If the reason is because the start node location is always changing, can't we just modify the g cost of each node in the OPEN set instead of the h cost? (e.g. subtract by the cost of the edge you just traversed)
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D* Lite is an incremental heuristic search algorithm based on LPA* (Lifelong Planning A*). LPA* performs a search a from the start to the goal vertex and uses the g-values as estimates of the start distances. Unlike LPA*, D* Lite searches the graph backwards, i.e. from the goal to the start vertex. That way, the g-values are estimates of the goal distances.
Actually, D* Lite is derived from LPA* by exchanging the start and goal vertex and reversing all edges. Therefore, both algorithms have the same preconditions to be applied to graphs, the successor and predecessor of all nodes must be obtainable.
In summary and answering your question,
can't we just modify the g cost of each node in the OPEN set instead of the h cost?
no, the g-cost is the cost of the path already traversed, while the h-cost is the estimated cost to reach the goal. What is uncertain is the cost of the path to reach the goal, not the path already traversed.
FrankS101
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