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## Robot Motion Planning: A Distributed Representation Approach (1991)

Citations: | 402 - 26 self |

### Citations

5126 | Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images - Geman, Geman - 1984 |

2506 |
Robot Motion Planning
- Latombe
- 1991
(Show Context)
Citation Context ...ows us to extend the planner and solve path-planning problems with robots having many DOFs. 2. Relation to Other Work Much research has been devoted to robot motion planning during the past 10 years (=-=Latombe 1990-=-). Most of this research has focused on path planning (i.e., the geometric problem of finding a collisionfree path between two given configurations of a robot). Today the mathematic and computational ... |

1626 |
Image Analysis and Mathematical Morphology.
- Serra
- 1982
(Show Context)
Citation Context ...bset 9’ of ~ of co-dimension 1. We call this subset the work space skeleton. In two dimensions, it is a network of one-dimensional curves similar to the skeleton widely used in mathematic morphology (=-=Serra 1982-=-) and to the generalized Voronoi diagram (Lee and Drysdale 1981). Second, we compute the potential functions Vpi using both the d, map and the skeleton ~. The first step is detailed later in this sect... |

1345 | Real-time obstacle avoidance for manipulators and mobile robots.
- Khatib
- 1986
(Show Context)
Citation Context ... leading the search to dead-ends from which it is difficult to escape. For example, a widely used heuristics consists of guiding the robot along the negated gradient of an artificial potential field (=-=Khatib 1986-=-). However, this technique may get stuck at local minima of the potential and provides no systematic way to escape these minima. The problem of defining an analytic &dquo;navigation function&dquo; (i.... |

888 |
Data Structures and Algorithms.
- Aho, Ullman, et al.
- 1983
(Show Context)
Citation Context ... Q is stored in a balanced tree sorted according to d I so that each insertion of a new point and extraction of a point at maximum distance from the obstacles takes logarithmic time in the size of Q (=-=Aho et al. 1983-=-). At the end of the second step, all the points x E 9, connected to x,,,,, in 9, have a label l(x). 3. The third step is a wavefront expansion starting from the subset S of 3p labeled at the previous... |

679 |
Principles of Artificial Intelligence,
- Nilsson
- 1980
(Show Context)
Citation Context ...ccess as soon as it has generated a path. It terminates with failure if, after having considered the finest bitmap, it still has not generated a path. At each level, BFP performs a best-first search (=-=Nilsson 1980-=-) of the collision-free subset ~f,-ee of the configuration space grid using the potential U defined in formula (1) as the heuristic function. If r is the resolution of the work space bitmap, R; = r - ... |

597 |
The Complexity of Robot Motion Planning.
- Canny
- 2006
(Show Context)
Citation Context ... given configurations of a robot). Today the mathematic and computational structures of the general problem (when stated in algebraic terms) are reasonably well understood (Schwartz and Sharir 1983b; =-=Canny 1988-=-). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6rez 1987; Faver... |

501 |
A thermodynamical approach to the traveling salesman problem.
- Cerny
- 1985
(Show Context)
Citation Context ...example 1). function). In fact, similar randomized techniques (e.g., &dquo;simulated annealing&dquo;) have proven to be useful for solving other NP-hard problems-e.g., the traveling salesman problem (=-=Cerny 1985-=-) and VLSI placement and routing (Kirkpatrick et al. 1983; Sechen 1988). In these problems the very large search space is associated with a large number of &dquo;good&dquo; suboptimal solutions. Fig. ... |

289 |
Complexity of the mover’s problem and generalizations.
- Reif
- 1979
(Show Context)
Citation Context ...016ijr.sagepub.comDownloaded froms631 interchange their positions in a work space made of narrow corridors. We successfully run our planner on several examples of this kind. Since Reif’s early paper (=-=Reif 1979-=-), the computational complexity of path planning has been analyzed by many authors when the problem is stated in semi-algebraic form (Schwartz and Sharir 1988). The bitmap representations used in our ... |

228 | On the “piano movers” problem II: General techniques for computing topological properties of real algebraic manifolds
- Schwartz, Sharir
- 1983
(Show Context)
Citation Context ...lisionfree path between two given configurations of a robot). Today the mathematic and computational structures of the general problem (when stated in algebraic terms) are reasonably well understood (=-=Schwartz and Sharir 1983-=-b; Canny 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6re... |

220 | On multiple moving objects,” - Erdmann, Lozano-Perez - 1986 |

174 |
Toward efficient trajectory planning: The pathvelocity decomposition,
- Kant, Zucker
- 1986
(Show Context)
Citation Context ... able to solve. Nevertheless, the approach described later derives from this earlier work. The problem of generating paths for multiple robots has attracted some attention (Schwartz and Sharir 1983c; =-=Kant and Zucker 1986-=-; Erdmann and Lozano-P6rez 1986; O’Donnell and Lozano-P6rez 1989). Implemented systems rely on a simple paradigm with multiple variants-e.g., &dquo;velocity tuning&dquo; and &dquo;prioritizing&dquo;-w... |

143 | A subdivision algorithm in configuration space for findpath with rotation,” - Brooks, Lozano-Perez - 1985 |

124 | Exact robot navigation by means of potential functions: some topological considerations”, - Koditschek - 1987 |

96 |
On the piano movers problem: I. the case of a two-dimensional rigid polygonal body moving amidst polygonal barriers.
- Schwartz, Sharir
- 1983
(Show Context)
Citation Context ...lisionfree path between two given configurations of a robot). Today the mathematic and computational structures of the general problem (when stated in algebraic terms) are reasonably well understood (=-=Schwartz and Sharir 1983-=-b; Canny 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6re... |

92 |
VLSI Placement and Global Routing Using Simulated Annealing.
- Sechen
- 1988
(Show Context)
Citation Context ...&dquo;simulated annealing&dquo;) have proven to be useful for solving other NP-hard problems-e.g., the traveling salesman problem (Cerny 1985) and VLSI placement and routing (Kirkpatrick et al. 1983; =-=Sechen 1988-=-). In these problems the very large search space is associated with a large number of &dquo;good&dquo; suboptimal solutions. Fig. 20. Coordinated path for the corridor problem (example 2).sat PENNSYLV... |

89 | On nonholonomic mobile robots and optimal maneuvering,” in - Barraquand, Latombe - 1989 |

84 | Stochastic Stereo Matching over Scale”, - Barnard - 1985 |

77 |
Optimization by simulated annealing” Science 220:671–680,
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...omized techniques (e.g., &dquo;simulated annealing&dquo;) have proven to be useful for solving other NP-hard problems-e.g., the traveling salesman problem (Cerny 1985) and VLSI placement and routing (=-=Kirkpatrick et al. 1983-=-; Sechen 1988). In these problems the very large search space is associated with a large number of &dquo;good&dquo; suboptimal solutions. Fig. 20. Coordinated path for the corridor problem (example 2)... |

76 |
Generalization of voronoi diagrams in the plane.
- Lee, Drysdale
- 1981
(Show Context)
Citation Context ...the work space skeleton. In two dimensions, it is a network of one-dimensional curves similar to the skeleton widely used in mathematic morphology (Serra 1982) and to the generalized Voronoi diagram (=-=Lee and Drysdale 1981-=-). Second, we compute the potential functions Vpi using both the d, map and the skeleton ~. The first step is detailed later in this section. The second is described in the next subsection. The distan... |

76 | On the piano movers’ problem III: Coordinating the motion of several independent bodies: The special case of circular bodies moving amidst polygonal obstacles.
- Schwartz, Sharir
- 1983
(Show Context)
Citation Context ...lisionfree path between two given configurations of a robot). Today the mathematic and computational structures of the general problem (when stated in algebraic terms) are reasonably well understood (=-=Schwartz and Sharir 1983-=-b; Canny 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6re... |

63 |
A local based approach for path planning of manipulators with high number of degrees of freedom”,
- Faverjon, Tournassoud
- 1987
(Show Context)
Citation Context ... 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6rez 1987; =-=Faverjon and Tournassoud 1987-=-; Barraquand et al. 1989; Zhu and Latombe 1989). One of the most widely studied path-planning approaches is the &dquo;cell decomposition&dquo; approach (Schwartz and Sharir 1983a; Brooks and LozanoPdr... |

63 |
Diffusions for global optimization,
- GEMAN, HWANG
- 1986
(Show Context)
Citation Context ... say that the algorithm is probabilistically resolution complete. However, this convergence-in-distribution property, which is well known for the so-called &dquo;simulated annealing&dquo; algorithms (=-=Geman and Hwang 1986-=-), is a very weak one. Indeed, the totally uninformed algorithm that executes a Brownian motion from the initial configuration qini, and terminates when it enters a small neighborhood of the goal conf... |

49 |
New Heuristic Algorithms for Efficient Hierarchical Path Planning”,
- Zhu, Latombe
- 1991
(Show Context)
Citation Context ...lemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6rez 1987; Faverjon and Tournassoud 1987; Barraquand et al. 1989; =-=Zhu and Latombe 1989-=-). One of the most widely studied path-planning approaches is the &dquo;cell decomposition&dquo; approach (Schwartz and Sharir 1983a; Brooks and LozanoPdrez 1983). It consists of first decomposing (ex... |

48 | A survey of motion planning and related geometric algorithms.
- Schwartz, Sharir
- 1988
(Show Context)
Citation Context ...several examples of this kind. Since Reif’s early paper (Reif 1979), the computational complexity of path planning has been analyzed by many authors when the problem is stated in semi-algebraic form (=-=Schwartz and Sharir 1988-=-). The bitmap representations used in our planner may open new perspectives on some computational complexity aspects. The worst-case complexity of our planner is still exponential in the number of DOF... |

46 | A geometrical approach to planning manipulation tasks. the case of discrete placements and grasps,” in ISRR, - Alami, Simeon, et al. - 1990 |

43 | Obstacle Avoidance Using an Octree in the Configuration Space of a Manipulator - Faverjon - 1984 |

41 | Small Random Perturbations of Dynamical Systems with Reflecting Boundary. - Anderson, Orey - 1976 |

37 |
Robot motion planning with many degrees of freedom and dynamic constraints
- Baxraquand, Latombe
- 1989
(Show Context)
Citation Context ...algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; Faverjon 1986; Lozano-P6rez 1987; Faverjon and Tournassoud 1987; =-=Barraquand et al. 1989-=-; Zhu and Latombe 1989). One of the most widely studied path-planning approaches is the &dquo;cell decomposition&dquo; approach (Schwartz and Sharir 1983a; Brooks and LozanoPdrez 1983). It consists of... |

35 | Planning, geometry, and complexity of robot motion - Schwartz, Sharir, et al. - 1987 |

33 |
Motion Planning with Six Degrees of Freedom,''
- Donald
- 1984
(Show Context)
Citation Context ...ng the &dquo;global&dquo; topology of the robot’s free space, &dquo;local&dquo; methods to path planning have been developed for handling more DOFs, and some successful systems have been implemented (=-=Donald 1984-=-; Faverjon and Tournassoud 1987). A local pathplanning method consists of placing a grid (at some resolution) over the robot configuration space and searching this grid. Heuristics computed from parti... |

26 | Spatial planning: A configuration space approach - Lozano-Pé, T - 1983 |

9 | Controllability of mobile robots with kinematic constraints - Barraquand, Latombe - 1990 |

8 |
An Adaptative Collision-Free Trajectory Planner
- Laugier, Germain
- 1985
(Show Context)
Citation Context ...reasonably well understood (Schwartz and Sharir 1983b; Canny 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; =-=Laugier and Germain 1985-=-; Faverjon 1986; Lozano-P6rez 1987; Faverjon and Tournassoud 1987; Barraquand et al. 1989; Zhu and Latombe 1989). One of the most widely studied path-planning approaches is the &dquo;cell decompositio... |

2 | Markovian random fields in computer vision: Applications to seismic data understanding - Barraquand - 1988 |

1 |
San Francisco). Object level programming of industrial robots
- Faverjon
- 1986
(Show Context)
Citation Context ... (Schwartz and Sharir 1983b; Canny 1988). In addition, practical algorithms have been implemented in more or less specific cases (Brooks and LozanoP6rez 1983; Gouz~nes 1984; Laugier and Germain 1985; =-=Faverjon 1986-=-; Lozano-P6rez 1987; Faverjon and Tournassoud 1987; Barraquand et al. 1989; Zhu and Latombe 1989). One of the most widely studied path-planning approaches is the &dquo;cell decomposition&dquo; approac... |

1 | Strategies for solving collision-free trajectories problems for mobile and manipulator - Gouzè, L - 1984 |

1 | A simple motion-planning algoat PENNSYLVANIA STATE UNIV on May 9, 2016ijr.sagepub.comDownloaded from rithm for general robot manipulators - Lozano-Pé, T - 1987 |

1 | Los Angeles). Algorithmic issues of sensor-based robot motion planning - Lumelsky - 1987 |

1 | Run-time statistical analysis of a robot motion planning algorithm. Internal technical note. Robotics - Mé, C, et al. - 1990 |

1 | Scottsdale, AZ). Deadlock-free and collision-free coordination of two robot manipulators - O’Donnell, Lozano-Pé, et al. - 1989 |

1 | Retraction: A new approach to motion planning - Ó, nlaing, et al. - 1983 |

1 |
Scottsdale, AZ). The construction of analytic diffeomorphisms for exact robot navigation on star worlds
- Rimon, Koditschek
- 1989
(Show Context)
Citation Context ...een investigated with only limited success so far. Solutions have been proposed only in Euclidean configuration spaces when all the configuration space obstacles are spherical or star-shaped objects (=-=Rimon and Koditschek 1989-=-). Furthermore, if such a navigation function could be defined in the general case, its computation would probably be expensive and would constitute a precomputation step before search, similar in dra... |

1 | A simple motion-planning algoDownloaded from ijr.sagepub.com by Matthew Mason on October 9, 2012 for general robot manipulators - Lozano-Pé, T - 1987 |