Path Planning in a Dynamic Environment

1. Path Planning in a Dynamic Environment Scott McKeever, Nora Szasz, Dennis Gregorovic, Angel Chang Amit Seshan

2. Introduction • What is path planning and whom does it concern? • Agents in Games • UAVs • You! • Unmanned Autonomous Vehicles (UAVs) should perform “intelligently” • One problem UAVs encounter is getting from point A to B “safely and cheaply”

3. Overview • Problem Description • Network Description • Algorithms • Demonstration of Algorithms • Conclusion

4. Problem Description • Maneuver a vehicle from point A to point B, using little to no a-priori information, with limited sensor range, while in the presence of dynamic obstacles. • Ojective: Find a path that is optimal according to some cost function.

5. Network Description • What is the Structure of the Network? • Nodes are a transformation of the map • Grid Idea (used in our demonstration) • Beacon Approach • Arcs • General definition: (if node j is neighbor(node k) then arc {k,j} exists) • A neighbor of node x (or gridpoint x) is usually the spatially adjacent gridpoints to x

6. Network Description (cont.) • Arc Cost Metrics • Can take on many forms • Usually a function of fuel or battery usage • Can be as simple as time to maneuver along an arc, or the distance of the arc • Arcs that are forbidden (due to obstacles) are assigned an infinitely high cost

7. Algorithms • Greedy Algorithms • Static Case • Dijkstra’s Shortest Path • A* Algorithm • Dynamic Case with limited visibility • D* Algorithm

8. A* Pseudo-code Begin //find potentials in G (i):=heuristic(i) i  N; //preprocess G: generate G  do := cij - (i) + (j) (i,j)  A //find shortest reduced cost paths s  t Dijkstra(G ) • Advantages • Disadvantages

9. D* Pseudo-code Begin //initialize variables t(i):=NEW i  N d(s):= 0; t(s):=OPEN S:={s} while Xt; //compute shortest path while X  S do PROCESS-STATE; //shortest path {X} is now computed proceed on {X} until obstacle is detected; if obstacle is detected MODIFY-COST; end; end;

10. Demonstration • Dijkstra • A* • D* • Greedy Algorithms • Learning Algorithm • Background • Gridded Map • Agent can only move left, right, up, or down • Varying Terrain • Distance = Manhattan Distance Link to Demo

11. Future Challenges and Obstacles • Many Pieces to the Puzzle are Still Unsolved • Smooth Trajectories • Stochastic Nature of Data • Moving Target

12. Questions ?