A Method to Compute Efficient 3D Helicopters Flight Trajectories Based on a Motion Polymorph-Primitives Algorithm
Finding the optimal 3D path of an aerial vehicle under
flight mechanics constraints is a major challenge, especially when
the algorithm has to produce real time results in flight. Kinematics
models and Pythagorian Hodograph curves have been widely used
in mobile robotics to solve this problematic. The level of difficulty
is mainly driven by the number of constraints to be saturated at the
same time while minimizing the total length of the path. In this paper,
we suggest a pragmatic algorithm capable of saturating at the same
time most of dimensioning helicopter 3D trajectories’ constraints
like: curvature, curvature derivative, torsion, torsion derivative, climb
angle, climb angle derivative, positions. The trajectories generation
algorithm is able to generate versatile complex 3D motion primitives
feasible by a helicopter with parameterization of the curvature and the
climb angle. An upper ”motion primitives’ concatenation” algorithm
is presented based. In this article we introduce a new way of designing
three-dimensional trajectories based on what we call the ”Dubins
gliding symmetry conjecture”. This extremely performing algorithm
will be soon integrated to a real-time decisional system dealing with
inflight safety issues.
[1] T. F. Banchoff and S. T. Lovett, Differential geometry of curves and
surfaces. CRC Press, 2010.
[2] Y. Bestaoui, “General representation of 3d curves for an unmanned aerial
vehicle using the frenet-serret frame,” AIAA, 2007.
[3] P. Bezier, “Essais de definition numeriques des courbes et surfaces non
mathematiques,” Systeme Unisurf, Automatisme,13, 1968.
[4] C. L. Bottasso, D. Leonello, and B. Savini, “Path planning for
autonomous vehicles by trajectory smoothing using motion primitives,”
Control Systems Technology, IEEE Transactions on, vol. 16, no. 6, pp.
1152–1168, 2008.
[5] L. E. Dubins, “On curves of minimal length with a constraint on
average curvature, and with prescribed initial and terminal positions and
tangents,” American Journal of mathematics, pp. 497–516, 1957. [6] M. Hwangbo, J. Kuffner, and T. Kanade, “Efficient two-phase 3d motion
planning for small fixed-wing uavs,” in Robotics and Automation, 2007
IEEE International Conference on. IEEE, 2007, pp. 1035–1041.
[7] V. P. Kostov, E. V. Degtiariova-Kostova et al., “The planar motion with
bounded derivative of the curvature and its suboptimal paths,” Acta
Math. Univ. Comenianae, vol. 64, no. 2, pp. 185–226, 1995.
[8] N. Ozalp and O. K. Sahingoz, “Optimal uav path planning in a 3d threat
environment by using parallel evolutionary algorithms,” in Unmanned
Aircraft Systems (ICUAS), 2013 International Conference on. IEEE,
2013, pp. 308–317.
[9] M. Shah and N. Aouf, “3d cooperative pythagorean hodograph path
planning and obstacle avoidance for multiple uavs,” in Cybernetic
Intelligent Systems (CIS), 2010 IEEE 9th International Conference on.
IEEE, 2010, pp. 1–6.
[10] M. Shanmugavel, A. Tsourdos, R. Zbikowski, B. A. White, C. Rabbath,
and N. Lechevin, “A solution to simultaneous arrival of multiple uavs
using pythagorean hodograph curves,” in American Control Conference,
2006. IEEE, 2006, pp. 6–pp.
[11] T. R. Wan, W. Tang, and H. Chen, “A real-time 3d motion planning and
simulation scheme for nonholonomic systems,” Simulation Modelling
Practice and Theory, vol. 19, no. 1, pp. 423–439, 2011.
[12] K. Yang, S. K. Gan, and S. Sukkarieh, “An efficient path planning and
control algorithm for ruavs in unknown and cluttered environments,”
Journal of Intelligent and Robotic Systems, vol. 57, no. 1-4, pp. 101–122,
2010.
[1] T. F. Banchoff and S. T. Lovett, Differential geometry of curves and
surfaces. CRC Press, 2010.
[2] Y. Bestaoui, “General representation of 3d curves for an unmanned aerial
vehicle using the frenet-serret frame,” AIAA, 2007.
[3] P. Bezier, “Essais de definition numeriques des courbes et surfaces non
mathematiques,” Systeme Unisurf, Automatisme,13, 1968.
[4] C. L. Bottasso, D. Leonello, and B. Savini, “Path planning for
autonomous vehicles by trajectory smoothing using motion primitives,”
Control Systems Technology, IEEE Transactions on, vol. 16, no. 6, pp.
1152–1168, 2008.
[5] L. E. Dubins, “On curves of minimal length with a constraint on
average curvature, and with prescribed initial and terminal positions and
tangents,” American Journal of mathematics, pp. 497–516, 1957. [6] M. Hwangbo, J. Kuffner, and T. Kanade, “Efficient two-phase 3d motion
planning for small fixed-wing uavs,” in Robotics and Automation, 2007
IEEE International Conference on. IEEE, 2007, pp. 1035–1041.
[7] V. P. Kostov, E. V. Degtiariova-Kostova et al., “The planar motion with
bounded derivative of the curvature and its suboptimal paths,” Acta
Math. Univ. Comenianae, vol. 64, no. 2, pp. 185–226, 1995.
[8] N. Ozalp and O. K. Sahingoz, “Optimal uav path planning in a 3d threat
environment by using parallel evolutionary algorithms,” in Unmanned
Aircraft Systems (ICUAS), 2013 International Conference on. IEEE,
2013, pp. 308–317.
[9] M. Shah and N. Aouf, “3d cooperative pythagorean hodograph path
planning and obstacle avoidance for multiple uavs,” in Cybernetic
Intelligent Systems (CIS), 2010 IEEE 9th International Conference on.
IEEE, 2010, pp. 1–6.
[10] M. Shanmugavel, A. Tsourdos, R. Zbikowski, B. A. White, C. Rabbath,
and N. Lechevin, “A solution to simultaneous arrival of multiple uavs
using pythagorean hodograph curves,” in American Control Conference,
2006. IEEE, 2006, pp. 6–pp.
[11] T. R. Wan, W. Tang, and H. Chen, “A real-time 3d motion planning and
simulation scheme for nonholonomic systems,” Simulation Modelling
Practice and Theory, vol. 19, no. 1, pp. 423–439, 2011.
[12] K. Yang, S. K. Gan, and S. Sukkarieh, “An efficient path planning and
control algorithm for ruavs in unknown and cluttered environments,”
Journal of Intelligent and Robotic Systems, vol. 57, no. 1-4, pp. 101–122,
2010.
@article{"International Journal of Information, Control and Computer Sciences:71532", author = "Konstanca Nikolajevic and Nicolas Belanger and David Duvivier and Rabie Ben Atitallah and Abdelhakim Artiba", title = "A Method to Compute Efficient 3D Helicopters Flight Trajectories Based on a Motion Polymorph-Primitives Algorithm", abstract = "Finding the optimal 3D path of an aerial vehicle under
flight mechanics constraints is a major challenge, especially when
the algorithm has to produce real time results in flight. Kinematics
models and Pythagorian Hodograph curves have been widely used
in mobile robotics to solve this problematic. The level of difficulty
is mainly driven by the number of constraints to be saturated at the
same time while minimizing the total length of the path. In this paper,
we suggest a pragmatic algorithm capable of saturating at the same
time most of dimensioning helicopter 3D trajectories’ constraints
like: curvature, curvature derivative, torsion, torsion derivative, climb
angle, climb angle derivative, positions. The trajectories generation
algorithm is able to generate versatile complex 3D motion primitives
feasible by a helicopter with parameterization of the curvature and the
climb angle. An upper ”motion primitives’ concatenation” algorithm
is presented based. In this article we introduce a new way of designing
three-dimensional trajectories based on what we call the ”Dubins
gliding symmetry conjecture”. This extremely performing algorithm
will be soon integrated to a real-time decisional system dealing with
inflight safety issues.", keywords = "Aerial robots, Motion primitives, Robotics.", volume = "9", number = "8", pages = "2026-9", }