A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 2: Application

Lantoine, Gregory; Russell, Ryan P.

doi:10.1007/s10957-012-0038-1

Cited by 50 publications

(25 citation statements)

References 11 publications

(15 reference statements)

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“…In the simulations, the specific impulse is I sp = 2000 s and the initial mass of the spacecraft is m 0 = 1000 kg. The BCs are taken from (Lantoine and Russell, 2012) where the position and velocity of Earth and Mars are given by [−16.427384, −14.860506, 9.21486 × 10 −2 ] T (km/s).…”

Section: Earth-to-mars Problemmentioning

confidence: 99%

Co-state initialization for the minimum-time low-thrust trajectory optimization

Taheri

Kolmanovsky

2017

Advances in Space Research

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This paper presents an approach for co-state initialization which is a critical step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories typically result in two-point boundary-value problems and are solved by single-or multiple-shooting numerical methods. Accurate initialization of the co-state variables facilitates the numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by the so-called pseudo-equinoctial and three-dimensional finite Fourier series shape-based methods to estimate the initial values of the co-states. The performance of the approach for two interplanetary rendezvous missions from Earth to Mars and from Earth to asteroid Dionysus is compared against three other approaches which, respectively, exploit random initialization of co-states, adjoint-control transformation and a standard genetic algorithm. The results indicate that by using our proposed approach the percent of the converged cases is higher for trajectories with higher number of revolutions while the computation time is much lower. These features are advantageous

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Section: Earth-to-mars Problemmentioning

confidence: 99%

Co-state initialization for the minimum-time low-thrust trajectory optimization

Taheri

Kolmanovsky

2017

Advances in Space Research

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“…In this section, we implement the Hybrid Differential Dynamic Programming (HDDP) algorithm [33,34]: a robust, second-order optimal control method that is a variant of the conventional Differential Dynamic Programming (DDP), a continuous and local version of Bellman's Dynamic Programming [35,36]. A key component of the DDP approach is its ability to handle long time horizon problems without requiring large matrix inversions.…”

Section: A Second-order Optimal Control Solvermentioning

confidence: 99%

“…For this study we solve the fixed initial state and fixed final time problem and require minimum and maximum bounds on each control variable. The details of the solution procedure to the problem posed in equation (18) are beyond the scope of this paper, for details see references [33,34].…”

Section: Optimal Control Of Relative Motion In Arbitrary Fieldsmentioning

confidence: 99%

Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos

Russell

Lantoine

2012

J of Astronaut Sci

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A second-order, general dynamics, relative motion framework is formulated to solve for optimal finite-burn transfers in complex gravity fields that are not amenable to analytic solutions. The second-order variational equations are employed in a Cartesian frame that is general in fidelity and simple to implement. For a passive chief orbit we show that only 16 coefficient functions are necessary to accommodate most dynamical environments of interest. We pre-compute and curve-fit the coefficient functions which represent the time-varying Jacobians and Hessians of the state equations evaluated along the chief orbit. Once the coefficient functions are evaluated, the resulting CUrve-fit quadRatic Variational Equations (CURVE) model is almost transparent to the fidelity level and therefore is well suited for the repeated iterations required by nonlinear optimization. The optimal control problem is solved using a robust, second-order technique that is a variant of differential dynamic programming. The model and optimal rendezvous problems are demonstrated in the highly perturbed dynamical environment of the Martian moon Deimos. The resulting implementation is useful for any relative motion application requiring optimal targeting, particularly in the context of complex force fields. While intended primarily for exotic destinations such as the Moon, asteroids, comets, and planetary satellites, the CURVE model and optimal control framework can also be useful for Earth orbiters, especially in cases of large eccentricity and high fidelity geopotentials.

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“…2. The low-thrust optimal control problem is solved using the hybrid differential dynamic programming (HDDP) method described in [29,30]. It is noted that the HDDP optimal control solver satisfies both the necessary and sufficient conditions of optimality.…”

Section: Orbit-raising Capabilitymentioning

confidence: 99%

Utilization of Residual Helium to Extend Satellite Lifetimes and Mitigate Space Debris

Walker

Russell

Singh

2012

Journal of Propulsion and Power

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A new electric propulsion device concept takes advantage of residual helium gas that is trapped in the chemical propellant feed system and currently unused at end of life. The helium ion thruster provides additional propellant resources to extend satellite lifetimes and transfer geostationary orbit space assets to ultrasafe disposal orbits. The predicted capability, if fully allotted to the disposal, allows for perigee heights above the geostationary altitude that are one order of magnitude greater than existing international guidelines of 250 km. Furthermore, the proposed helium ion thruster concept makes the classic propellant gauge uncertainty problem moot, as satellite operators could use all of their conventional propellant for nominal station-keeping operations. The helium ion thruster concept therefore mitigates future space debris arising from depleted assets in the geostationary orbit belt through both aggressive orbit raising and depressurization of satellites at end of life. An analysis of the helium ion thruster theoretical performance shows that the device could raise the altitude of an end-of-life 2500 kg, 5 kW spacecraft by 2200 km in two months using 2 kg of residual helium.

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A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 2: Application

Cited by 50 publications

References 11 publications

Co-state initialization for the minimum-time low-thrust trajectory optimization

Co-state initialization for the minimum-time low-thrust trajectory optimization

Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos

Utilization of Residual Helium to Extend Satellite Lifetimes and Mitigate Space Debris

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