Trajectory optimisation of six degree of freedom aircraft using differential flatness
TL;DR: In this article, the flatness of a 6DoF aircraft model with conventional control surfaces is established, along with thrust vectoring ability, and an application for flatness-based trajectory optimisation for dynamic soaring is shown.
Abstract: The flatness of a six-degree-of-freedom (6DoF) aircraft model with conventional control surfaces – aileron, flap, rudder and elevator, along with thrust vectoring ability is established in this work. Trajectory optimisation of an aircraft can be cast as an inverse problem where the solution for control inputs that yield desired trajectories for certain states is sought. The solution to the inverse problems for certain systems is made tractable when they exhibit differential flatness. Flatness-based trajectory optimisation has a significant advantage over an equivalent collocation-based method in terms of computational efficiency and viability for real-time implementation. An application for the flatness of 6DoF aircraft is shown in the trajectory optimisation for dynamic soaring, and its connection with an equivalent 3DoF flatness-based implementation is also brought out. The results are compared with that from a collocation-based approach.
Citations
More filters
TL;DR: A time-domain approach using Fourier collocation for solving the Floquet eigenvalue problem with real-time constraints is presented.
Abstract: Periodic trajectories that satisfy stability-based requirements are useful in many engineering applications. In this work, a time-domain approach using Fourier collocation for solving the Floquet e...
5 citations
TL;DR: In this article , a community-oriented approach to the multiobjective optimisation of sustainable takeoff and landing procedures of commercial aircraft is presented, where the objective functions to be minimised are defined as the measure of area surrounding the airport where the Sound Exposure Level (SEL) is higher than 60 dBA, and the amount of fuel burned during the procedure.
Abstract: The paper deals with a community-oriented approach to the multiobjective optimisation of sustainable takeoff and landing procedures of commercial aircraft. The objective functions to be minimised are defined as the measure of area surrounding the airport where the Sound Exposure Level (SEL) is higher than 60 dBA, and the amount of fuel burned during the procedure. The first merit factor is a measure of the number of citizens affected by a potentially harmful noise level, whereas the second is proportional to the chemical emissions. The novelty of the present approach is the use of a criterion based on sound quality for the selection of the optimal procedure from the Pareto front set. The spectrum of the noise produced by each non-dominated solution is compared to a reference spectrum, the target sound. This is synthesised to meet the acceptance requirements that emerged by a campaign of psychometric tests. The rationale underlying the research is tightly linked to the expected transformation of civil aviation, with the advent of new air transport solutions in urban and suburban environments. The breakthrough nature of the emerging scenarios requires a drastic renewal of the approaches used in the management of operations, and the present work represents a contribution to this evolution. The optimisation is attained adopting a global, deterministic method, and numerical results are obtained for singleand twin-aisle aircraft.
2 citations
TL;DR: In this article , a community-oriented approach to the multiobjective optimisation of sustainable takeoff and landing procedures of commercial aircraft is presented, where the objective functions to be minimised are defined as the measure of area surrounding the airport where the Sound Exposure Level (SEL) is higher than 60 dBA, and the amount of fuel burned during the procedure.
Abstract: The paper deals with a community-oriented approach to the multiobjective optimisation of sustainable takeoff and landing procedures of commercial aircraft. The objective functions to be minimised are defined as the measure of area surrounding the airport where the Sound Exposure Level (SEL) is higher than 60 dBA, and the amount of fuel burned during the procedure. The first merit factor is a measure of the number of citizens affected by a potentially harmful noise level, whereas the second is proportional to the chemical emissions. The novelty of the present approach is the use of a criterion based on sound quality for the selection of the optimal procedure from the Pareto front set. The spectrum of the noise produced by each non-dominated solution is compared to a reference spectrum, the target sound. This is synthesised to meet the acceptance requirements that emerged by a campaign of psychometric tests. The rationale underlying the research is tightly linked to the expected transformation of civil aviation, with the advent of new air transport solutions in urban and suburban environments. The breakthrough nature of the emerging scenarios requires a drastic renewal of the approaches used in the management of operations, and the present work represents a contribution to this evolution. The optimisation is attained adopting a global, deterministic method, and numerical results are obtained for single- and twin-aisle aircraft.
2 citations
02 Jul 2019
TL;DR: A flatness based model predictive control (FMPC) algorithm is proposed and simulated for a 6DoF UAV to alleviate the computational cost associated with LMPC and leads to a significant increase in computational efficiency.
Abstract: Trajectory tracking using linear model predictive control (LMPC) ensures optimal tracking of the system trajectory subject to constraints imposed by system dynamics and actuator limitations. Even though the method is attractive for most applications, solving an optimization problem tends to be a computationally intensive task. In order to alleviate the computational cost associated with LMPC, a flatness based model predictive control (FMPC) algorithm is proposed and simulated for a 6DoF UAV. The reduction in the dimension of the optimization problem due to flatness leads to a significant increase in computational efficiency. In order to show the computational advantages of the FMPC algorithm, it is compared with a standard LMPC algorithm.
2 citations
Cites background or methods from "Trajectory optimisation of six degr..."
...in [12] for trajectory optimization and the same model is adopted throughout this paper for all the simulations....
[...]
...More details on the modeling of forces, moments and parameters used can be found in [12]....
[...]
06 Jan 2020
1 citations
References
More filters
TL;DR: In this paper, the authors introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous feedback, which subsumes the physical properties of a linearizing output and provides another nonlinear extension of Kalman's controllability.
Abstract: We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.
3,025 citations
"Trajectory optimisation of six degr..." refers background in this paper
...The set of 12 differential equations ((2), (3), (5) and (7)) for the 12 states – x, y, z, u, v, w, φ, θ, ψ, p, q, r constitute the aircraft’s six-degree-of-freedom (6DoF) equations of motion involving 6 control inputs – δf, δa, δe, δr, CTx, CTy....
[...]
...Flatness-based control was originally introduced by Fliess et al.(3), and its application to trajectory optimisation was explored by Nieuwstadt and Murray(4)....
[...]
..._ u _ v _ w 2 4 3 5 + S _ S uv w 2 4 3 5= f m + S 0 0 g 2 4 3 5 S Wxz _ z 0 0 2 4 3 5 ...(3)...
[...]
...introduced by Fliess et al.((3)), and its application to trajectory optimisation was explored by Nieuwstadt and Murray((4))....
[...]
...Rearrangement of the time derivative of (2) yields us (3) and (4), which concern the forces on the body and the rate of change of the components of the relative wind along the body axes:...
[...]
TL;DR: A Chebyshev pseudospectral method is presented in this paper for directly solving a generic optimal control problem with state and control constraints and yields more accurate results than those obtained from the traditional collocation methods.
Abstract: We present a Chebyshev pseudospectral method for directly solving a generic Bolza optimal control problem with state and control constraints. This method employs Nth-degree Lagrange polynomial approximations for the stateand control variables with the values of these variables at the Chebyshev-Gauss-Lobatto (CGL) points as the expansion coefficients. This process yields a nonlinear programming problem (NLP) with the state and control values at the CGL points as unknown NLP parameters. Numerical examples demonstrate that this method yields more accurate results than those obtained from the traditional collocation methods.
484 citations
Book•
02 Nov 2015TL;DR: The Kinematics and Dynamics of Aircraft Motion, Modeling the Aircraft, and Modeling, Design, and Simulation Tools are presented.
Abstract: 1 The Kinematics and Dynamics of Aircraft Motion
2 Modeling the Aircraft
3 Modeling, Design, and Simulation Tools
4 Aircraft Dynamics and Classical Control Design
5 Modern Design Techniques
6 Robustness and Multivariable Frequency-Domain Techniques
7 Digital Control
8 Modeling and Simulation of Miniature Aerial Vehicles
9 Adaptive Control With Application to Miniature Aerial Vehicles
451 citations
"Trajectory optimisation of six degr..." refers background or methods in this paper
...CL is determined by plugging this solution for CTx into (15) while Cm is known from (10)....
[...]
...The x and z components of the body axes force f in (9) can be rearranged to yield (15):...
[...]
...The aerodynamic forces and moments are estimated using a look-up table((15)) that spans across operating points....
[...]
...A quadratic equation (17) for CTx can be obtained from (15) and (16):...
[...]
TL;DR: In this article, the authors consider the problem of real-time trajectory generation and tracking for nonlinear control systems and employ a two-degree-of-freedom approach that separates the non-linear tracking problem into real time trajectory generation followed by local gain-scheduled stabilization.
Abstract: This paper considers the problem of real-time trajectory generation and tracking for nonlinear control systems. We employ a two-degree-of-freedom approach that separates the nonlinear tracking problem into real-time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real-time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included. © 1998 John Wiley & Sons, Ltd.
270 citations
"Trajectory optimisation of six degr..." refers background in this paper
...Flatness-based control was originally introduced by Fliess et al.(3), and its application to trajectory optimisation was explored by Nieuwstadt and Murray(4)....
[...]
...These are then substituted into (4) and (7) to obtain f and m, respectively....
[...]
...f = Fx Fy Fz 2 4 3 5=m _ u_ v _ w 2 4 3 5 + wq vr ru pw pv qu 2 4 3 5 g Sθ CθSφ CθCφ 2 4 3 5 +Wxz _ z CψCθ CψSθSφ SψCφ CψSθCφ + SψSφ 2 4 3 5 0 @ 1 A ...(4)...
[...]
...Rearrangement of the time derivative of (2) yields us (3) and (4), which concern the forces on the body and the rate of change of the components of the relative wind along the body axes:...
[...]
..., and its application to trajectory optimisation was explored by Nieuwstadt and Murray((4))....
[...]
01 Jan 2002
TL;DR: In this article, a Chebyshev pseudospectral method is presented for directly solving a generic optimal control problem with state and control constraints, which yields more accurate results than those obtained from the traditional collocation methods.
Abstract: A Chebyshev pseudospectral method is presented in this paper for directly solving a generic optimal control problem with state and control constraints. This method employs N t h degree Lagrange polynomial approxiniations for the state and control variables with the values of these variables at the Chebyshev-GaussLobatto (CGL) points as the expansion coefficients. This process yields a nonlinear programming problem (NLP) with the state and control values at the CGL points as unknown NLP parameters. Numerical examples demonstrate this method yields more accurate results than those obtained from the traditional collocation methods.
267 citations