Pseudospectral Optimal Control for Military and Industrial Applications

Gong, Qi; Kang, Wei; Bedrossian, Nazareth; Fahroo, Fariba; Sekhavat, Pooya; Bollino, Kevin

doi:10.1109/cdc.2007.4435052

Cited by 53 publications

(24 citation statements)

References 38 publications

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“…Given the progress made in applying optimal control methods to online aerospace applications 12 and being aware of the ability to eliminate the associated computational burden 13,14 , this paper focuses on applying these techniques to the endemic tactical UAV problem, sharing attributes with both aerospace and robotics applications. As such, the research presented herein investigates the concept of trajectory planning for tactical UAVs using optimal control methods.…”

Section: The Optimal Path Planning Approachmentioning

confidence: 99%

Collision-Free Multi-UAV Optimal Path Planning and Cooperative Control for Tactical Applications

Lewis

Bollino

2008

AIAA Guidance, Navigation and Control Conference and Exhibit

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Stemming from previous work that addressed the optimal path planning of an unmanned aerial vehicle (UAV) in obstacle-rich environments, this paper demonstrates the approach's scalability to that of a multi-UAV application. The proposed concept, based on optimal control techniques and pseudospectral methods, offers the improved system flexibility and autonomy demanded by UAV tactical missions in urban areas. As demonstrated, employing optimal control methods for path planning problems provides a simplistic yet powerful capability of flight trajectory optimization that includes simultaneous collision avoidance between vehicles and terrain obstacles. Departing from traditional techniques that harbor non-optimal architectures, the employed method facilitates real-time, onboard computations that may potentially improve overall system performance. Recent developments in the field of optimal control theory point at an emerging paradigm shift that may involve less dependency on the typical inner-loop control. Extending these developments, this paper provides not only a fresh perspective, but also illustrates a viable technique for efficiently generating maneuvering flight trajectories for single vehicles or multiple vehicle sorties.

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Section: The Optimal Path Planning Approachmentioning

confidence: 99%

Collision-Free Multi-UAV Optimal Path Planning and Cooperative Control for Tactical Applications

Lewis

Bollino

2008

AIAA Guidance, Navigation and Control Conference and Exhibit

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“…The issue of real time solutions of OCP using direct pseudo-spectral methods has been investigated, 13,14 as well as the theoretical foundation of such methods and their connection to the continuous problem. 15,16 It is well known that the size and shape of the grid has a major impact on computational efficiency of a numeric solver [17][18][19] and the issue of grid selection in RHC-OCP formulations has also been studied.…”

Section: Goal Selectionmentioning

confidence: 99%

Receding Horizon Control of UAVs using Gradual Dense-Sparse Discretizations

Ögren

Robinson

2010

AIAA Guidance, Navigation, and Control Conference

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In this paper we propose a way of increasing the efficiency of some direct Receding Horizon Control (RHC) schemes. The basic idea is to adapt the allocation of computational resources to how the iterative plans are used. By using Gradual Dense-Sparse discretizations (GDS), we make sure that the plans are detailed where they need to be, i.e., in the very near future, and less detailed further ahead. The gradual transition in discretization density reflects increased uncertainty and reduced need for detail near the end of the planning horizon.The proposed extension is natural, since the standard RHC approach already contains a computational asymmetry in terms of the coarse cost-to-go computations and the more detailed short horizon plans. Using GDS discretizations, we bring this asymmetry one step further, and let the short horizon plans themselves be detailed in the near term and more coarse in the long term.The rationale for different levels of detail is as follows. 1) Near future plans need to be implemented soon, while far future plans can be refined or revised later. 2) More accurate sensor information is available about the system and its surroundings in the near future, and detailed planning is only rational in low uncertainty situations. 3) It has been shown that reducing the node density in the later parts of fixed horizon optimal control problems gives a very small reduction in the solution quality of the first part of the trajectory.The reduced level of detail in the later parts of a plan can increase the efficiency of the RHC in two ways. If the discretization is made sparse by removing nodes, fewer computations are necessary, and if the discretization is made sparse by spreading the last nodes over a longer time-horizon, the performance will be improved.

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“…(1) must be chosen to define the areas of the space shown in figure 2 that pose the greatest risk to the vehicle. In an obstacle avoidance problem, the threat shapes would be treated as path constraints, as investigated by Gong et al 41 and Lewis et al, 42 making any trajectory that passes through those areas of the space inadmissible.…”

Section: Via Deterministic Problem Formulationmentioning

confidence: 99%

Hybrid Gauss Pseudospectral and Generalized Polynomial Chaos Algorithm to Solve Stochastic Optimal Control Problems

Cottrill¹,

Harmon²

2011

Control and Applications

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A numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized PolynomialChaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. The GPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved using standard solvers to generate a set of deterministic solutions used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. The proposed algorithm investigates using GPM optimization software in place of deterministic differential equation solvers traditionally used in the gPC, providing minimum cost deterministic solutions that meet path, control, and boundary constraints. A trajectory optimization problem is considered where the objectives are to find the path through a two-dimensional space that minimizes the probability a vehicle will be 'killed' by lethal threats whose locations are uncertain and to characterize the effects those uncertainties have on the solution by estimating the statistical properties.

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Pseudospectral Optimal Control for Military and Industrial Applications

Cited by 53 publications

References 38 publications

Collision-Free Multi-UAV Optimal Path Planning and Cooperative Control for Tactical Applications

Collision-Free Multi-UAV Optimal Path Planning and Cooperative Control for Tactical Applications

Receding Horizon Control of UAVs using Gradual Dense-Sparse Discretizations

Hybrid Gauss Pseudospectral and Generalized Polynomial Chaos Algorithm to Solve Stochastic Optimal Control Problems

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