Analysis of Time Optimal 3D Paths for an Autonomous Aircraft with a Piecewise Constant Acceleration

2011 ◽  
Author(s):  
Yasmina Bestaoui ◽  
Elie Kahale
Keyword(s):  
Constant Acceleration ◽  
Piecewise Constant ◽  
Time Optimal ◽  
Autonomous Aircraft

scholarly journals A minimal time optimal control for a drone landing problem

2021 ◽  
Author(s):  
Filippo Gazzola ◽  
Elsa Maria Marchini
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Aerospace Engineering ◽  
Time Optimal Control ◽  
Height Velocity ◽  
The Moon ◽  
Piecewise Constant ◽  
Time Optimal

We study a variant of the classical safe landing optimal control problem in aerospace engineering, introduced by Miele in 1962, where the target was to land a spacecraft on the moon by minimizing the consumption of fuel. A more modern model consists in replacing the spacecraft by a hybrid gas-electric drone. Assuming that the drone has a failure and that the thrust (representing the control) can act in both vertical directions, the new target is to land safely by minimizing time, no matter of what the consumption is. In dependence of the initial data (height, velocity, and fuel), we prove that the optimal control can be of four different kinds, all being piecewise constant. Our analysis covers all possible situations, including the nonexistence of a safe landing strategy due to the lack of fuel or for heights/velocities for which also a total braking is insufficient to stop the drone.

Efficiency of the piecewise constant acceleration modeling - GOCE case study

2020 ◽  
Author(s):  
Andrzej Bobojć
Keyword(s):  
Gravity Field ◽  
European Space Agency ◽  
Constant Acceleration ◽  
Gravity Field Model ◽  
Piecewise Constant ◽  
Orbit Modeling ◽  
Cross Track ◽  
Along Track ◽  
Orbit Improvement ◽  
Goce Satellite

<p>One of the valuable products of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission is a centimeter-accuracy orbit of the GOCE satellite called the precise science orbit (PSO). This orbit, delivered by the European Space Agency (ESA), was the reference for the GOCE orbit modeling using the piecewise constant acceleration approach. Besides initial conditions, the piecewise constant accelerations (i.e. empirical accelerations) were estimated in the radial, along-track and cross-track direction, employing the dedicated package called Torun Orbit Processor (TOP). The TOP software is based on the classical least squares adjustment including the Cowell 8-th order numerical integration for an orbit prediction and the orbit improvement module, taking into account the gravity field model and the background models (BM) describing gravitational and non-gravitational perturbing forces. The positions of GOCE satellite on the reduced-dynamic PSO orbit were treated as observations in the orbit improvement process. A measure of the fit of estimated arcs and their accuracy was the RMS of the residuals between the estimated orbits and the corresponding reference ones. Different variants of the orbit estimation were obtained for the shorter  arcs (22.5, 45, 90 and 180 minutes)  and for the longer 1-day arcs. The solution variants were determined for different numbers of the estimated piecewise constant accelerations. Moreover, these numbers were different for the radial, along-track and cross-track direction. The obtained solutions depend on a kind of computational mode – with and without the BM models in the GOCE orbit modeling using the estimated piecewise constant accelerations. Additionally, for selected solutions, the distributions of the residuals in the aforementioned directions along the estimated arcs are presented. </p>

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