Multiresolution-based direct trajectory optimization

Jain, Sachin; Tsiotras, Panagiotis

doi:10.1109/cdc.2007.4434076

Cited by 6 publications

(27 citation statements)

References 17 publications

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“…For simplicity, we henceforth denote x j;k xt j;k and u j;k ut j;k . We convert the optimal control problem (1-5) into an NLP problem using Runge-Kutta (RK) discretizations [14,15]. To this end, let a nonuniform grid of the form…”

Section: Nlp Problem Formulation On Dyadic Gridsmentioning

confidence: 99%

“…The cost functional is discretized by introducing a new state and then using a RK discretization, as mentioned previously. Then the subsequent NLP problem [14,15] is to find the variables X, U,Ũ, and f that minimize (11) subject to the following constraints:…”

Section: Nlp Problem Formulation On Dyadic Gridsmentioning

confidence: 99%

“…Next, we incorporate the information of the trajectory profile of the target (33) in the optimal control problem itself. Because the trajectory profile of the target is assumed to be given for the optimal control problem at hand, the resulting problem can be solved in a single step using the MTOA [14,15]. The results found using the MTOA are shown in Fig.…”

Section: Sequential Trajectory Optimization Algorithm Imentioning

confidence: 99%

“…In this paper, we present two algorithms, based on the recently proposed multiresolution trajectory optimization algorithm (MTOA) developed by the authors [14,15], which autonomously discretize the trajectory with more nodes (finer grid) near the current time (not necessarily uniformly placed) and use fewer nodes (coarser grid) for the rest of the trajectory, the latter to capture the overall trend. Furthermore, if the states or controls are irregular in the vicinity of the current time, the algorithm will automatically further refine the mesh in this region to capture the irregularities in the solution more accurately.…”

Section: Introductionmentioning

confidence: 99%

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Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets

Jain

Tsiotras

2009

Journal of Guidance, Control, and Dynamics

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In this paper, we present two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and dynamically changing environments. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation algorithm is proposed, enabled by the introduction of the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a nonuniform grid across time. The grid is adapted to the immediate future and to potential discontinuities in the state and control variables.

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Section: Nlp Problem Formulation On Dyadic Gridsmentioning

confidence: 99%

Section: Nlp Problem Formulation On Dyadic Gridsmentioning

confidence: 99%

Section: Sequential Trajectory Optimization Algorithm Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets

Jain

Tsiotras

2009

Journal of Guidance, Control, and Dynamics

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“…The so-called "pseudospectral" methods use orthogonal polynomials to choose the collocation points and are very efficient, exhibiting superlinear convergence when the solution is smooth. Numerical optimal control software packages that implement direct methods for the solution of OCPs include SOCS [11], RIOTS [70], DIDO [62], PSOPT [7], GPOPS [60], MTOA [42] and DENMRA [84] among many others. A recent survey of numerical optimal control techniques for trajectory optimization can be found in [9].…”

Section: Optimal Trajectory Generationmentioning

confidence: 99%

Mathematical Models for Aircraft Trajectory Design: A Survey

Delahaye

Puechmorel

Tsiotras

et al. 2014

Lecture Notes in Electrical Engineering

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Air traffic management ensures the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more efficient representations. Some dimension reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air traffic control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really efficient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming.

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Adaptive mesh refinement method for solving optimal control problems using interpolation error analysis and improved data compression

Zhao

2020

Journal of the Franklin Institute

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Multiresolution-based direct trajectory optimization

Cited by 6 publications

References 17 publications

Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets

Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets

Mathematical Models for Aircraft Trajectory Design: A Survey

Adaptive mesh refinement method for solving optimal control problems using interpolation error analysis and improved data compression

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