Trajectory Planning of Quadrotor Systems for Various Objective Functions

Abstract

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.

Design and Analysis of a Novel Concept-Based Unmanned Aerial Vehicle with Ground Traversing Capability

“…An extensive review article on motion planning of quadcopters or drones and their various control techniques was reported by Elijah et al [8] , and although these authors discussed the physical results associated with the experimental deployment of a quadcopter, they were not elaborately reported in that work. Moreover, Heidari and Saska [9] briefly discussed the different types of quadcopters such as fixed-wing and multi-rotor and their advantages and disadvantages in various applications with a comparative analysis. The research by Abdalla and Al-Baradie [10] integrated the PSO algorithm with the PID controller to design a steer control scheme for a quadcopter.…”

“…However, Besada-Portas et al [18]; Cui and Wang [19]; and Yao and Zhao [20] have shown the software-based computer simulation results of UAVs in their studies. Heidari and Saska [9] developed a heuristic approach-based open-loop control system to select optimal values of the dynamic control parameters such as thrust force and torque of a quadcopter for trajectory optimisation.…”

Autonomous landing of a quadrotor on a moving platform using vision-based FOFPID control

“…There are a few kinds of research in this area that represents a complete solution for autonomous landing problem and takes into the account the real-world challenges [25,26]. In general, optimal path generation should make the autonomous landing maneuver faster [27]. But, in our opinion, development of a fast and robust motion controller for quadrotor system can make critical improvements on landing time and precision in the real-world experiments that wind-induced disturbance forces are unavoidable.…”

Any-time randomized kinodynamic path planning algorithm in dynamic environments with application to quadrotor

“…In this context, various studies conducted and number of methods have been proposed. Detailed articles survey were accomplished to define the current state of the art of path planning problem in literature [11][12][13]. For motion planning and autonomy subjects, numerous researches exist in different manuscripts and number of methods are being presented.…”

“…This approach is implemented in a lightweight quadrotor platform and is evaluated in unknown cluttered indoor and outdoor workspaces. In, The optimal path planning algorithm was proposed by Heidari and Saska [23] for a quadrotor by considering various objective functions, such as energy efficiency. The necessary conditions of optimality are formulated here as a normal form of a two-point boundary-value problem using Pontryagin's minimum principle.…”