Three Dimensional Trajectory Generation for an Autonomous Plane

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


A 3D optimal trim trajectories planner algorithm for an autonomous plane is presented in this paper. This planner can generate a sequence of 3D elementary trajectories for a set of predefined waypoints in space. The proposed algorithm uses a sequence of five elementary trim trajectories to generate a three dimensional global trajectory in space.  The trim property reduces significantly the complexity of the dynamical model and thus the resolution of the trajectory planning and tracking problems. This approach is based on the Bang-Zero-Bang strategy, taking into account the state and inputs constraints due to the vehicle dynamics, flight envelope and the actuators limitations. In this study, we demonstrate that this strategy satisfies the necessary optimality condition of Pontryaguin.
Copyright © 2014 Praise Worthy Prize - All rights reserved.


Autonomous Plane; Trajectory Generation; Ttrim Conditions

Full Text:



D. Boukraa, Y. Bestaoui, N. Azouz “A New Approach To Trajectories Planner Design For a Subsonic Autonomous Aerial Fixed Wing Vehicle”, American Control Conference, Minneapolis, MN, 2006.

N. Faiz, S. Agrawal, R. Murray “Trajectory Planning of Differentially Flat Systems with Dynamics and Inequalities”, AIAA Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, 2001.

J. How, E. King, Y. Kuwata “Flight Demonstrations of Cooperative Control for UAV Teams”, AIAA 3rd Unmanned Unlimited Technical Conference, 2004, Chicago, Il.

S. Jeyaraman et al, “Formal Techniques for the Modeling and Validation of a Co-Operating UAV Team That Uses Dubins Set For Path Planning”, American Control Conference,2005, Portland, OR, pp. 4690-4695.

J. Spinkle, J. Eklund, S. Sastry “Deciding to Land a UAV Safely in Real Time”, American Control Conference, 2005, Portland, OR, USA.

G. Yang, V. Kapila “Optimal Path Planning for Unmanned Air Vehicles with Kinematic and Tactical Constraints”, 41st IEEE Conference on Decision and Control, Las Vegas, NV, 2002.

M. Milam “Real-Time Optimal Trajectory Generation for Constrained Dynamical Systems”, PhD Thesis, California Institute of Technology, Pasadena, CA, 2003.

S. Hima, Y. Bestaoui, “Time Optimal Path Planning for an Underactuated Airship”, proceedings of the AIAA Control and Guidance conference, Austin, TX, 2003.

J. Mardsen, T. Ratiu “Introduction to Mechanics and Symmetry”, Springer, second edition, 1999.

M. Van Nieuwstadt “Trajectory Generation for Nonlinear Control Systems”, PhD Thesis, California Institute of Technology, Pasadena, California,1996.

M. Rathinam, R. Murray “Configuration Flatness of Lagrangian Systems Underactuated by one Control”, IEEE Control and Decision Conference, 1996.

S. Lavalle “Planning Algorithms”, Cambridge University press, 2006

S. Hansen, T. McLain, M. Goodrich ‘Probabilistic searching using a small unmanned aerial vehicle’, AIAA Infotech@aerospace conference, 2007, Rohnert Park, Ca.

L. Dubins “On curves of minimal length with a constraints with a constraint on average curvature and with prescribed initial and terminal positions and tangents”, American Journal of Mathematics, Vol. 79, pp 497-516, 1957.

P. Chandler, M. Pachter, S. Rasmussen, S., “UAV Cooperative Control”, American Control Conference, Arlington, VA, 2001.

E. Anderson, R. Beard, T. McLain “Real Time Dynamic Trajectory Smoothing for Unmanned Air Vehicles”, IEEE Transactions on Control Systems Technology, Vol. 13, 2005.

D. Boukraa, Y. Bestaoui, N. Azouz “Trajectories characterization of an autonomous aerial vehicle with a small angle of attack”, 23rd Digital Avionics Systems Conference, Salt Lake City, Utah, 2004

D. Boukraa, Y. Bestaoui, N. Azouz “Transition Trajectories Characterization for Uninhabited aerial Vehicle”, 24th Digital Avionics Systems Conference , Washington D.C., 2005

D. Boukraa, Y. Bestaoui, N. Azouz “Non Trim trajectories Characterization Of An Unmanned Aerial Fixed Wing Vehicle”, 11th IEEE International conference on Methods and Models in Automation and Robotics, 2005, Miedzyzdroje, Poland.

B. Stevens, F. Lewis“Aircraft Control and Simulation”, Editions Wiley Interscience, 2003.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize