Need for Unmanned . . . Need for Easily . . . Technical Details of . . . Need for an Optimal . . . Toward Computing Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem an Optimal Trajectory for Solution: How to . . . What If We Want . . . an Environment-Oriented What If We Want . . . Implementation Is . . . Unmanned Aerial Vehicle Tailwind Problem. I. . . . Missed Spot Problem. . . . (UAV) Title Page ◭◭ ◮◮ Jerald Brady, Octavio Lerma, ◭ ◮ Vladik Kreinovich, and Craig Tweedie Page 1 of 20 Cyber-ShARE Center for Sharing Resources through Go Back Cyber-Infrastructure to Advance Research and Education University of Texas at El Paso Full Screen jerald.brady@gmail.com, lolerma@episd.org, Close vladik@utep.edu, ctweedie@utep.edu Quit
Need for Easily . . . Technical Details of . . . 1. Need for Unmanned Aerial Vehicles (UAV) Need for an Optimal . . . Towards an Optimal . . . • Arctic observing systems need to be enhanced with im- An (Almost) Optimal . . . proved remote sensing technologies and capabilities. Minor Problem • Especially needed are mid-altitude remote sensing us- Solution: How to . . . ing air-borne platforms. What If We Want . . . • Over the past decade a few but increasing number of What If We Want . . . researchers have begun using UAVs in the Arctic. Implementation Is . . . Tailwind Problem. I. . . . • Typically UAVs tend to be designed for a specific task Missed Spot Problem. . . . or area of operation. Title Page • Thus, UASs are usually not easily customizable. ◭◭ ◮◮ • Our objective: develop easily customizable UAVs. ◭ ◮ Page 2 of 20 Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 2. Need for Easily Customizable Unmanned Aerial Ve- Need for an Optimal . . . hicles (UAV) Towards an Optimal . . . An (Almost) Optimal . . . • Our objective: develop UAVs that allow for: Minor Problem – customizable sensor packages, Solution: How to . . . – reliable communications between ground and air- What If We Want . . . craft, What If We Want . . . – tools to optimize flight control, Implementation Is . . . Tailwind Problem. I. . . . – real time data processing, Missed Spot Problem. . . . – the ability to visually ascertaining the quantity of Title Page data while the UAV is air-borne, and ◭◭ ◮◮ – the ability to launch and land safely in these remote regions. ◭ ◮ • We present: a prototype software system that allows Page 3 of 20 for this customization. Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 3. Technical Details of Our System Need for an Optimal . . . Towards an Optimal . . . • A paraglider UAV allows low and slow flying with up An (Almost) Optimal . . . to 13 kg payload. Minor Problem • A suite of sensors for measuring hyperspectral reflectance Solution: How to . . . and other surface properties. What If We Want . . . • Onboard sensors relay airspeed, ground speed, latitude, What If We Want . . . longitude, pitch, yaw, roll, and video. Implementation Is . . . Tailwind Problem. I. . . . • Additional sensors can be added. Missed Spot Problem. . . . • Software: Title Page – has enhanced communication ground ↔ UAV; ◭◭ ◮◮ – can synthesize near real time data acquired from ◭ ◮ sensors onboard; Page 4 of 20 – can log operation data during flights; Go Back – can visually demonstrate the amount/quality of data. Full Screen Close
Need for Easily . . . Technical Details of . . . 4. Need for an Optimal Trajectory Need for an Optimal . . . Towards an Optimal . . . • Task: cover all the points points from a given area. An (Almost) Optimal . . . • Problem: UAVs have limited flight time. Minor Problem • Consequence: minimize the flight time among all cov- Solution: How to . . . ering trajectories. What If We Want . . . What If We Want . . . • Geometric reformulation: we need a trajectories with Implementation Is . . . the smallest possible length. Tailwind Problem. I. . . . • Usual assumptions: Missed Spot Problem. . . . Title Page – we cover a rectangular area; ◭◭ ◮◮ – each on-board sensor covers all the points within a given radius r . ◭ ◮ • What we do: describe the trajectories which are (asymp- Page 5 of 20 totically) optimal under these assumptions. Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 5. Towards an Optimal Trajectory Need for an Optimal . . . Towards an Optimal . . . • Each trajectory piece of length ∆ L i covers the area An (Almost) Optimal . . . A i ≈ 2 r · ∆ L i : Minor Problem Solution: How to . . . What If We Want . . . ✛ r r ✲ ∆ L i What If We Want . . . Implementation Is . . . Tailwind Problem. I. . . . Missed Spot Problem. . . . • So, a trajectory of length L = � ∆ L i covers the area Title Page i ◭◭ ◮◮ � � � A ≤ A i = (2 r · ∆ L i ) = 2 r · ∆ L i = 2 r · L. ◭ ◮ i i i Page 6 of 20 • Conclusion: to cover a region of area A 0 , we need a trajectory of length L ≥ A 0 Go Back 2 r . Full Screen Close
Need for Easily . . . Technical Details of . . . 6. An (Almost) Optimal Trajectory Need for an Optimal . . . Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem Solution: How to . . . What If We Want . . . r r L 2 ✛ ✲ ✛ ✲ What If We Want . . . Implementation Is . . . Tailwind Problem. I. . . . Missed Spot Problem. . . . Title Page ◭◭ ◮◮ L 1 • In the region of area A 0 = L 1 · L 2 , we have L 1 ◭ ◮ 2 r pieces of length ≈ L 2 each. Page 7 of 20 • The total length is L ≈ L 1 2 r · L 2 = L 1 · L 2 = A 0 Go Back 2 r , i.e., 2 r Full Screen this trajectory is (almost) optimal. Close
Need for Easily . . . Technical Details of . . . 7. Minor Problem Need for an Optimal . . . t t Towards an Optimal . . . ■ ❅ � ✒ ❅ ❘ � ✠ An (Almost) Optimal . . . Minor Problem Solution: How to . . . What If We Want . . . r r ✛ ✲ ✛ ✲ What If We Want . . . Implementation Is . . . Tailwind Problem. I. . . . Missed Spot Problem. . . . Title Page ◭◭ ◮◮ • Problem: corner points (marked bold) are not covered. ◭ ◮ Page 8 of 20 • Explanation: the distance from the trajectory to each √ √ r 2 + r 2 = corner point is 2 · r > r . Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 8. Solution: How to Cover Corner Points Need for an Optimal . . . Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem Solution: How to . . . t t What If We Want . . . PPPPPPP ✏ ✏ ❇ ✏ ✂ What If We Want . . . ✏ ✏ ❇ ✏ ✂ ✏ P ✏ ❇ ✂ Implementation Is . . . ❇ ✂ ❇ ✂ Tailwind Problem. I. . . . ❇ ✂ Missed Spot Problem. . . . ❇ ✂ . . . ❇ ✂ Title Page ◭◭ ◮◮ ◭ ◮ Page 9 of 20 Go Back Full Screen • Comment: this way, corner points are covered. Close
Need for Easily . . . Technical Details of . . . 9. What If We Want Different Coverage In Different Need for an Optimal . . . Sub-Regions: Asymptotically Optimal Solution Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem Solution: How to . . . ✛ ✲ r 2 What If We Want . . . What If We Want . . . Implementation Is . . . ✻ r 1 Tailwind Problem. I. . . . ❄ Missed Spot Problem. . . . Title Page ◭◭ ◮◮ ◭ ◮ • Idea: use (asymptotically optimal) arrangement in each Page 10 of 20 sub-region; this sub-division can be iterated. Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 10. What If We Want Different Coverage In Different Need for an Optimal . . . Sub-Regions: General Case Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem . . . . . . Solution: How to . . . . . . . Optimal Optimal What If We Want . . . . . . . . trajectory . . trajectory . What If We Want . . . for r 2 for r 3 Implementation Is . . . Tailwind Problem. I. . . . . . . . . . Missed Spot Problem. . . . Title Page Optimal Optimal . . trajectory . . trajectory ◭◭ ◮◮ . . for r 1 for r 4 ◭ ◮ . . . . . . Page 11 of 20 Go Back Full Screen Close
Need for Easily . . . Technical Details of . . . 11. Implementation Is Imperfect: Additional Prob- Need for an Optimal . . . lems Towards an Optimal . . . An (Almost) Optimal . . . • In practice: an UAV can deviate from the planned tra- Minor Problem jectory. Solution: How to . . . • As a result: we may not cover some points in the re- What If We Want . . . gion. What If We Want . . . • First example: tailwind. Implementation Is . . . • Why it is a problem: the UAV flies too fast, not enough Tailwind Problem. I. . . . time for sensing. Missed Spot Problem. . . . Title Page • Solution: change the direction of the trajectory. ◭◭ ◮◮ • Second example: missing one spot. ◭ ◮ • Possible explanation: a sensor malfunctioned. Page 12 of 20 • Solution: come back and cover the missed spot. Go Back • Question: what is the optimal way to cover the missed Full Screen spot? Close
Need for Easily . . . Technical Details of . . . 12. Tailwind Problem. I. Original Plan Need for an Optimal . . . Towards an Optimal . . . An (Almost) Optimal . . . Minor Problem Solution: How to . . . What If We Want . . . What If We Want . . . Implementation Is . . . Tailwind Problem. I. . . . Missed Spot Problem. . . . Title Page ◭◭ ◮◮ ◭ ◮ Page 13 of 20 Go Back Full Screen Close
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