Implementation and extension of the ladder algorithm

Bañón, José M.

doi:10.1109/robot.1990.126228

Cited by 11 publications

(9 citation statements)

References 9 publications

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“…However, it has more than purely theoretical interest. It may be reasonable to apply to feedback planning for the rod [28] or for polygonal robots translating and rotating in the plane [29]. Additionally, these ideas can be applied to other specialized cell decompositions, or used in conjunction with a precomputed path to provide feedback in a neighborhood of the path.…”

Section: Discussionmentioning

confidence: 99%

Computing Smooth Feedback Plans Over Cylindrical Algebraic Decompositions

Lindemann

LaValle²

2006

Robotics: Science and Systems II

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Abstract-In this paper, we construct smooth feedback plans over cylindrical algebraic decompositions. Given a cylindrical algebraic decomposition on R n , a goal state xg, and a connectivity graph of cells reachable from the goal cell, we construct a vector field that is smooth everywhere except on a set of measure zero and the integral curves of which are smooth (i.e., C ∞ ) and arrive at a neighborhood of the goal state in finite time. We call a vector field with these properties a smooth feedback plan. The smoothness of the integral curves guarantees that they can be followed by a system with finite acceleration inputs:ẍ = u. We accomplish this by defining vector fields for each cylindrical cell and face and smoothly interpolating between them. Schwartz and Sharir showed that cylindrical algebraic decompositions can be used to solve the generalized piano movers' problem, in which multiple (possibly linked) robots described as semi-algebraic sets must travel from their initial to goal configurations without intersecting each other or a set of semi-algebraic obstacles. Since we build a vector field over the decomposition, this implies that we can obtain smooth feedback plans for the generalized piano movers' problem.

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Section: Discussionmentioning

confidence: 99%

Computing Smooth Feedback Plans Over Cylindrical Algebraic Decompositions

Lindemann

LaValle²

2006

Robotics: Science and Systems II

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“…The problem of planning the motion of a fixed-length rod in the plane has been addressed in [31,2]. While this solution is not directly applicable to our surveillance problem, the representation introduced there can be extended to the case of a rod with variable length, and this extended representation provides the basis for the sufficient conditions for escape given in Section 4.…”

Section: The Configuration Space For the Surveillance Problemmentioning

confidence: 99%

“…While this solution is not directly applicable to our surveillance problem, the representation introduced there can be extended to the case of a rod with variable length, and this extended representation provides the basis for the sufficient conditions for escape given in Section 4. In the remainder of this section, we define the configuration space for our problem, briefly review the method of [31,2], and show how this representation can be extended to our surveillance problem.…”

Section: The Configuration Space For the Surveillance Problemmentioning

confidence: 99%

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Surveillance Strategies for a Pursuer with Finite Sensor Range

Murrieta-Cid

Muppirala²,

Sarmiento³

et al. 2007

The International Journal of Robotics Research

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This paper addresses the pursuit-evasion problem of maintaining surveillance by a pursuer of an evader in a world populated by polygonal obstacles. This requires the pursuer to plan collision-free motions that honor distance constraints imposed by sensor capabilities, while avoiding occlusion of the evader by any obstacle. We extend the three-dimensional cellular decomposition of Schwartz and Sharir to represent the four-dimensional configuration space of the pursuer-evader system, and derive necessary conditions for surveillance (equivalently, sufficient conditions for escape) in terms of this new representation. We then give a game theoretic formulation of the problem, and use this formulation to characterize optimal escape trajectories for the evader. We propose a shooting algorithm that finds these trajectories using the minimum principle. Finally, noting the similarities between this surveillance problem and the problem of cooperative manipulation by two robots, we present several cooperation strategies that maximize system performance for cooperative motions.

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“…Implementing even the complete algorithms for motion-planning problems with a small number of dofs is far from trivial. Some complete algorithms were implemented over a decade ago [5,6]. Notice however, that a genuinely complete implementation, namely an implementation that can correctly cope with all instances of the problem, requires the usage of special arithmetic in order to deal with arbitrary input 1 and in particular to handle tight or narrow passages for the robot in the workspace.…”

Section: Complete Solutions: Theory and Practicementioning

confidence: 99%

Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane

Hirsch

Halperin

2004

Springer Tracts in Advanced Robotics

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The basic motion-planning problem is to plan a collision-free motion for objects moving among obstacles between free initial and goal positions, or to determine that no such motion exists. The basic problem as well as numerous variants of it have been intensively studied over the past two decades yielding a wealth of results and techniques, both theoretical and practical. In this paper, we propose a novel approach to motion planning, hybrid motion planning, in which we integrate complete solutions along with Probabilistic Roadmap (PRM) techniques in order to combine their strengths and offset their weaknesses. We incorporate robust tools, that have not been available before, in order to implement the complete solutions. We exemplify our approach in the case of two discs moving among polygonal obstacles in the plane. The planner we present easily solves problems where a narrow passage in the workspace can be arbitrarily small. Our planner is also capable of providing correct nontrivial "no" answers, namely it can, for some queries, detect the situation where no solution exists. We envision our planner not as a total solution but rather as a new tool that cooperates with existing planners. We demonstrate the advantages and shortcomings of our planner with experimental results.

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Implementation and extension of the ladder algorithm

Cited by 11 publications

References 9 publications

Computing Smooth Feedback Plans Over Cylindrical Algebraic Decompositions

Computing Smooth Feedback Plans Over Cylindrical Algebraic Decompositions

Surveillance Strategies for a Pursuer with Finite Sensor Range

Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane

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