A robust homotopic approach for continuous variable low-thrust trajectory optimization

Saghamanesh, Mohammadreza; Baoyin, Hexi

doi:10.1016/j.asr.2018.08.046

Cited by 22 publications

(12 citation statements)

References 34 publications

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“…In order to eliminate the discontinuity problem in the shooting function caused by the step change of u , a homotopic approach was introduced to release the control profile and enforce discontinuity in a gentle way. 41,42 In this way, the performance index is rewritten aswhere ε is homotopy stepsize, ε ∈[0 , 1].…”

Section: The Controlled Nominal Nrho In the Real Ephemerismentioning

confidence: 99%

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Starinova

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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The near rectilinear halo orbit (NRHO) is a potential orbit for the establishment of lunar space station. This research is focused on the analysis of major orbital perturbations on NRHOs and the generation of nominal orbit using a low-thrust engine in the ephemeris model. First, the NRHO family is defined in the circular restricted three-body problem (CRTBP). Then, different perturbations are performed to integrate the spacecraft motion along the NRHOs; meanwhile, a modified momentum integral is employed to calculate the orbit deviation in the case of each perturbation examined independently. By this way, these perturbations are classified according to the magnitude of impact on NRHOs. Finally, combined with a fuel-optimal control, a target-point strategy generating the nominal-controlled NRHO in the real Earth–Moon system is proposed using low-thrust technology. By selecting a fixed point from the original NRHO, the spacecraft is forced to depart from this point and then return to it, thereby forming a controlled closed trajectory. This provides an alternative nominal orbit for the future application of the low-thrust engine to lunar exploration missions.

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Section: The Controlled Nominal Nrho In the Real Ephemerismentioning

confidence: 99%

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Starinova

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…As the continuation parameters approach zero, the smooth control vector, U s approaches the values corresponding to the non-smooth OCP, U * . The numerical continuation procedure is straightforward and is analogous to methods widely used for solving optimal control problems [59,60]. In the next section, the results of applying the outlined set of steps on a low-thrust fuel-optimal trajectory optimization problem is demonstrated.…”

Section: Numerical Continuation Proceduresmentioning

confidence: 99%

A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

et al. 2020

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Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines).Each engine can be switched on/off independently and "optimal" operating power of each engine depends on the available solar power, which depends on the distance from the Sun. Application of the Composite Smooth Control (CSC) framework to a heliocentric fuel-optimal trajectory optimization from the Earth to the comet 67P/Churyumov-Gerasimenko is demonstrated, which presents a new approach to deal with multiple-engine problems. Operation of engine clusters with 4, 6, 10 and even 20 engines of the same type can be optimized.Moreover, engine clusters with different/mixed electric engines are considered with either 2, 3 or 4 different types of engines. Remarkably, the CSC framework allows us 1) to reduce the original multi-point boundary-value problem to a two-point boundary-value problem (TPBVP), and 2) to solve the resulting TP-BVPs using a single-shooting solution scheme and with a random initialization of the missing costates. While the approach we present is a continuous neighbor of the discontinuous extremals, we show that the discontinuous necessary conditions are satisfied in the asymptotic limit. We believe this is the first indirect method to accommodate a multi-mode control of this level of complexity with realistic engine performance curves. The results are interesting and promising for dealing with a large family of such challenging multi-mode optimal control problems.

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“…For discontinuous controls with state-and costate-dependent switch times, note that conventional step-bystep integrators will not yield a valid integration step if a force discontinuity is contained interior to an integration step. Therefore, without smoothing, conventional integrators must be augmented with a logic to locate precisely the switch times and to use these times to adjust integration step size values [68].…”

Section: Control Smoothing For Vivt Enginesmentioning

confidence: 99%

A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1

Taheri¹,

Junkins²,

Kolmanovsky³

et al. 2019

Preprint

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Efficient performance of a number of engineering systems is achieved through different modes of operation -yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such systems, in space applications, could be spacecraft equipped with 1) a variable-I sp , variable-thrust engine or 2) multiple engines each capable of switching on/off independently. To alleviate the challenges that arise when an indirect optimization method is used, a new framework -Composite Smooth Control (CSC)is proposed that seeks smoothness over the entire spectrum of distinct control inputs. A salient aftermath of the application of the CSC framework is that the original multi-point boundary-value problem can be treated as a two-point boundary-value problem with smooth, differentiable control inputs; the latter is notably easier to solve, yet can be made to accurately approximate the former hybrid problem. The utility of the CSC framework is demonstrated through a

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A robust homotopic approach for continuous variable low-thrust trajectory optimization

Cited by 22 publications

References 34 publications

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

Orbital perturbation analysis and generation of nominal near rectilinear halo orbits using low-thrust propulsion

A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1

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