## A Probabilistic Roadmap Approach for Systems with Closed Kinematic Chains (1999)

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Citations: | 70 - 4 self |

### BibTeX

@MISC{LaValle99aprobabilistic,

author = {Steven M. LaValle and Jeffery H. Yakey and Lydia E. Kavraki},

title = {A Probabilistic Roadmap Approach for Systems with Closed Kinematic Chains},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a randomized approach to path planning for articulated robots that have closed kinematic chains. The approach extends the probabilistic roadmap technique which has previously been applied to rigid and elastic objects, and articulated robots without closed chains. Our work provides a framework for path planning problems that must satisfy closure constraints in addition to standard collision constraints. This expands the power of the probabilistic roadmap technique to include a variety of problems such as manipulation planning using two open-chain manipulators that cooperatively grasp an object, forming a system with a closed chain, and planning for reconfigurable robots where the robot links may be rearranged in a loop to ease manipulation or locomotion. We generate the vertices in our probabilistic roadmap by sampling random con gurations that ignore kinematic closure, and by performing randomized gradient descent to force satisfaction of the closure constraints. We generate...

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Citation Context ... can be applied to our problem with minor adaptation. The major difficulty is that existing methods are designed for planning in a configuration space, which is assumed to be a parameterized manifold =-=[21]-=-. When closed kinematic chains exist, such luxuries disappear because path planning must be performed on a variety. In this case it is less straightforward to generate allowable configurations or loca... |

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Citation Context ...st be performed on a variety. In this case it is less straightforward to generate allowable configurations or local motions, which are needed for successful methods such as the potential field method =-=[5, 8, 18]-=- or probabilistic roadmaps [2, 17]. Our approach is to extend the probabilistic roadmap paradigm to generate a roadmap on a variety instead of a configuration space. This paradigm was chosen because o... |

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Citation Context ... case it is less straightforward to generate allowable configurations or local motions, which are needed for successful methods such as the potential field method [5, 8, 18] or probabilistic roadmaps =-=[2, 17]-=-. Our approach is to extend the probabilistic roadmap paradigm to generate a roadmap on a variety instead of a configuration space. This paradigm was chosen because of its recent success, its simplici... |

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Citation Context ... can generally be formulated as an algebraic variety (the zeros of the system of implicit polynomial equations). Many techniques exist that exactly and completely determine the structure of a variety =-=[3, 12, 7]-=-. Although there have been many interesting recent advances in computational algebraic geometry [22, 6], the complexity of these algorithms still limits their use to simpler problems. This observation... |

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Citation Context ...st be performed on a variety. In this case it is less straightforward to generate allowable configurations or local motions, which are needed for successful methods such as the potential field method =-=[5, 8, 18]-=- or probabilistic roadmaps [2, 17]. Our approach is to extend the probabilistic roadmap paradigm to generate a roadmap on a variety instead of a configuration space. This paradigm was chosen because o... |

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A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
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Citation Context ...orrespond to edges. Therefore, let GM denote the underlying graph of A/I. Now consider the kinematics of A/[. Using a standard parameterization technique, such as the DenavitHartenburg representation =-=[13, 15]-=-, the configuration of A/[ can be expressed as a vector, q, of real-valued parameters. Letsdenote the configuration space or C-space. Let A/g(q) denote the transformation of A/[ to the configuration g... |

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Citation Context ... case it is less straightforward to generate allowable configurations or local motions, which are needed for successful methods such as the potential field method [5, 8, 18] or probabilistic roadmaps =-=[2, 17]-=-. Our approach is to extend the probabilistic roadmap paradigm to generate a roadmap on a variety instead of a configuration space. This paradigm was chosen because of its recent success, its simplici... |

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Citation Context ...rasp and manipulate an object [19]. It could also correspond to a closed loop that may result from the rearrangement of the links of a reconfigurable robot in order to ease manipulation or locomotion =-=[10, 20, 24]-=-. We are working towards having an efficient planner for systems with closed kinematic chains. Our planner is based on the probabilistic roadmap approach to planning [16]. We construct a graph on the ... |

70 |
Random networks in configuration space for fast path planning
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Citation Context ...ulation or locomotion [lo, 20, 241. We are working towards having an efficient planner for systems with closed kinematic chains. Our planner is based on the probabilistic roadmap approach to planning =-=[16]-=-. We construct a graph on the portion of 0-7803-51 80-0-5/99 $10.00 0 1999 IEEE 1671 Kinematic Chains Lydia E. Kavraki Department of Computer Science Rice University Houston, TX 77005 USA kavraki@cs.r... |

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Citation Context ...rasp and manipulate an object [19]. It could also correspond to a closed loop that may result from the rearrangement of the links of a reconfigurable robot in order to ease manipulation or locomotion =-=[10, 20, 24]-=-. We are working towards having an efficient planner for systems with closed kinematic chains. Our planner is based on the probabilistic roadmap approach to planning [16]. We construct a graph on the ... |

49 | The Self-reconfiguring Robotic Molecule: Design and Control Algorithmsā€¯, Algorithmic Foundations of Robotics
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Citation Context ...rasp and manipulate an object [19]. It could also correspond to a closed loop that may result from the rearrangement of the links of a reconfigurable robot in order to ease manipulation or locomotion =-=[10, 20, 24]-=-. We are working towards having an efficient planner for systems with closed kinematic chains. Our planner is based on the probabilistic roadmap approach to planning [16]. We construct a graph on the ... |

42 | Multi-Arm Manipulation Planning
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Citation Context ...s in a cluttered environment (see Figure 1). This structure could correspond to a single robot, or, for example, to a pair of open-chain manipulators that cooperatively grasp and manipulate an object =-=[19]-=-. It could also correspond to a closed loop that may result from the rearrangement of the links of a reconfigurable robot in order to ease manipulation or locomotion [10, 20, 24]. We are working towar... |

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Geometric reasoning with logic and algebra
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Citation Context ...ns. If GM is a tree, then any configuration q yields an acceptable position and orientation for each of the links if we ignore collision issues and planning for such systems as has been considered in =-=[5, 9, 14, 17]-=-. In this paper, we are primarily concerned with the case in which A/[ contains closed kinematic chains, which implies that GM contains cycles. In this case, there will generally exist configurations ... |

5 | Random networks in con space for fast path planning - Kavraki - 1995 |

4 | Evaluating eciency of self-recon in a class of modular robots - Chirikjian, Pamecha, et al. - 1996 |

3 | Pharmacophoric pattern matching in of threedimensional chemical structures: Comparison of conformational searching algorithms for searching - Clark, Jones, et al. - 1994 |

2 | The self-recon guring robotic molecule: Design and control algorithms. Algorithmic Foundations of Robotics - Kotay, Rus, et al. - 1998 |

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Citation Context ...st be performed on a variety. In this case it is less straightforward to generate allowable configurations or local motions, which are needed for successful methods such as the potential field method =-=[5, 8, 18]-=- or probabilistic roadmaps [2, 17]. Our approach is to extend the probabilistic roadmap paradigm to generate a roadmap on a variety instead of a configuration space. This paradigm was chosen because o... |

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Random Networks in Confguration Space for Fast Path Planning
- Kavraki
- 1994
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Citation Context ...ulation or locomotion [10, 20, 24]. We are working towards having an efficient planner for systems with closed kinematic chains. Our planner is based on the probabilistic roadmap approach to planning =-=[16]-=-. We construct a graph on the portion of the configuration space that satisfies kinematic closure constraints. The vertices of the graph are obtained by Department of Computer Science Rice University ... |

1 | Practical motion planning for many de ees of freedom: A novel approach within sequentif framework - Gupta, Zhu - 1995 |

1 |
A geometricalapproach to planning manipulation tasks
- Alami, Sim'eon, et al.
- 1989
(Show Context)
Citation Context ...chain. Our approach may shed new light to manipulation planning and seed new research in that area. For example, manipulation planning algorithms consider all possible combinations of grasp positions =-=[1]-=-, which can be very large, or first plan for the object and then use inverse kinematics to plan for the robots. In the latter case, regrasping is 1sdone in configurations where the arms can not move a... |

1 |
Computingroadmaps of semi-algebraic sets on a variety
- Basu, Pollack, et al.
- 1998
(Show Context)
Citation Context ...ions). Many techniques exist that exactly and completely determine the structure of a variety [3, 12, 7]. Although there have been many interesting recent advances in computational algebraic geometry =-=[22, 6]-=-, the complexity of these algorithms still limits their use to simpler problems. This observation has also been the basis for the development of randomized path planning techniques for rigid robots or... |

1 |
The Complexity of Robot Motion Planning.MIT
- Canny
- 1988
(Show Context)
Citation Context ... can generally be formulated as an algebraic variety (the zeros of the system of implicit polynomial equations). Many techniques exist that exactly and completely determine the structure of a variety =-=[3, 12, 7]-=-. Although there have been many interesting recent advances in computational algebraic geometry [22, 6], the complexity of these algorithms still limits their use to simpler problems. This observation... |

1 |
Practical motion planning formany degrees of freedom: A novel approach within sequential framework
- Gupta, Zhu
- 1995
(Show Context)
Citation Context ...ns. If GM is a tree, then any configuration q yields an acceptable position and orientation for each of the links if we ignore collision issues and planning for such systems as has been considered in =-=[5, 9, 14, 17]-=-. In this paper, we are primarily concerned with the case in which M contains closed kinematic chains, which implies that GM contains cycles. In this case, there will generally exist configurations th... |

1 |
A kinematic notationfor lower pair mechanisms based on matrices
- Hartenburg, Denavit
- 1955
(Show Context)
Citation Context ...ks correspond to edges. Therefore, let GM denote the underlying graph of M. Now consider the kinematics of M. Using a standard parameterization technique, such as the DenavitHartenburg representation =-=[13, 15]-=-, the configuration of M can be expressed as a vector, q, of real-valued parameters. Let C denote the configuration space or C-space. Let M(q) denote the transformation of M to the configuration given... |

1 |
On multi-arm manipulationplanning
- Koga, Latombe
- 1994
(Show Context)
Citation Context ...s in a cluttered environment (see Figure 1). This structure could correspond to a single robot, or, for example, to a pair of open-chain manipulators that cooperatively grasp and manipulate an object =-=[19]-=-. It could also correspond to a closed loop that may result from the rearrangement of the links of a reconfigurable robot in order to ease manipulation or locomotion [10, 20, 24]. We are working towar... |

1 |
Estimation of planar curves, surfaces, andnonplanar space curves defined by implicit equations with applications to edge and range image segmen-tation
- Taubin
- 1991
(Show Context)
Citation Context ...efined in terms of each fi(q). If the constraints are expressed in polynomial form, the algebraic distance can be minimized, or an approximation to the Euclidean distance in C may easily be minimized =-=[23]-=-. We chose an alternative approach, though, which is to break the kinematic loops and minimize the sum of squares the Euclidean distances of each joint that is not where it should be to satisfy kinema... |

1 | Locomotion with a Unit-Modular Recon Robot - Yim - 1994 |