Optimal UAV Flight Path Selection Da-Wei Gu Control & Instrumentation Group

1. Optimal UAV Flight Path Selection • Da-Wei Gu • Control & Instrumentation Group

2. Objectives considered • “Optimal” in terms of low risk and flight length • Real-time flight path for single/multiple vehicle • Avoidance of collision in multiple vehicle case • 3-dimensional flight paths • Fixed (known a priori) and pop-up threats

3. Scenario considered • Operational range: • [0 200]x[0 200] km • Altitude: 1 km • Risk threshold: 0.05 • Threats: 18 (10 medium • and 8 short ranges) • Low risk path is preferable

4. Hit probability for a medium range SAM (25 km)

5. Path Planning Methods • Improved Voronoi graph method (a graph-based method) • Finite receding horizon with mixed integer linear programming (MILP) method

6. Voronoi graph method Voronoi graph

7. Weighted Cost Function Objective functions: risk level & fuel cost The cost on the ith edge:

8. Dynamic Programming: Dijkstra’s Algorithm (1) • Starting node: ns , Ending node: ne • Label assignment of nodes: temporary/permanent For Node p: q: preceding node, r: cost(ns, p) • Connection matrix, cost vector, … Initialisation: (0,0)  ns , (0,)  all other nodes the permanent node variable k= ns

9. Dynamic Programming: Dijkstra’s Algorithm (2) Step 1: Let the label of k be k(p,q). Consider all nodes connecting to k, y(r,s), in turn: if q+cost(k,y) < s, y(r,s)  y(k,q+cost(k,y)) Step 2: From the set of temporary labels, select the one with the smallest 2nd component and declare that label to permanent. That node becomes the new node k. If k= ne , goto Step 3; otherwise, goto Step 1, until no new node can be found (“no feasible path” exit).

10. Dynamic Programming: Dijkstra’s Algorithm (3) Step 3: For the destination node ne(x,z), z is the optimal cost from the starting node ns , x the preceding node. Recover the selected path (a sequence of waypoints) from ns to ne . NB: Other dynamic programming algorithms can be applied (from ne to ns ). No obvious difference in terms of efficiency.

11. Results of Voronoi graph method (without & with local minimisation)

12. Voronoi graph method Pros and cons • Global optimality (needs global information) • Guaranteed convergence • Fast path generation • Highly simplified threat model (no strength information) • Possibly high risk • Combined with the local minimisation method • Path tracking needed

13. Finite receding horizon with MILP Basic idea • LP (linear programming) with integer variables • All dynamic and relevant constraints are expressed as integer linear constraint in similar ways • The path planning problem becomes solving a MILP at each (or several) time step(s)

14. Speed and acceleration constraints

15. Modelling of the risk area with dynamical boundaries

16. Cost function where

17. Receding Horizon Control Scheme Reference Trajectory + Current State Model Predicted Outputs - Future Inputs UAV CPLEX Future Errors Optimum input Cost Function Constraints

18. MILP method Result

19. MILP method Pros and cons • Local optimality (only needs local information) • Guaranteed convergence with soft constraints • Full consideration of all necessary constraints • Relatively slow waypoint (path) generation • Simplified threat model • High risk when passes local minima • Could be combined with the graph based methods

20. Flight Path Planning PackageSoftware Developed at UL