Abstract
Spacecraft trajectory optimization is essential for all the different phases of a space mission, from its launch to end-of-life disposal. Due to the increase in the number of satellites and future space missions beyond our planet, increasing the level of autonomy of spacecraft is a key technical challenge. In this context, traditional trajectory optimization methods, like direct and indirect methods are not suited for autonomous or on-board operations due to the lack of guaranteed convergence or the high demand for computational power. Heuristic control laws represent an alternative in terms of computational power and convergence but they usually result in sub-optimal solutions. Successive convex programming (SCVX) enables to extend the application of convex optimization to non-linear optimal control problems. The definition of a good value of the trust region size plays a key role in the convergence of SCVX algorithms, and there is no systematic procedure to define it. This work presents an improved trust region based on the information given by the nonlinearities of the constraints which is unique for each optimization variable. In addition, differential algebra is adopted to automatize the transcription process required for SCVX algorithms. This new technique is first tested on a simple 2D problem as a benchmark of its performance and then applied to solve complex astrodynamics problems while providing a comparison with indirect, direct, and standard SCVX solutions.
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Abbreviations
- DA:
-
differential algebra
- DACX:
-
differential algebra successive convex optimization algorithm
- g 0 :
-
standard gravity acceleration (m/s)
- I sp :
-
specific impulse (s)
- J :
-
nonlinear cost function
- L :
-
linear cost function
- m :
-
spacecraft mass (kg)
- SCVX:
-
successive convex optimization
- STM:
-
state transition matrix
- t 0, t f :
-
initial and final time (s)
- \(\cal{T}^{p}\) :
-
Taylor polynomial of order p
- T max :
-
maximum thrust (N)
- u :
-
spacecraft control vector
- x :
-
spacecraft state (km, km/s)
- z :
-
augmented spacecraft state (km, km/s, kg)
- δ s :
-
trust region scaling factor
- Δ:
-
state dependent trust region
- λ :
-
penalty weight
- ρ 0, ρ 1, ρ 2 :
-
SCVX acceptance metric
- ϕ :
-
state transition matrix
- σ :
-
time dilatation coefficient
- ν :
-
nonlinearity indicator
- ν :
-
virtual control
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Nicolò Bernardini obtained his M.Sc. degree in aerospace engineering from ISAE-Suapero and he holds a B.Sc. degree in aerospace engineering from Politecnico di Milano. He is currently a Ph.D. candidate in space engineering at the University of Surrey. The main focus of his Ph.D. is guidance and navigation algorithms for autonomous spacecraft and his research interest spreads from trajectory optimization to nonlinear dynamical systems.
Nicola Baresi graduated from the University of Colorado Boulder in 2017 with a Ph.D. thesis on spacecraft formation flight and quasi-periodic invariant tori. He later moved to Japan working on the MMX and EQUULEUS missions as a postdoctoral fellow at the Institute of Space and Astronautical Sciences (ISAS) of JAXA. Starting from 2019, Dr. Baresi has joined the University of Surrey, where he is now a lecturer in orbital mechanics at Surrey Space Centre. Nicola has authored more than 60 scientific contributions, including conference proceedings and peer-reviewed articles in top-ranked astrodynamics journals. He is an elected member of the Space Flight Mechanics Committee of the American Astronautical Society, as well as a Fellow of the UK Higher Education Academy.
Roberto Armellin received his M.Sc. and Ph.D. degrees in aerospace engineering from Politecnico di Milano, Italy in 2003 and 2007, respectively. Since November 2020 he has been a professor at Te P.unaha Atea–Space Institute, University of Auckland, New Zealand. His current research interests include space trajectory optimization, spacecraft navigation and guidance, and space situational awareness.
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Bernardini, N., Baresi, N. & Armellin, R. State-dependent trust region for successive convex programming for autonomous spacecraft. Astrodyn (2024). https://doi.org/10.1007/s42064-024-0200-1
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DOI: https://doi.org/10.1007/s42064-024-0200-1