scholarly journals Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mohammadreza Radmanesh ◽  
Manish Kumar ◽  
Donald French
Keyword(s):  
Trajectory Planning ◽  
Dynamical Property ◽  
Optimization Methods ◽  
Computational Effort ◽  
Three Dimensions ◽  
Computational Domain ◽  
Uncertain Environments ◽  
Partial Differential ◽  
Aerial Vehicle ◽  
Hostile Environments

Abstract This paper proposes a physics-inspired method for unmanned aerial vehicle (UAV) trajectory planning in three dimensions using partial differential equations (PDEs) for application in dynamic hostile environments. The proposed method exploits the dynamical property of fluid flowing through a porous medium. This method evaluates risk to generate porosity values throughout the computational domain. The trajectory that encounters the highest porosity values determines the trajectory from the point of origin to the goal position. The best trajectory is found using the reaction of the fluid in porous media by the way of streamlines obtained by numerically solving the PDEs representing the fluid flow. Constraints due to UAV dynamics, obstacles, and predefined way points are applied to the problem after solving for the best trajectory to find the optimal and feasible trajectory. This method shows near-optimality and much reduced computational effort when compared to the other typical numerical optimization methods.

scholarly journals Analysis of Methods and Control Systems of Unmanned Platforms

2021 ◽  
Vol 51 (4) ◽  
pp. 143-156
Author(s):  
Mirosław Adamski ◽  
Andrzej Żyluk ◽  
Marcin Chodnicki
Keyword(s):  
Control Systems ◽  
Unmanned Aerial Vehicle ◽  
Trajectory Planning ◽  
Three Dimensions ◽  
Control Algorithms ◽  
Aerial Vehicle ◽  
And Control

Abstract The key aspect affecting the safety of routing and the unmanned platform mission execution is the autonomy of control systems. To achieve the mission goal, control algorithms supported by advanced sensors have to estimate the obstacle location. Moreover, it is needed to identify potential obstacles, as well as algorithms for trajectory planning in two or three dimensions space. The use of these algorithms allows to create an intelligent object that performs tasks in difficult conditions in which communication between the platform and the operator is constricted. The article mainly focuses on unmanned aerial vehicle (UAV) control systems.

Optimized artificial potential field algorithm to multi-unmanned aerial vehicle coordinated trajectory planning and collision avoidance in three-dimensional environment

2019 ◽  
Vol 233 (16) ◽  
pp. 6032-6043 ◽  
Author(s):  
Jun Tang ◽  
Jiayi Sun ◽  
Cong Lu ◽  
Songyang Lao
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Collision Avoidance ◽  
Unmanned Aerial Vehicle ◽  
Trajectory Planning ◽  
Potential Field ◽  
Three Dimensional ◽  
Artificial Potential Field ◽  
Aerial Vehicles ◽  
Aerial Vehicle ◽  
Vehicle Trajectory

Multi-unmanned aerial vehicle trajectory planning is one of the most complex global optimum problems in multi-unmanned aerial vehicle coordinated control. Results of recent research works on trajectory planning reveal persisting theoretical and practical problems. To mitigate them, this paper proposes a novel optimized artificial potential field algorithm for multi-unmanned aerial vehicle operations in a three-dimensional dynamic space. For all purposes, this study considers the unmanned aerial vehicles and obstacles as spheres and cylinders with negative electricity, respectively, while the targets are considered spheres with positive electricity. However, the conventional artificial potential field algorithm is restricted to a single unmanned aerial vehicle trajectory planning in two-dimensional space and usually fails to ensure collision avoidance. To deal with this challenge, we propose a method with a distance factor and jump strategy to resolve common problems such as unreachable targets and ensure that the unmanned aerial vehicle does not collide into the obstacles. The method takes companion unmanned aerial vehicles as the dynamic obstacles to realize collaborative trajectory planning. Besides, the method solves jitter problems using the dynamic step adjustment method and climb strategy. It is validated in quantitative test simulation models and reasonable results are generated for a three-dimensional simulated urban environment.

Simulation of Turbulent Flows Using a Finite-Volume Based Lattice Boltzmann Flow Solver

2014 ◽  
Vol 17 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Goktan Guzel ◽  
Ilteris Koc
Keyword(s):  
Fluid Flow ◽  
Turbulent Flows ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Computational Effort ◽  
Computational Domain ◽  
Flow Solver ◽  
Turbulent Fluid Flow ◽  
Finite Volume Approach ◽  
Volume Method

AbstractIn this study, the Lattice Boltzmann Method (LBM) is implemented through a finite-volume approach to perform 2-D, incompressible, and turbulent fluid flow analyses on structured grids. Even though the approach followed in this study necessitates more computational effort compared to the standard LBM (the so called stream and collide scheme), using the finite-volume method, the known limitations of the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy (CFL) number to be one are removed. Moreover, the curved boundaries in the computational domain are handled more accurately with less effort. These improvements pave the way for the possibility of solving fluid flow problems with the LBM using coarser grids that are refined only where it is necessary and the boundary layers might be resolved better.

The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Om Singh ◽  
Shireesh B. Kedare ◽  
Suneet Singh
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Significant Loss ◽  
Computational Effort ◽  
Computational Domain ◽  
Maximum Difference ◽  
Open Cavities ◽  
Shallow Cavities ◽  
Approximate Boundary Conditions ◽  
The Difference

Abstract The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than  106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

A comparison of numerical methods for optimizing even aged stand management

1990 ◽  
Vol 20 (7) ◽  
pp. 961-969 ◽  
Author(s):  
Lauri T. Valsta
Keyword(s):  
Dynamic Programming ◽  
Species Composition ◽  
Random Search ◽  
Optimization Methods ◽  
Global Optimum ◽  
Computational Effort ◽  
Direct Search ◽  
Computational Time ◽  
Discrete State ◽  
Stand Management

A two-species, whole-stand, deterministic growth model was combined with three optimization methods to derive management regimes for species composition, thinnings, and rotation age, with the objective of maximizing soil expectation value. The methods compared were discrete time – discrete state dynamic programming, direct search using the Hooke and Jeeves algorithm, and random search. Optimum solutions for each of the methods varied considerably, required unequal amounts of computational time, and were not equally stable. Dynamic programming located global optimal solutions but did not determine them accurately, owing to discretized state space. Direct search yielded the largest objective function values with comparable computational effort, although the likelihood of finding a global optimum solution was high only for smaller problems with up to two or three thinnings during the rotation. Random search solutions varied considerably with regard to growing stock level and species composition and did not define a consistent management guideline. In general, direct search and dynamic programming appeared to be superior to random search.

HIGH-ORDER GALERKIN APPROXIMATIONS FOR PARAMETRIC SECOND-ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 23 (09) ◽  
pp. 1729-1760 ◽  
Author(s):  
VICTOR NISTOR ◽  
CHRISTOPH SCHWAB
Keyword(s):  
Finite Element ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Regularity Result ◽  
Second Order ◽  
Three Dimensions ◽  
Open Unit ◽  
Partial Differential ◽  
Open Unit Ball ◽  
Galerkin Approximations

Let D ⊂ ℝd, d = 2, 3, be a bounded domain with piecewise smooth boundary, Y = ℓ∞(ℕ) and U = B1(Y), the open unit ball of Y. We consider a parametric family (Py)y∈U of uniformly strongly elliptic, second-order partial differential operators Py on D. Under suitable assumptions on the coefficients, we establish a regularity result for the solution u of the parametric boundary value problem Py u(x, y) = f(x, y), x ∈ D, y ∈ U, with mixed Dirichlet–Neumann boundary conditions on ∂d D and, respectively, on ∂n D. Our regularity and well-posedness results are formulated in a scale of weighted Sobolev spaces [Formula: see text] of Kondrat'ev type. We prove that the (Py)y ∈ U admit a shift theorem that is uniform in the parameter y ∈ U. Specifically, if the coefficients of P satisfy [Formula: see text], y = (yk)k≥1 ∈ U and if the sequences [Formula: see text] are p-summable in k, for 0 < p< 1, then the parametric solution u admits an expansion into tensorized Legendre polynomials Lν(y) such that the corresponding sequence [Formula: see text], where [Formula: see text]. We also show optimal algebraic orders of convergence for the Galerkin approximations uℓ of the solution u using suitable Finite Element spaces in two and three dimensions. Namely, let t = m/d and s = 1/p-1/2, where [Formula: see text], 0 < p < 1. We show that, for each m ∈ ℕ, there exists a sequence {Sℓ}ℓ≥0 of nested, finite-dimensional spaces Sℓ ⊂ L2(U;V) such that the Galerkin projections uℓ ∈ Sℓ of u satisfy ‖u - uℓ‖L2(U;V) ≤ C dim (Sℓ)- min {s, t} ‖f‖Hm-1(D), dim (Sℓ) → ∞. The sequence Sℓ is constructed using a sequence Vμ⊂V of Finite Element spaces in D with graded mesh refinements toward the singularities. Each subspace Sℓ is defined by a finite subset [Formula: see text] of "active polynomial chaos" coefficients uν ∈ V, ν ∈ Λℓ in the Legendre chaos expansion of u which are approximated by vν ∈ Vμ(ℓ, ν), for each ν ∈ Λℓ, with a suitable choice of μ(ℓ, ν).

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