Solving global two-dimensional routing problems using snell's law and a search

Richbourg, Robert; Rowe, Neil C.; Zyda, Michael; McGhee, Robert B.

doi:10.1109/robot.1987.1087800

Cited by 24 publications

(14 citation statements)

References 7 publications

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“…First consider isotropic regions. As we have shown in previous work [12,15,11], optimal paths in such regions must be straight line segments, with turns only possible on the boundaries of such regions such that the turn obeys Snell's Law, with special modifications necessary at boundary vertices. Identical conditions apply to type-I traversal of anisotropic regions, which we will define as traversal at a non-critical nonbraking heading.…”

Section: Isotropic Traversals and Anisotropic Traversals Of Type Imentioning

confidence: 92%

“…To facilitate mathematical analysis, we assume as in the Army Mobility Model [18] and our own earlier work based on it [12,15] http://faculty.nps.edu/ncrowe/elevation2.htm that the terrain is partitioned into polygonal regions within which the coefficient of friction can be assumed constant; any terrain can be sufficiently closely approximated by some such polygons [10]. For overland terrain, often this can be done from map overlays or classification of surface covering in aerial photography.…”

Section: The Physical Model the Basic Energy-cost Modelmentioning

confidence: 99%

“…The A* search is over all window sequences in the same way as [12,15]. For those window sequences that terminate at the goal, we can compute the locally-optimal path, and take the minimum-cost of these as the global optimum.…”

Section: Reducing Path-finding To A* Searchmentioning

confidence: 99%

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Optimal grid-free path planning across arbitrarily contoured terrain with anisotropic friction and gravity effects

Rowe

Ross

1990

IEEE Trans. Robot. Automat.

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Section: Isotropic Traversals and Anisotropic Traversals Of Type Imentioning

confidence: 92%

Section: The Physical Model the Basic Energy-cost Modelmentioning

confidence: 99%

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Optimal grid-free path planning across arbitrarily contoured terrain with anisotropic friction and gravity effects

Rowe

Ross

1990

IEEE Trans. Robot. Automat.

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“…They gave the first (1+ε)-approximation algorithm to compute optimal paths that runs in polynomial time, polynomial in n (the number of vertices of the subdivision) and logarithmic in ε / 1 (where 0 > ε is any given small number). Their algorithm exploits the local optimality property that shortest paths bend according to Snell's law of refraction; this is also exploited in the algorithms of [Rowe and Richbourg, 1990] and [Richbourg et al, 1987]. Recent alternative solution methods for the WRP have been devised based on discretizing links of the subdivision, placing "Steiner points" judiciously, and interconnecting them to form a discretization graph, G(V,E), which can then be searched for a minimumcost path.…”

Section: Related Workmentioning

confidence: 99%

Turn-Constrained Route Planning for Avoiding Hazardous Weather

Krozel

Lee

Mitchell

2006

Air Traffic Control Quarterly

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We investigate the problem of algorithmically synthesizing turn-constrained routes that minimize exposure to hazardous weather. Such a problem is suitable to air traffic management automation and aircraft flight management systems. Our algorithm synthesizes routes that aircraft may follow from a specified start to finish location. Example applications include synthesizing routes (1) from airport metering fix locations to runway final approach fixes, and (2) from sector boundary crossing locations to airport metering fix locations. The algorithm takes into account aircraft dynamics limits on velocity and acceleration, pilot and controller workload considerations (e.g., the number of turn maneuvers), and other constraints (e.g., utilizing arrival vs departure corridors or avoiding special use airspace regions). The solution approach is based on searching in an appropriate discretization of a geometric model of the airspace using a dynamic programming algorithm for optimal paths having a bounded number of turns. Examples are given for Dallas Ft. Worth Airport.

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“…We attribute this to a sensible prioritization -planetary surface exploration has had no immediate need for global navigation, and realistically, the large-scale problem cannot be solved until reliable solutions exist for the local problem. Richbourg et al [20] uses optical analogies to solve high-level path planning through polygonal homogeneous cost fields. Rowe [21] extends that work to include linear features like roads and rivers.…”

Section: Related Workmentioning

confidence: 99%

Global path planning for mars rover exploration

Tompkins

Stentz

Wettergreen

2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720)

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-TEMPEST is a planner for long-range planetary navigation that bridges the gap between path planning and classical planning and scheduling. In addition to planning routes, our approach yields the timing and placement of actions to conserve and restore expendable resources and that abide by operational constraints. TEMPEST calls upon the Incremental Search Engine (ISE) to enable heuristic path planning and efficient re-planning under global constraints, over a four dimensional state space. We describe our approach, then demonstrate how the planner operates in a simulated Mars science traverse. Following a brief summary of TEMPEST results from a recent rover field experiment, we evaluate our research progress and describe our current and future work. INTRODUCTION 1The NASA Mars Technology Program (MTP) [5] currently funds a wide range of technology projects in support of the Mobile Science Laboratory (MSL) mission concept, under investigation for the 2009 launch opportunity [35]. Under this umbrella, the MTP supports a number competitivelyselected robotics research tasks. In contrast with more general research calls, the MTP selects technologies based on specific MSL mission needs, and requires that they meet basic criteria for developmental maturity prior to selection. To ease software evaluation and possible inclusion in future missions, participating teams are expected to integrate their software within a new NASA software architecture, CLARAty (Coupled Layer Architecture for Robotic Autonomy) [34], by the conclusion of the project. Participants in the program include teams at NASA/JPL, NASA Field Centers and universities.As one of the MTP participants, our team is developing software for autonomous global path planning, combining longrange route planning, resource management and enforcement of constraints. Several MSL design features motivate our work. To enable the investigation of specific surface targets, the MSL mission seeks long-range mobility to overcome worst-case landing errors. Furthermore, MSL may involve travel to several distinct sites, interleaving periods of dedicated, localized science data collection with periods of traverse and opportunistic science. To alleviate the power constraints of previous missions, the MSL rover may be powered by RTG (Radioisotope Thermo-electric Generator), and possibly supplemented by solar arrays. However, the power sources may not be sufficient to supply locomotion for long time periods. Batteries will store energy for use in high-power activities. Finally, current plans dictate a primary mission lasting up to 500 sols, entailing daily and seasonal lighting changes. All these factors motivate global path planning.Our work in this area began under, and is supplemented by, other NASA-funded projects, namely the Sun-Synchronous Navigation project [36][37][31] and the Life in the Atacama project [38][32]. In this paper, we describe our progress to date, as a result of all these efforts, but with an emphasis on our work directed towards the MTP. We begin by fu...

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Solving global two-dimensional routing problems using snell's law and a search

Cited by 24 publications

References 7 publications

Optimal grid-free path planning across arbitrarily contoured terrain with anisotropic friction and gravity effects

Optimal grid-free path planning across arbitrarily contoured terrain with anisotropic friction and gravity effects

Turn-Constrained Route Planning for Avoiding Hazardous Weather

Global path planning for mars rover exploration

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