Exact Hybrid Jacobian Computation for Optimal Trajectories via Dual Number Theory

D’Onofrio, Vincenzo; Sagliano, Marco; Arslantas, Yunus Emre

doi:10.2514/6.2016-0867

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…1) An enhanced force model shall be developed, including winds and atmospheric time variations; 2) More specific vehicle data shall be used, first of all the aerodynamic coefficients; 3) A control law on the bank angle shall be implemented for the trajectory to fulfil the constraints; 4) In the estimation of the landing footprint, an optimal control problem shall be solved for a more accurate result [20]. The presented dynamic equations and thermo-mechanical constraints constitute a good start point for this activity.…”

Section: Discussionmentioning

confidence: 99%

A Gliding Vehicle for ISS Crew Rescue - Mission Operational Concept

Volo

Pietro²

2018

2018 SpaceOps Conference

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The purpose of this preliminary study is to analyse important operational aspects of using a generic gliding vehicle for ISS Crew Rescue Missions. In particular, mission duration, coast and re-entry windows, ground coverage and maximum loads are investigated. A fourstep approach is followed: first, re-entry corridor is computed taking into account thermomechanical constraints; second, the descent trajectory is simulated down to an altitude of 25 km, where the Terminal Area Energy Management (TAEM) guidance switches on. Third, footprint is computed for every point along the ISS orbit with a computationally-efficient approach to easily define both available re-entry windows and coast phases. Fourth, ground network coverage is analysed for a family of possible trajectories. The results of this preliminary analysis show that, considering a single target airport in Europe, the maximum coasting between two consecutive windows lasts about 6 hours. Moreover, it is demonstrated that the coast duration can be halved by adding an extra-runway in the Indian Ocean. Concerning ground coverage, it is shown that using a conventional network of stations does not provide sufficient link. Therefore, a satellite data relay system, like the American TDRSS, is highly recommended. Apart from number and comfort of the seats (important in case of injured astronauts), the short coasting duration, the possibility of landing on a runway and the low accelerations at re-entry are the main strengths of a gliding vehicle compared to a Soyuz-like capsule. I. Nomenclature= Earth oblateness r = geocentric radius t = time * Mission Analysis Engineer, Systems Engineering Department at AVIO Spa on behalf of AizoOn Consulting, strada del Lionetto, Turin, giuseppe.dicampli@aizoon.it.

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Section: Discussionmentioning

confidence: 99%

A Gliding Vehicle for ISS Crew Rescue - Mission Operational Concept

Volo

Pietro²

2018

2018 SpaceOps Conference

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“…The Jacobian can also be approximated using dual-numbers [17,18], although this yields a heavier computational load than the complex-step approach, with negligible changes in the results. Alternatively, tools for symbolic differentiation may be employed, but most of the time they require third-party tools, while complex-step can easily be coded with any programming language.…”

Section: Remark V2mentioning

confidence: 99%

Self-scaling Collocation Methods Preserving Constants of Motion

Sagliano

Holzel²

2021

AIAA Scitech 2021 Forum

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We present a class of self-scaling collocation integrators which, unlike explicit Runge-Kutta integrators, will automatically preserve quadratic constants of motion such as energy, linear momentum, and angular momentum, without the need for small stepsizes. However, collocation integrators in general require numerical optimization to solve an implicit set of equations which are difficult and computationally expensive to solve when the problem's Jacobian becomes ill-conditioned. Therefore, the integrators we present automatically scale the collocation conditions using a generalized eigenvalue problem (GEVP) approach, and exploit the Jacobian's structure to improve the optimization algorithm's precision and speed. Numerical results show that the presented integrators preserve invariants in a broader class of integration problems, with an improvement of approximately one order of magnitude over traditional Runge-Kutta 4(5) schemes.

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“…Fike & Alonso [40] used a similar idea known as hyper-dual numbers to compute accurate first and second-derivatives of engineering parameters (C L , C D , C M ) with respect to flow and geometric parameters such as Mach number (M ∞ ) and angle of attack (α). D'Onofrio et al [30], used dual numbers to form accurate jacobians for optimal control problems and found that compared to traditional methods they could get more accurate answers albeit at a higher computational cost.…”

Section: Numerical Perturbationmentioning

confidence: 99%

Development of Stability Analysis Tools for High Speed Compressible Flows

Bhagwat

Subbareddy

2018

2018 Fluid Dynamics Conference

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BHAGWAT, RUTVIJ. Development of Stability Analysis Tools for High Speed Compressible Flows. (Under the direction of Pramod Subbareddy.) Fluid flows experience transition to turbulence in ways which are not always easily explained through traditional ideas such as existence of a well defined flow instability. Experimentally, it can be seen that in many cases flows which are deemed stable by linear stability analysis experience transition. An idea that contributed towards bridging this gap was that of transient or nonmodal growth which was introduced in the early nineties. It proposed that for non-normal flow operators disturbances can grow over a short term before eventually decaying even if the system is stable and that this short term growth might be sufficient to trigger transition.Often earlier computational work was done for simplified configurations or by just analyzing a subsection of the system at a time, such as analyzing a boundary layer profile at a certain streamwise station or the flow profile in a certain crossflow plane. These analyses often miss out on capturing interconnected flow mechanisms in complex systems. Such systems demand a 'global analysis' which analyzes the system in its entirety all at once. These methods are computationally expensive but developments in scientific computing have led to an increased availability of computational resources which in turn broadened the range of problems accessible for these kinds of analyses.One such area of interest is transition in high-speed flows and so there is demand for tools and solvers which cater specially to these flows. This work involves the development of a suite of stability analysis solvers in a 3D parallel unstructured framework. We have tried to follow a methodology of developing these stability analyses tools from standard compressible flow solvers which is general enough that it can be applied to other standard compressible solvers. These tools can also be used to analyze turbulent flows where the focus is not on predicting the onset of transition but rather on extracting structural and dynamical features of these turbulent flows. The work also demonstrates the broad usage of these tools for analyzing transitional and turbulent flow fields across a wide range of physical regimes from incompressible to hypersonic flows. A number of flowfields such as: hypersonic flows over flat plates, shock-boundary layer interactions, flow over a sharp wedge among others were investigated as a part of this work. A novel resolvent based inflow-I/O framework for predicting the response of the flow to freestream waves has also been proposed.

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Exact Hybrid Jacobian Computation for Optimal Trajectories via Dual Number Theory

Cited by 8 publications

References 13 publications

A Gliding Vehicle for ISS Crew Rescue - Mission Operational Concept

A Gliding Vehicle for ISS Crew Rescue - Mission Operational Concept

Self-scaling Collocation Methods Preserving Constants of Motion

Development of Stability Analysis Tools for High Speed Compressible Flows

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