Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-11T04:37:45.057Z Has data issue: false hasContentIssue false
  • English
  • Français

Adaptation Mechanism of Asymmetrical Potential Field Improving Precision of Position Tracking in the Case of Nonholonomic UAVs

Published online by Cambridge University Press:  10 April 2019

Cezary Kownacki Open the ORCID record for Cezary Kownacki [Opens in a new window]  and
Leszek Ambroziak
Cezary Kownacki*
Affiliation:
Automatic Control and Robotics Department, Faculty of Mechanical Engineering, Bialystok University of Technology, Bialystok, Poland. E-mail: l.ambroziak@pb.edu.pl
Leszek Ambroziak
Affiliation:
Automatic Control and Robotics Department, Faculty of Mechanical Engineering, Bialystok University of Technology, Bialystok, Poland. E-mail: l.ambroziak@pb.edu.pl
*
*Corresponding author. E-mail: c.kownacki@pb.edu.pl
Get access Rights & Permissions [Opens in a new window]

Summary

Position-tracking problems in the structures of rigid formations of nonholonomic mobile robots, such as fixed-wing unmanned aerial vehicle (UAVs), must reconcile tracking precision and flight stability, which usually exclude each other due to nonholonomic motion constraints. Therefore, a position-tracking control that is based on distance and position displacement, defined as inputs of control loops, requires the application of dead zones around target positions, which are the points of instability. For this reason, the control becomes sensitive to any external disturbance causing oscillations of control signals and so it becomes difficult to maintain a zero value of position displacement over a long time horizon. Thus, we propose an approach based on the adaptive mechanism of an asymmetrical local artificial potential field, which is defined by a local frame of reference whose origin is located in the tracked position of a UAV in the formation frame. It couples controls of both airspeed and heading angle into a nonlinear potential function of relative position and orientation with respect to the tracked position and adapts it according to heading rate of the leader. The function splits the area around the tracked position longitudinally into two zones of acceleration and deceleration; therefore, velocity vectors are longer (higher airspeed) only when a UAV is behind the tracked position and shorter (lower airspeed) when it is ahead. The area is laterally symmetrical, and orientations of velocity vectors align asymptotically to the longitudinal direction accordingly with the decrease in the lateral error. Finally, velocity vectors are rotated proportionally to the heading rate of the leader, which improves the tracking precision during turns. If we assumed that a UAV’s tracked position is in motion, it could easily be proven that the position control based on the adaptive asymmetrical potential function becomes asymptotically stable in the tracked position. Numerical simulation verifies this thesis and presents more precise and stable position tracking due to the adaptation mechanism.

Keywords

FormationsRigid structureArtificial potential functionAsymmetrical potential functionMulti-UAV system
Type
Articles
Information
Robotica , Volume 37 , Issue 10 , October 2019 , pp. 1823 - 1834
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambroziak, L. and Gosiewski, Z., “Two stage switching control for autonomous formation flight of nmanned aerial vehicles,” Aerosp. Sci. Technol. 46, 221–226 (2015).CrossRefGoogle Scholar
Ambroziak, L., Kondratiuk, M., Ciezkowski, M. and Kownacki, C., “Hardware in the loop tests of the potential field based algorithm for formation flight control of unmanned aerial vehicles, Mechatronic Systems and Materials 2018,” AIP Conference Proceedings 2029, (Zakopane, 2018) 020002-1–020002-10; https://doi.org/10.1063/1.5066464CrossRefGoogle Scholar
Bennet, D. J. and McInnes, C. R., “Space craft formation flying using bifurcating potential fields,” International Astronautical Congress (Curran Associates, Inc., Glasgow, Scotland, 2008) pp. 4991–4999.Google Scholar
Budiyanto, A., Cahyadi, A., Adji, T. B. and Wahyunggoro, O., “UAV obstacle avoidance using potential field under dynamic environment,” 2015 International Conference on Control, Electronics, Renewable Energy and Communications (Bandung, 2015).CrossRefGoogle Scholar
Cetin, O. and Yilmaz, G., “Real-time autonomous UAV formation flight with collision and obstacle avoidance in unknown environment,” J. Intell. Robot. Syst. 84(1), 415–433 (2016).CrossRefGoogle Scholar
Chen, Y., Luo, G., Mei, Y., Yu, J. and Su, X., “UAV path planning using artificial potential field method updated by optimal control theory,” Int. J. Syst. Sci. 47(6), 1407–1420 (2016).CrossRefGoogle Scholar
Chen, Y., Yu, J., Su, X. and Luo, G., “Path planning for multi-UAV formation,” J. Intell Robot Syst. 77(1), 229–246 (2015).CrossRefGoogle Scholar
Frew, E. W., Lawrence, D. A., Dixon, C., Elston, J. and Pisano, W. J., “Lyapunov guidance vector fields for unmanned aircraft applications,” IEEE American Control Conference, New York, USA (2007).CrossRefGoogle Scholar
Gosiewski, Z. and Ambroziak, L., “Formation flight control scheme for unmanned aerial vehicles,” Lect. Notes Control Inf. Sci. 422, 331–340 (2012).Google Scholar
Hatton, R. L. and Choset, H., “Geometric motion planning: The local connection, Stokes’ theorem, and the importance of coordinate choice,” Inter. J. Robot. Res, 30(8), 988–1014 (2011).CrossRefGoogle Scholar
Kokume, N. and Uchiyama, K., “Guidance law based on bifurcating velocity field for formation flight,” AIAA Guidance, Navigation, and Control Conference, Nashville, USA (2010).CrossRefGoogle Scholar
Kownacki, C. and Ambroziak, L., “Local and asymmetrical potential field approach to leader tracking problem in rigid formations of fixed-wing UAVs, Aerospace Sci. Tech, 68, 465–474 (2017).CrossRefGoogle Scholar
Kownacki, C. and Ołdziej, O., “Fixed-wing UAVs flock control through cohesion and repulsion behaviours combined with a leadership,” Inter. J. Adv. Robot. Syst. 13, 36 (2016). doi:10.5772/62249.CrossRefGoogle Scholar
Kownacki, C., “Multi-UAV flight using virtual structure combined with behavioral approach,” Acta Mechanica et Automatica, 10(2), 92–99 (2016).CrossRefGoogle Scholar
Li, K., Han, X. and Qi, G. “Formation and obstacle-avoidance control for mobile swarm robots based on artificial potential field,” Conference on Robotics and Biomimetics, ROBIO 2009, Guilin, Guangxi, China (2009).Google Scholar
Mukherjee, R. and Anderson, D. P., “Nonholonomic motion planning using stokes’ theorem,” IEEE International Conference on Robotics and Automation, St. Petersburg, Russia (1993) pp. 3794–3801.Google Scholar
Nagao, Y. and Uchiyama, K., “Formation flight of fixed-wing UAVs using artificial potential field,” 29th Congress of the International Council of the Aerospace Sciences (St. Petersburg, 2014).Google Scholar
Nelson, D. R., Barber, D. B., McLain, T. W. and Beard, R. W., “Vector field path following for miniature air vehicles,” IEEE Trans. Robot. 23(3), 519–529 (2007).CrossRefGoogle Scholar
Nieuwenhuisen, M., Schadler, M. and Behnke, S., “Predictive potential field-based collision avoidance for multicopters,” Inter. Arch. Photogramm. Remote Sens. Spatial Inf. Sci, XL-1/W2 (2013).CrossRefGoogle Scholar
Suzuki, M. and Uchiyama, K. “Three-dimensional formation flying using bifurcating potential fields,” AIAA Guidance, Navigation, and Control Conference (AIAA, Chicago, 2009).CrossRefGoogle Scholar
Suzuki, M. and Uchiyama, K. “Autonomous formation flight using bifurcating potential fields,” 27th International Congress of the Aeronautical Sciences, Nice, France (2010).CrossRefGoogle Scholar
Virágh, C., Vásárhelyi, G., Tarcai, N., Szörényi, T., Somorjai, G., Nepusz, T. and Vicsek, T. “Flocking algorithm for autonomous flying robots,” Bioinspiration Biomimetics, 9(2), 025012, (2014).CrossRefGoogle ScholarPubMed