### Citations

236 |
Numerical Potential Field Techniques for Robot Path Planning,
- Barraquand, Langlois, et al.
- 1992
(Show Context)
Citation Context ...d and the new cost-to-go map Uk+TD is calculated. Depending on model information available to the guidance layer, an additional term êi can be added to the update rule xi+1 = xi − ∇U(xi) + ei − êi =-=(14)-=- where the estimate êi is derived from a simple update law like êi+1 = êi + γ(xopt,i+1 − xi+1) (15) where γ is a weight used to determine the frequency response of the update and xopt,i+1 is the lo... |

136 | Ordered upwind methods for static Hamilton-Jacobi equations: theory and algorithms,
- Sethian, Vladimirsky
- 2003
(Show Context)
Citation Context ...ance layer, an additional term êi can be added to the update rule xi+1 = xi − ∇U(xi) + ei − êi (14) where the estimate êi is derived from a simple update law like êi+1 = êi + γ(xopt,i+1 − xi+1) =-=(15)-=- where γ is a weight used to determine the frequency response of the update and xopt,i+1 is the location the aircraft would have moved to had the wind field been exact. So far derivation of the intell... |

50 | Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. - Gilmore, Straka, et al. - 2004 |

33 |
An interpolated dynamic navigation function.”
- Philippsen, Siegwart
- 2005
(Show Context)
Citation Context ... it is also advisable to avoid precipitation when possible, a second rain term, βr can be added to the cost function: τ = √ ∆− 〈d · c〉 v2w − c2 + αr + βr (8) βr(x, y, z, t) = krain · rain(x, y, z, t) =-=(9)-=- B. Wavefront Expansion Wavefront expansion is performed using ordered upwind methods to propagate cost-go-to values over the discretized configuration space of the unmanned aircraft. Unlike standard ... |

12 | Adapting the wavefront expansion in presence of strong currents
- Soulignac, Taillibert, et al.
- 2008
(Show Context)
Citation Context ...t Vxj ,xk(xi) be a consistent upwinding approximation when the characteristic xi lies in the simplex xixjxj , which we take here to be Vxj ,xk(xi) = min ζ∈{0,1} (ζ(τij + U(xj)) + (1− ζ)(τik + U(xk))) =-=(11)-=- where τij is the value of the penalty function when moving from xj to xi, e.g. (8). Finally, let Ω be the domain representing the environment, δΩ be the goal region in the environment, and q(xi) be t... |

4 |
The eyewallpenetration reconnaissance observation of Typhoon Longwang
- Lin, Lee
- 2008
(Show Context)
Citation Context ...for safe aircraft flight, rather than a cumulative effect. Given this assumption, the rain can be treated as an obstacle, and a rain term is added to the cost function: τ = √ ∆− 〈d · c〉 v2w − c2 + αr =-=(6)-=-{ αr(x, y, z, t) = 0 : rain(x, y, z, t) ≤ rainmax αr(x, y, z, t) =∞ : rain(x, y, z, t) > rainmax (7) Should the case present itself where it is also advisable to avoid precipitation when possible, a s... |

4 | The Numerical simulations of microburst-producing thunderstorms: Some results from storms observed during the COHMEX experiment - Straka, Anderson - 1993 |

1 |
Use of the Aerosonde Unihabited Aerial Vehicle (UAV
- 4Hipskind, Tyrell, et al.
- 2002
(Show Context)
Citation Context ...stant in time for an altitude of 500 meters. Storm data is given on a 210 by 210 grid with a resolution of 500 meters between grid points in a reference frame that moves with the storm (with velocity =-=[18, 4]-=- m/s). Data includes rain, hail, and three-dimensional wind velocity components (relative to the storm frame of reference). The storm simulation is aligned such that the positive y-axis corresponds to... |

1 |
Fly into typhoon Haiyan with
- 5Lin, Lee
- 2003
(Show Context)
Citation Context ...−(Wx · dx −Wy · dy) + √ ∆ v2w − c2 = √ ∆− 〈d · c〉 v2w − c2 (4) where ∆ = v2w · (d2x + d2y)− (Wx · dy −Wy · dx)2. Considering the case where Va = Vw, the equation can be simplified to: τ = d2 2〈d · c〉 =-=(5)-=- The time τ is only defined when ∆ ≥ 0. The union of the set where τ is undefined, and when τ < 0 identifies infeasible regions of travel. Precipitation can also be accounted for using the cost functi... |

1 |
Planning Algorithms
- 7LaValle
- 2006
(Show Context)
Citation Context ...eated as an obstacle, and a rain term is added to the cost function: τ = √ ∆− 〈d · c〉 v2w − c2 + αr (6){ αr(x, y, z, t) = 0 : rain(x, y, z, t) ≤ rainmax αr(x, y, z, t) =∞ : rain(x, y, z, t) > rainmax =-=(7)-=- Should the case present itself where it is also advisable to avoid precipitation when possible, a second rain term, βr can be added to the cost function: τ = √ ∆− 〈d · c〉 v2w − c2 + αr + βr (8) βr(x,... |

1 |
The Flexible, Extensible and Efficient Toolbox of Level Set Methods
- 8Mitchell
- 2007
(Show Context)
Citation Context ...inmax (7) Should the case present itself where it is also advisable to avoid precipitation when possible, a second rain term, βr can be added to the cost function: τ = √ ∆− 〈d · c〉 v2w − c2 + αr + βr =-=(8)-=- βr(x, y, z, t) = krain · rain(x, y, z, t) (9) B. Wavefront Expansion Wavefront expansion is performed using ordered upwind methods to propagate cost-go-to values over the discretized configuration sp... |

1 |
Collision-free trajectory planning using the distance transforms,” Mechanical Engineering Transactions of the Institution of Engineers
- 12Jarvis
- 1985
(Show Context)
Citation Context ...eld does not change. Given the map, the optimal path to the goal point can be defined by the set of points, xi, i = 1, . . . , n where x0 is the deployment location of the UA and: xi+1 = xi − ∇U(xi) =-=(12)-=- where is the step size. Although knowing the complete optimal trajectory can be beneficial for higher level reasoning, it is not necessary for aircraft guidance. Instead, the aircraft at xi simply ... |

1 | Robots III , edited by W - SPIE - 1988 |