Optimizing Autonomous Drone Delivery

Transcription

1 Optimizing Autonomous Drone Delivery Application of the Travelling Salesman Problem to an emerging Issue ABHINAV SINHA

2 Why Address Drone delivery? It is an upcoming sector in the consumer industry with a lot of potential There are real world constraints that make it a challenging application to scale Delivery Drones are expensive to acquire, requiring optimal usage Payload parameters are defined, adding limitations Total flight time is limited, reducing the total number of Home Trips

3 Problem Statement Application: Autonomous Drones Constraints: Travel Distance Payload Flight time/battery Capacity * Note: Payload and Flight time are inversely related

4 DJI S900 Acquisition Cost: $1400 Max Payload: 18-pound payload Max Flight Time at full payload: 10 minutes full payload Notable Design Features: 900 cm wing span Pros/Cons: Required frequent charging for longer trips

5 Acquisition Cost: $12000 Max Payload: 20-pound payload Max Flight full payload: 18 minutes full payload Notable Design Features: Compact design Pro: State of the art Con: Not scalable FreeFly Alta 6

6 What is the Travelling Salesman Problem (TSP) A Common optimization model of a salesman who must visit X cities while minimizing total distance travelled. Applications range from straightforward (1 salesman) to computationally intense (Multiple Agents and constraints) Also referred to as travelling purchaser problem and the vehicle routing problem.

7 Basic TSP Model N cities, 1 salesman Problem is considered NP- Hard Naïve solution find all (n-1)! Routes Calculate cost and return minimum cost Works for one agent

8 Approach to problem Implement a basic TSP model, one agent (Drone) multiples nodes Add constraints one at a time Test model on a small scale Add agents (Drones) as the model gets bigger Add nodes (Destinations) and test optimal paths Create a visualization/simulation of model. Use the Austin street data to plot the networks

9 Objectives and Constraints Objectives: Minimize cost of Delivery Complete all deliveries Minimal recharges Constraints: Weight of Payload Flight time Proximity to Charge station Number of delivery agents available Expected time to delivery

10 General tsp Model Constraint 1, 2 each node has only one entering and exiting edge Constraint 3, 4 Number of drones leaving is the number entering

11 Generalizing the model With the addition of drones and nodes the model becomes more complicated. Add charging stations based on minimum distance between the new building and existing charging station.

12 Python Packages To implement a TSP-based model a lot of python packages and tools can be used: Tsp package Pyomo (represent problem as a optimization model) Networkx (Represent as a graph search algorithm) Visualization Tools: Gephi Graph-tool (faster as compared to gephi)

13 Graph-tool Graph-tool is an efficient Python module for manipulation and statistical analysis of graphs (a.k.a. networks) Performance of this tool is comparable (both in memory usage and computation time) to that of a pure C/C++ library.

14 Graph-tool example from graph_tool.all import * g = Graph() ug= Graph(directed=False) ug = Graph() ug.set_directed(false) assert(ug.is_directed() == False) v1 = g.add_vertex() v2 = g.add_vertex() e = g.add_edge(v1, v2) graph_draw(g, vertex_text=g.vertex_index, vertex_font_size=18, output_size=(200, 200), output="two-nodes.png")

15 Animations with graph-tool

16 Test Scenario 1 Five destinations Three charging stations One main Hub (home base) Two multi-rotor vehicles The cost of any journey here is measured using the distance between the two nodes (Destinations)

17 Solution to Scenario 1 D1-D5 are destinations Cost of edge is mentioned Charging stations at D5 and D4 For a single Drone (agent): [Hub-D1-D5(recharge)-D2- D4(recharge)-D3-Hub]

18 Difficulties Incorporating a large number of delivery agents Addition of nodes to generalize the algorithm Maximize flight time based multiple dynamic factors adds complexity

19 Results After implementing the basic scenario mentioned earlier Obtained a near optimal solution Optimality is difficult as the placement of charging stations is a one time affair and with addition of nodes we can not remove and place charging stations everywhere On decently sized graphs 10 nodes or so obtain a near optimal solution Efficiency of large graphs is poor as the algorithm is exponentially complex

20 Things to work on Addition of payload as a constraint Visualization of the model Increasing efficiency for large scaled operation, multiple nodes and agents

21 Thank You