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## Real-time motion planning for agile autonomous vehicles, (2002)

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Venue: | AIAA Journal of Guidance and Control |

Citations: | 225 - 16 self |

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Citation Context ...ditions are such that 10 ¸ 0, then U D¡umax , and U D umax otherwise. The time length of the twobang-bang segments can be determined as follows: t1 D t2 ¡ C=U t2 D log £ 1C p 1¡ exp.C=U /.1¡ v0=U / ¤ =-=(8)-=- with C D x0 C v0¡ x f . 126 FRAZZOLI, DAHLEH, AND FERON The policy used to control the vehicle described by Eqs. (5) is then de ned as follows: Considering the two degrees of freedom x1 and x2 , t... |

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Motion Planning: A Journey of Robots, Molecules,
- 1Latombe
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(Show Context)
Citation Context ...entation via Ordinary Differential Equations The usual representation of the dynamics of an autonomous vehicle or robot is a set of ordinary differential equations (ODEs) of the form dx dt D f .x; u/ =-=(1)-=- where x 2X is the state, belonging to a n-dimensional manifold X (the state space), and u is the control input, taking values in the set U µRm . The preceding formulation can include both nonholonomi... |

1 |
Robot Motion Planning,
- 2Latombe
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(Show Context)
Citation Context ...ontrol input, taking values in the set U µRm . The preceding formulation can include both nonholonomic and dynamic constraints.38 In some cases additional inequality constraints of the form F .x/ · 0 =-=(2)-=- must be added on the state variables to ensure safe operation of the system (e.g., ight envelope protection). In Eq. (2) F.x/ can represent a vector of constraints, and the inequality must be under... |

1 |
ed.),RobotMotion Planning andControl
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(Show Context)
Citation Context ...s are present, andwe assume that themotion of the obstacles (or conservative estimates thereof) is known in advance. In this case obstacle avoidance constraints can be written a priori as G.x; t/ · 0 =-=(4)-=- where G.x; t/ can be a vector of constraints and the inequality must be understood component-wise. Because the environment is time-varying, collisions must be checked on (state, time) pairs .x; t/ 2X... |

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(Show Context)
Citation Context ...0 simulation runs for each example. A. Ground Robot In this sectionwe are interested inminimum timemotion planning for a planar system with (scaled) equations of motion Rx1 C Px1 D u1; Rx2 C Px2 D u2 =-=(5)-=- The magnitude of each control u1 and u2 is assumed to be bounded by umax. Although this system model is quite simple, it is a good representation of the ground robots used by the Cornell University t... |

1 |
AnAlgorithm for PlanningCollisionFree Paths Among Polyhedral Obstacles
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(Show Context)
Citation Context ...igin to destination for each of the degrees of freedom (assuming a general maximum control intensity umax) is a bang-bang control law24 given by u.t/ D U for 0 < t < t1 u.t/ D ¡U for t1 < t < t1 C t2 =-=(6)-=- The sign of the initial control value U can be determined through the switching function: 10 :D » x0 ¡ x f C v0 ¡ umax log.1C v0=umax/ for v0 ¸ 0 x0 ¡ x f C v0 C umax log.1¡ v0=umax/ for v0 < 0 (7) I... |

1 |
Algorithms in Combinatorial Geometry,
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(Show Context)
Citation Context ...2 (6) The sign of the initial control value U can be determined through the switching function: 10 :D » x0 ¡ x f C v0 ¡ umax log.1C v0=umax/ for v0 ¸ 0 x0 ¡ x f C v0 C umax log.1¡ v0=umax/ for v0 < 0 =-=(7)-=- If the initial conditions are such that 10 ¸ 0, then U D¡umax , and U D umax otherwise. The time length of the twobang-bang segments can be determined as follows: t1 D t2 ¡ C=U t2 D log £ 1C p 1¡ exp... |

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An AlgorithmforPlanningCollisionFree Paths Among Polyhedral Obstacles,”
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(Show Context)
Citation Context ...he ground robots used by the Cornell University team to win the RoboCup-2000 contest.61;62 The following control law is adapted from the same references. 1. Minimum-Time, Minimum-Energy Control Law For any one axis let the initial position and velocity be x0 and v0; the nal (equilibrium)conditionsare characterizedby a desired nal position x f and zero velocity. The minimum time maneuver from origin to destination for each of the degrees of freedom (assuming a general maximum control intensity umax) is a bang-bang control law24 given by u.t/ D U for 0 < t < t1 u.t/ D ¡U for t1 < t < t1 C t2 (6) The sign of the initial control value U can be determined through the switching function: 10 :D » x0 ¡ x f C v0 ¡ umax log.1 C v0=umax/ for v0 ¸ 0 x0 ¡ x f C v0 C umax log.1 ¡ v0=umax/ for v0 < 0 (7) If the initial conditions are such that 10 ¸ 0, then U D ¡umax , and U D umax otherwise. The time lengthof the two bang-bangsegmentscanbedetermined as follows: t1 D t2 ¡ C=U t2 D log £ 1 C p 1 ¡ exp.C=U /.1 ¡ v0=U / ¤ (8) with C D x0 C v0 ¡ x f . 126 FRAZZOLI, DAHLEH, AND FERON The policy used to control the vehicle described by Eqs. (5) is then de ned as follows: Considering the two degrees o... |

1 | The Complexity of Robot Motion Planning: ACM Doctoral Dissertation Award, Massachusetts Inst. - 16Canny - 1988 |

1 | Trajectory Planningof Differentially Flat Systems with Dynamics and - 19Faiz, Agrawal, et al. - 2001 |

1 | Mathematical De nition of Helicopter - 48Thomson, Bradley - 1997 |

1 | Autonomous Maneuver Tracking for - 49Boyle, Chamitoff - 1999 |