This paper addresses trajectory generation problem of a fixed-wing miniature air vehicle, constrained by bounded turn rate, to follow a given sequence of waypoints. An extremal path, named as γ-trajectory, that transitions between two consecutive waypoint segments (obtained by joining two waypoints in sequence) in a time-optimal fashion is obtained. This algorithm is also used to track the maximum portion of waypoint segments with the desired shortest distance between the trajectory and the associated waypoint. Subsequently, the proposed trajectory is compared with the existing transition trajectory in the literature to show better performance in several aspects. Another optimal path, named as loop trajectory, is developed for the purpose of tracking the waypoints as well as the entire waypoint segments. This paper also proposes algorithms to generate trajectories in the presence of steady wind to meet the same objective as that of no-wind case. Due to low computational burden and simplicity in the design procedure, these trajectory generation approaches are implementable in real time for miniature air vehicles.
DubinsLE. On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. Am J Math1957; 79: 497–516.
2.
AndersonEPBeardRWMcLainTW. Real-time dynamic trajectory smoothing for unmanned air vehicles. IEEE Trans Control Syst Technol2005; 13: 471–477.
3.
LeeSChoAKeeC. Integrated waypoint path generation and following of an unmanned aerial vehicle. Aircraft Eng Aerospace Technol2010; 82: 296–304.
4.
WhangIHHwangTW. Horizontal waypoint guidance design using optimal control. IEEE Trans Aerospace Electron Syst2002; 38: 1116–1120.
5.
BabaeiARMortazaviM. Fast trajectory planning based on in-flight waypoints for unmanned aerial vehicles. Aircraft Eng Aerospace Technol2010; 82: 107–115.
6.
Noonan A, Schinstock D, Lewis C, et al. Optimal turning path generation for unmanned aerial vehicles. In: Proceedings of the 9th IASTED international conference on control and applications, Montreal, Canada, 2007, pp.21–26.
7.
ZhuRSunDZhouZ. Integrated design of trajectory planning and control for micro air vehicles. Mechatronics2007; 17: 245–253.
8.
McGee TG, Spry S and Hedrick JK. Optimal path planning in a constant wind with a bounded turning rate. In: Proceedings of the AIAA guidance, navigation and control conference and exhibit, San Francisco, CA, August 2005, AIAA paper no. 2005-6186.
9.
NelsonDRBarberDBMclainTW. Vector field path following for miniature air vehicle. IEEE Trans on Robotics2007; 23: 519–529.
10.
Ratnoo A, Sujit PB and Kothari M. Adaptive optimal path following for high wind flights. In: 18th International federation of automatic control world congress, Milano, Italy, August–September, 2011, pp.12985–12990.
11.
Osborne J and Rysdyk R. Waypoint guidance for small UAVs in wind. In: Proceedings of the AIAA Infotech@Aerospace, Arlington, VA, September 2005, paper no. AIAA-2005-6951.
12.
Jennings AL, Ordóñez R and Ceccarelli N. Dynamic programming applied to UAV way point path planning in wind. In: IEEE International symposium on computer-aided control system design, San Antonio, TX, USA, September 2008, pp.215–220.
13.
Zollars M, Blue P and Burns B. Wind corrected flight path planning for autonomous micro air vehicles utilizing optimization techniques. In: Atmospheric flight mechanics conference and exhibit, Hilton Head, SC, August 2007, AIAA paper 2007-6497.
14.
KetemaYZhaoYJ. Micro air vehicle trajectory planning in winds. J Aircraft2010; 47: 1460–1462.
15.
KetemaYZhaoYJ. Controllability and reachability for micro-aerial-vehicle trajectory planning in winds. J Guidance Control Dyn2010; 33: 1020–1023.
16.
Stolle S and Rysdyk R. Flight path following guidance for unmanned air vehicles with pan-tilt camera for target observation. In: Digital avionics systems conference, October 2003, pp. (8.B.3) 1–12. USA: IEEE.
17.
RysdykR. Unmanned aerial vehicle path following for target observation in wind. J Guidance Control Dyn2006; 29: 1092–1100.
18.
Sussmann HJ. Shortest 3-dimensional paths with a prescribed curvature bound. In: 34th IEEE conference on decision and control, New Orleans, LA, 1995, pp.3306–3312.
19.
Hota S and Ghose D. Optimal path planning for an aerial vehicle in 3D space. In: 49th IEEE conference on decision and control, Atlanta, GA, USA, December 2010, pp.4902–4907.
20.
Yang K and Sukkarieh S. 3D smooth path planning for a UAV in cluttered natural environments. In: Proceedings of the 2008 IEEE/RSJ international conference on intelligent robots and systems, Nice, France, September 2008, pp.794–800.
21.
Shanmugavel M, Tsourdos A, Żbikowski R, et al. 3D Dubins sets based coordinated path planning for swarm of UAVs. In: AIAA guidance, navigation, and control conference and exhibit, Keystone, CO, August 2006, AIAA 2006-6211.
22.
BabaeiARMortazaviM. Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints. J Aircraft2010; 47: 1391–1398.
23.
BottassoCLLeonelloDSaviniB. Path planning for autonomous vehicles by trajectory smoothing using motion primitives. IEEE Trans Control Syst Technol2008; 16: 1152–1168.
24.
Hota S and Ghose D. Optimal trajectory planning for path convergence in 3D space. Proc IMechE, Part G: J Aerospace Engineering. Epub ahead of print 20 March 2013. DOI: 10.1177/0954410013479714.
25.
Hota S and Ghose D. A modified Dubins method for optimal path planning of a miniature air vehicle converging to a straight line path. In: Proceedings of the American control conference, St. Louis, MO, USA, June 2009, pp.2397–2402.
26.
BrysonAYu-ChiH. Applied optimal control: optimization, estimation, and control, New York: John Wiley and Sons, 1975.
27.
Betts JT. Practical methods for optimal control using nonlinear programming. Philadelphia, PA: The Society for Industrial and Applied Mathematics, 2001.
