Trajectory planning for a quadrotor helicopter

Bouktir, Y.; Haddad, Moussa; Chettibi, Taha

doi:10.1109/med.2008.4602025

Cited by 123 publications

(99 citation statements)

References 9 publications

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“…The question of the feasibility of a given trajectory has been studied more recently. Hoffmann et al [2008], Cowling et al [2007], and Bouktir et al [2008] present algorithms that split the planning problem into two parts: First, trajectories containing no time information are calculated from a class of motion primitives (lines, polynomials, or splines). The trajectory is then parametrized in time by choosing the trajectory speed such that dynamic feasibility constraints are enforced.…”

Section: Introductionmentioning

confidence: 99%

Quadrocopter Trajectory Generation and Control

Hehn

D’Andrea

2011

IFAC Proceedings Volumes

149

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An algorithm is presented that allows the calculation of flight trajectories for quadrocopters. Trajectory feasibility constraints regarding the vehicle dynamics and input constraints are derived. They are then used in the planning algorithm to guarantee the feasibility of generated trajectories. The translational degrees of freedom of the quadrotor are decoupled, and time-optimal trajectories are found for each degree of freedom separately. The trajectory generation is fast enough to be performed online. Control inputs are calculated from the generated trajectory, and used to achieve closed-loop control similar to model predictive control. The trajectory generation and tracking performance is demonstrated in the ETH Zurich Flying Machine Arena testbed. Experimental results show good performance, with unmodeled aerodynamic effects causing trajectory deviations when decelerating from high speeds. Development potential for the future is highlighted, focusing on improving the performance and correcting for aerodynamic effects.

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Section: Introductionmentioning

confidence: 99%

Quadrocopter Trajectory Generation and Control

Hehn

D’Andrea

2011

IFAC Proceedings Volumes

149

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“…Most of the literature brings simulated results essentially. Bouktir et al (2008) achieved promising results in simulation. They proposed a method that is able to generate timeoptimal trajectories for a micro quadrotor based on its trajectory parameterization and using a nonlinear optimization technique.…”

Section: Introductionmentioning

confidence: 88%

In-flight collision avoidance controller based only on OS4 embedded sensors

Becker¹,

Sampaio²,

Bouabdallah³

et al. 2012

J. Braz. Soc. Mech. Sci. & Eng.

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“…The coordinates of the no-fly zone center are (11,14), and R = 2 m with no limitation on altitude. The quadrotor is required to pass waypoint-1 (5,8,10), and waypoint-2 (16,16,16) with specific attitude and velocity requirements. In detail, the quadrotor optimal control can be described to minimize the cost functional: …”

Section: Trajectory Generationmentioning

confidence: 99%

“…To show the validity of the proposed method, a popular quadrotor model was chosen as an example because the quadrotor is a typical under-actuated system with multiple variables, highly nonlinear, and strongly coupled control inputs and outputs. 5 This paper is organized as follows. First, the optimal trajectory generation problem is defined in Section 2.…”

Section: Introductionmentioning

confidence: 99%

A multiphase DMOC‐based trajectory optimization method

Zhang

Wang

Inanc

2017

Optim Control Appl Methods

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SummaryDiscrete mechanics and optimal control (DMOC) is a methodology that takes advantage of variational structure to solve certain optimal control problems for mechanical systems. This paper proposes to combine a multiphase strategy with the original DMOC method, resulting in a new multiphase DMOC (MDMOC) method and making optimal trajectory generation more efficient. The advantages of the proposed method are demonstrated mathematically, and in addition, a quadrotor, unmanned aerial vehicle, simulation example is presented to show its superiority over the DMOC method. Furthermore, to show its potential application, an arbitrarily chosen controller was used to track the desired trajectory generated by MDMOC. This new MDMOC methodology can also be applied to other mechanical systems such as mobile robots and underwater gliders.KEYWORDS discrete mechanics and optimal control, optimal control applications, quadrotor, trajectory optimization | INTRODUCTIONRobotic vehicles are becoming increasingly popular because of their great flexibility and mobility. They are widely used in military, civilian, commercial, and many other fields. Traditionally, robotic vehicles can be categorized into 4 main types: underwater robots, land mobile robots, unmanned aircraft, and space robots. Recently, small unmanned aerial vehicles (UAVs), as a kind of self-propelled aerial robot, have attracted widespread research attention because of their potential applications, including reconnaissance, surveillance, search and rescue, and environmental monitoring.In practice, it is always preferable for UAVs to generate a real-time trajectory, which is the foundation of reconnaissance, exploration, or tracking missions. However, due to their limited payload, it is essential to plan the optimal trajectory to achieve minimum time and/or minimum energy objectives.1 Therefore, an efficient trajectory optimization method and corresponding tracking controller design are indispensable. Generally, trajectory optimization can be considered as an optimal control problem. 2 Many kinds of optimization algorithm have been proposed for different systems. Betts 3 presented a survey showing that numerical methods for solving optimal trajectory problems can normally be classified into 2 categories: indirect and direct. Direct methods have been widely used by transforming a continuous optimal control problem into a nonlinear programming (NLP) problem. 4 Bouktir et al 5 presented a numerical method to generate a minimum-time optimal trajectory for a quadrotor with nonlinear under-actuated properties; Ross et al 2 proposed a guess-free spectral algorithm with several limiting assumptions in which the problem must be reasonably bounded and scaled; Chamseddine et al 6 applied a planning/replanning strategy to a quadrotor and illustrated the simplicity and efficiency of the method. All these approaches can solve the specified problems with relative efficiency. However, they are applicable only to trajectory optimization problems for certain specific simple mechanical...

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Trajectory planning for a quadrotor helicopter

Cited by 123 publications

References 9 publications

Quadrocopter Trajectory Generation and Control

Quadrocopter Trajectory Generation and Control

In-flight collision avoidance controller based only on OS4 embedded sensors

A multiphase DMOC‐based trajectory optimization method

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