## Abstract

Inspired by an idea of Rimon and Koditschek [1], we develop a motion planning algorithm for a point robot traveling among moving obstacles in an N-dimensional space. The navigating point must meet a goal point at a fixed time T, while avoiding several translating, nonrotating, nonintersecting obstacles on its way. All obstacles, the goal point, and the navigating point are confined to the interior of a star-shaped set in R^{N} over the time interval [0, T]. Full a priori knowledge of the goal's location and of the obstacle's trajectories is assumed. We observe that the topology of the obstacle-free space is invariant in the time interval [0, T] as long as the obstacles are nonintersecting and as long as they do not cover the goal point at any time during [0, T]. Using this fact we reduce the problem, for any fixed time to ∈ [0, T], to a stationary-obstacle problem, which is then solved using the method of Rimon and Koditschek [1]. The fact that the obstacle-free space is topologically invariant allows a solution to the moving-obstacle problem over [0, T] through a continuous deformation of the stationary-obstacle solution obtained at time t_{0}. We construct a vector field whose flow is in fact one such deformation. We believe that ours is the first global solution to the moving-obstacle path-planning problem which uses vector fields.

Original language | English (US) |
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Pages (from-to) | 320-325 |

Number of pages | 6 |

Journal | IEEE Transactions on Robotics and Automation |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Electrical and Electronic Engineering

## Keywords

- Motion planning
- Moving obstacles
- Vector fields