))
-    Found path to goal after 92 expansions
-
-    Planning for agent:  StartAndGoal(index=10, start=Position(x=1, y=10), goal=Position(x=19, y=9))
-    Found path to goal after 1042 expansions
-
-    Planning for agent:  StartAndGoal(index=11, start=Position(x=1, y=11), goal=Position(x=19, y=8))
-    Found path to goal after 1062 expansions
-
-    Planning for agent:  StartAndGoal(index=12, start=Position(x=1, y=12), goal=Position(x=19, y=7))
-    Found path to goal after 1000 expansions
-
-    Planning for agent:  StartAndGoal(index=13, start=Position(x=1, y=13), goal=Position(x=19, y=6))
-    Found path to goal after 867 expansions
-
-    Planning for agent:  StartAndGoal(index=14, start=Position(x=1, y=14), goal=Position(x=19, y=5))
-    Found path to goal after 964 expansions
-
-    Planning for agent:  StartAndGoal(index=15, start=Position(x=1, y=15), goal=Position(x=19, y=4))
-    Found path to goal after 1146 expansions
-
-    Planning took: 0.11520 seconds
+TODO: include a gif
 
 
 References
 ~~~~~~~~~~~
 
 -  `Cooperative Pathfinding <https://www.davidsilver.uk/wp-content/uploads/2020/03/coop-path-AIWisdom.pdf>`__
 -  `SIPP: Safe Interval Path Planning for Dynamic Environments <https://www.cs.cmu.edu/~maxim/files/sipp_icra11.pdf>`__
+- `Prioritized Planning Algorithms for Trajectory Coordination of Multiple Mobile Robots <https://pure.tudelft.nl/ws/portalfiles/portal/67074672/07138650.pdf>`__