Direct Trajectory Optimization by a Chebyshev Pseudospectral Method

Fahroo, Fariba; Ross, I. Michael

doi:10.2514/2.4862

Cited by 462 publications

(227 citation statements)

References 18 publications

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“…The optimal control problem now can be defined as a discretised problem as follows: (19). This above discretisation approach has been implemented in the DIRCOL [22,23] package which employed the sequential quadratic programming method SNOPT by Gill et al [24].…”

Section: Methodsmentioning

confidence: 99%

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Subchan¹

2010

MST

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This paper presents trajectory shaping of a surface-to-surface missile attacking a fixed with terminal impact angle constraint. The missile must hit the target from above, subject to the missile dynamics and path constraints. The problem is reinterpreted using optimal control theory resulting in the formulation of minimum integrated altitude. The formulation entails nonlinear, two-dimensional missile flight dynamics, boundary conditions and path constraints. The generic shape of optimal trajectory is: level flight, climbing, diving; this combination of the three flight phases is called the bunt manoeuvre. The numerical solution of optimal control problem is solved by a direct collocation method. The computational results is used to reveal the structure of optimal solution which is composed of several arcs, each of which can be identified by the corresponding manoeuvre executed and constraints active.

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Section: Methodsmentioning

confidence: 99%

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Subchan¹

2010

MST

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“…where µ (µ 1 , ..., µ q ) T corresponds to the zero dynamics (16). Thus, the stationarity adjoint equations (18) write…”

Section: Proposition 1 (Weak Minimum Principle [8]) Consider the Sysmentioning

confidence: 99%

“…Then Z * is connected and there is a globally defined diffeomorphism Υ : R n → Z * × R r which changes (12) into the following normal form (15,16),…”

Section: Problem Statement and Feedback Linearizationmentioning

confidence: 99%

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Inversion in indirect optimal control of multivariable systems

Chaplais

Petit

2008

ESAIM: COCV

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Abstract. This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.Mathematics Subject Classification. 34C20, 34H05, 49K15, 93C10, 93C35.

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“…Direct numerical methods for trajectory optimization have been widely investigated, not requiring the explicit consideration of the necessary conditions and with better convergence properties (Betts, 1998). These methods have been used together with Chebyshev pseudospectral techniques, to allow the reduction of the number of the optimization variables (Fahroo and Ross, 2002). Also convex programming has been proposed to guarantee the convergence of the optimization; this approach, coupled with direct collocation methods, has proved that the size of the region of feasible initial states, for which there exist feasible trajectories, can be increased drastically (more than twice) compared to the traditional polynomial-based guidance approaches, but at the price of a higher computational cost (Açikmeşe and Ploen, 2007).…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical guidance algorithm for autonomous landing

Lunghi¹,

Lavagna²,

Armellín³

2015

Advances in Space Research

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One of the main challenges posed by the next space systems generation is the high level of autonomy they will require. Hazard Detection and Avoidance is a key technology in this context. An adaptive guidance algorithm for landing that updates the trajectory to the surface by means of an optimal control problem solving is here presented. A semi-analytical approach is proposed. The trajectory is expressed in a polynomial form of minimum order to satisfy a set of boundary constraints derived from initial and final states and attitude requirements. By imposing boundary conditions, a fully determined guidance profile is obtained, function of a restricted set of parameters. The guidance computation is reduced to the determination of these parameters in order to satisfy path constraints and other additional constraints not implicitly satisfied by the polynomial formulation. The algorithm is applied to two different scenarios, a lunar landing and an asteroidal landing, to highlight its general validity. verify the versatility of the algorithm in realistic cases, by the introduction of attitude control systems, thrust modulation, and navigation errors. The proposed approach proved to be flexible and accurate, granting a precision of a few meters at touchdown.

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Direct Trajectory Optimization by a Chebyshev Pseudospectral Method

Cited by 462 publications

References 18 publications

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Trajectory Shaping of Surface-to-Surface Missile With Terminal Impact Angle Constraint

Inversion in indirect optimal control of multivariable systems

A semi-analytical guidance algorithm for autonomous landing

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