1. CGDD4003 – Spring 2010
A* Path Planning

2. Background Developed in 1968 Searches state space
Move from start state to goal state (source and destination)
Iteratively expands options based upon
Adjacent states (transition via “moves”)
Heuristics

3. Workings of A* A* (pronounced A star):
Maintains an Open and Closed sets
Keeps working on “most promising” state
Generates successors of current state
Successors “placed” into Open or Closed set
Updates Open state if it already exists in Open
Maintains “parent path” for each node

4. Attributes of Each State
Heuristic estimate g(v) from start to v
CostFromStart(v)
Heuristic estimate h(v) from v to goal
CostToGoal(v)
Total path estimate t(v)
Used to select “most promising”
TotalCost(v)
t(v) = g(v) + h(v)

5. A* Algorithm: Initialize
Initialize(start, goal, agent) Open = {} Closed = {} s = start CostFromStart[s] = 0 CostToGoal[s] = PathCostEstimate(start, goal, agent) [s] = null Open += s

6. A* Algorithm: Search
A_Star_Search(start, goal, agent) Initialize(start, goal, agent) while Open != {} s = Open.Pop() if (s == goal) construct path backward using  values return true else for each v  Adjacency[s] cost = CostFromStart[s] + w(s, v, agent) if (cost < CostFromStart[v]) or (v  Open and v  Closed) [v] = s CostFromStart[v] = cost CostToGoal[v] = PathCostEstimate(v, goal, agent) TotalCost[v] = cost + CostToGoal[v] if (v  Closed) remove v from Closed if (v  Open) adjust v’s location in Open // move “up” Open.Push(v) Closed.Push(s) return false

7. Estimation/Heuristic Function
CostToGoal(v) = 0
CostToGoal(v) = 1

8. Properties of Heuristics in A*
CostToGoal[v] estimate always decreases
PathCostEstimate(v) is the deciding factor
If PCE(v) is small, search space increases
If PCE(v) is big, search space decreases
But PCE must be <= true cost to ensure optimal path
If PCE > true cost, we’ll generate sub-optimal path
But do so in better (quicker) time!

9. PCE Heuristic Comparison
Non-overestimating
heuristic
Overestimating
heuristic

10. Considerations of A*
A significant consideration in A* path planning is memory
Must maintain Open and Closed sets
These take up large amounts of space
O(breadthdepth)
A* also requires us to re-sort the Open list frequently (which can be costly)