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## Real-Time Motion Planning For Agile Autonomous Vehicles (2000)

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Venue: | AIAA JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS |

Citations: | 220 - 16 self |

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(Show Context)
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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(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
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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
- 4Laumond
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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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