Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-12T19:49:28.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Trajectory Planning of Quadrotor Systems for Various Objective Functions

Published online by Cambridge University Press:  20 May 2020

Hamidreza Heidari Open the ORCID record for Hamidreza Heidari [Opens in a new window]  and
Martin Saska
Hamidreza Heidari*
Affiliation:
Faculty of Mechanical Engineering, Malayer University, Malayer, Iran
Martin Saska
Affiliation:
Faculty of Electrical Engineering, Czech Technical University, Prague, Czech
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Quadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

Keywords

QuadrotorOptimal controlFuel efficiencyStable flightPath planning
Type
Articles
Information
Robotica , Volume 39 , Issue 1 , January 2021 , pp. 137 - 152
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press

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

Bouabdallah, S., Murrieri, P. and Siegwart, R., “Design and control of an indoor micro quadrotor”, IEEE Trans. Robot. Autom. 5(1), 4393–4398 (2004).Google Scholar
Liu, Y. and Bucknall, R., “A survey of formation control and motion planning of multiple unmanned vehicles”, Robotica. 36(3), 1–29 (2018).CrossRefGoogle Scholar
Shafei, A. M. and Korayem, M. H., “Theoretical and experimental study of dynamic load-carrying capacity for flexible robotic arms in point-to-point motion”, Optim. Contr. Appl. Met. 38(6), 963–972 (2017).CrossRefGoogle Scholar
Rendon, A. and Martins, F., “Path following control tuning for an autonomous unmanned quadrotor using particle swarm optimization”, Appl. Math. Model. 50(1), 325–330 (2017).Google Scholar
Navarro, A.S., Loianno, G. and Kumar, V., “Autonomous navigation of micro aerial vehicles using high-rate and low-cost sensors”, Auton. Robots. 42(6), 1263–1280 (2018).CrossRefGoogle Scholar
Beni, Z., Piljek, P. and Kotarski, D., “Mathematical modelling of unmanned aerial vehicles with four rotors”, Interdiscip. Descrip. Compl. Syst. 14(1), 88–100 (2016).CrossRefGoogle Scholar
Bousbaine, A., Wu, M. H. and Poyi, G. T., “Modeling and Simulation of a Quad-Rotor Helicopter”, In: 6th IET International Conference on Power Electronics, Machines and Drives (PEMD 2012), Bristol (2012) pp. 1–6.Google Scholar
Tang, Y., Xiao, X. and Li, Y., “Nonlinear dynamic modeling and hybrid control design with dynamic compensator for a small-scale UAV quadrotor,” Meas. J. 109(1), 51–64 (2017).CrossRefGoogle Scholar
Sayyaadi, H. and Soltani, A., “Decentralized polynomial trajectory generation for flight formation of quadrotors”, Proc. Inst. Mech. Eng. Part K: J. Multi-Body Dyn. 231(4), 690–707 (2017).Google Scholar
Shafei, A. M. and Shafei, H. R., “A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment”, Multibody Syst. Dyn. 38(1), 21–42 (2016).CrossRefGoogle Scholar
Bouktir, Y., Haddad, M. and Chettibi, T., “Trajectory Planning for a Quadrotor Helicopter”, Proceedings of the Mediterranean Conference on Control and Automation (2008) pp 1258–1263.CrossRefGoogle Scholar
Hehn, M., Ritz, R. and D’Andrea, R., “Performance benchmarking of quadrotor systems using time-optimal control”, Auton. Robots. 33(1), 69–88 (2012).CrossRefGoogle Scholar
Heidari, H. R., Korayem, M. H., Haghpanahi, M. and Batlle, V. F., “Optimal trajectory planning for flexible link manipulators with large deflection using a new displacements approach”, J. Intell. Robot. Syst. 72(3), 287–300 (2013).CrossRefGoogle Scholar
Hehn, M. and D’Andrea, R., “Quadrocopter Trajectory Generation and Control”, In: Proceedings of the 18th World Congress, The International Federation of Automatic Control (IFAC), Milano, Italy, vol. 44(1) (2011) pp. 1485–1491.Google Scholar
Guerrero, J.A. and Bestaoui, Y., “UAV path planning for structure inspection in windy environments”, J. Intell. Robot. Syst. 69(1), 297–311 (2013).CrossRefGoogle Scholar
Lai, L., Yang, Ch and Wu, Ch, “Time-optimal control of a hovering quad-rotor helicopter”, J. Intell. Robot. Syst. 45(2), 115–135 (2006).CrossRefGoogle Scholar
Li, F., Zlatanova, S. and Koopman, M., “Universal path planning for an indoor drone”, Appl. Math. Model. 95(1), 275–283 (2018).Google Scholar
Tayebi, A. and McGilvray, S., “Attitude Stabilization of a Four-Rotor Aerial Robot”, In: 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), Nassau, vol. 2 (2004) pp. 1216–1221.Google Scholar