Optimal UAV Flight Path Selection Da-Wei Gu Control & Instrumentation Group 11/12/2018

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 11/12/2018

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 11/12/2018

Hit probability for a medium range SAM (25 km) 11/12/2018

Path Planning Methods Improved Voronoi graph method (a graph-based method) Finite receding horizon with mixed integer linear programming (MILP) method 11/12/2018

Voronoi graph method Voronoi graph 11/12/2018

Weighted Cost Function Objective functions: risk level & fuel cost The cost on the ith edge: 11/12/2018

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 11/12/2018

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). 11/12/2018

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. 11/12/2018

Results of Voronoi graph method (without & with local minimisation) 11/12/2018

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 11/12/2018

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) 11/12/2018

Speed and acceleration constraints 11/12/2018

Modelling of the risk area with dynamical boundaries 11/12/2018

Cost function where 11/12/2018

Receding Horizon Control Scheme Reference Trajectory + Current State Model Predicted Outputs - Future Inputs UAV CPLEX Future Errors Optimum input Cost Function Constraints 11/12/2018

MILP method Result 11/12/2018

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 11/12/2018

Flight Path Planning Package Software Developed at UL 11/12/2018