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## Iterative MILP methods for vehicle-control problems

Venue: | IEEE Transactions on Robotics |

Citations: | 20 - 0 self |

### Citations

14063 |
Computers and Intractability: A Guide to the Theory of NPCompleteness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ... can solve MILPs efficiently for problems in which the number of binary variables is of reasonable size. However, a major disadvantage of MILP is its computational complexity. Because MILP is NP-hard =-=[12]-=-, computational requirements can grow significantly as the number of binary variables needed to model the problem increases. Motivated to generate efficient MILP problem formulations, we have develope... |

412 | Control of systems integrating logic, dynamics and constraints
- Bemporad, Morari
- 1999
(Show Context)
Citation Context ...(MILP) methods have attracted attention because of their modeling capability and because powerful solvers are available commercially. The use of MILP for modeling and control problems is described in =-=[3]-=-. MILP methods have been used for cooperative reconnaissance [16], air traffic management [17], coordinated robot motion [1], [18], unmanned aerial vehicle (UAV) path planning [5], and cooperative con... |

177 |
Tsitsiklis, Introduction to Linear Optimization
- Bertsimas, N
- 1997
(Show Context)
Citation Context ... cost function to linear form, we introduce auxiliary continuous variables and and the inequality constraints Minimizing , subject to the inequalities and , is equivalent to minimizing (similarly for =-=[4]-=-. Using the auxiliary variables, the cost function can be written as a linear function (8) (9) (10) The resulting optimization problem (minimize (10), subject to (5), (7), (9), and the boundary condit... |

117 |
Aircraft Trajectory Planning With Collision Avoidance Using Mixed Integer Linear
- Richards, How
- 2002
(Show Context)
Citation Context ...ajectory-planning problems with avoidance constraints is described in [19]. Next, we consider the minimum-time trajectory-generation problem using MILP. The MILP approach to this problem presented in =-=[20]-=- and [21] generates an approximate solution. Time is discretized uniformly, and an auxiliary binary variable and a set of inequality constraints are added for each discrete time. This approach gives a... |

115 | Equivalence of hybrid dynamical models,”
- Heemels, Schutter, et al.
- 2001
(Show Context)
Citation Context ...l (MLD) systems, which are governed by a mixture of logical rules (or state machines) and linear dynamical equations. This form of hybrid system is equivalent to piecewise affine systems, as shown in =-=[13]-=-. In this paper, we use an omnidirectional vehicle in an obstacle field, which is an MLD system, to motivate our methods. See [3] to learn how to represent various types of hybrid systems in MLD form.... |

49 |
Cooperative Path Planning for Multiple UAVs in Dynamic and Uncertain Environments. In
- Bellingham, Tillerson, et al.
- 2002
(Show Context)
Citation Context ...P methods have been used for cooperative reconnaissance [16], air traffic management [17], coordinated robot motion [1], [18], unmanned aerial vehicle (UAV) path planning [5], and cooperative control =-=[2]-=-, [9]. Powerful software packages such as CPLEX [14] can solve MILPs efficiently for problems in which the number of binary variables is of reasonable size. However, a major disadvantage of MILP is it... |

45 |
Conflict resolution problems for air traffic management systems solved with mixed integer programming,”IEEE
- Pallottino, Feron, et al.
- 2002
(Show Context)
Citation Context ...rful solvers are available commercially. The use of MILP for modeling and control problems is described in [3]. MILP methods have been used for cooperative reconnaissance [16], air traffic management =-=[17]-=-, coordinated robot motion [1], [18], unmanned aerial vehicle (UAV) path planning [5], and cooperative control [2], [9]. Powerful software packages such as CPLEX [14] can solve MILPs efficiently for p... |

44 | Coordinating the motions of multiple robots with specified trajectories,
- Akella, Hurchinson
- 2002
(Show Context)
Citation Context ...ercially. The use of MILP for modeling and control problems is described in [3]. MILP methods have been used for cooperative reconnaissance [16], air traffic management [17], coordinated robot motion =-=[1]-=-, [18], unmanned aerial vehicle (UAV) path planning [5], and cooperative control [2], [9]. Powerful software packages such as CPLEX [14] can solve MILPs efficiently for problems in which the number of... |

29 | Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle, Robotics and Autonomous Systems 46
- Kalmár-Nagy, D’Andrea, et al.
- 2004
(Show Context)
Citation Context ...is section, we show how to 1552-3098/$20.00 © 2005 IEEEEARL AND D’ANDREA: ITERATIVE MILP METHODS FOR VEHICLE CONTROL PROBLEMS 1159 simplify their nonlinear governing equations using a procedure from =-=[15]-=-. The result is a linear set of governing equations coupled by a nonlinear constraint on the control input. This procedure allows real-time calculation of many near-optimal trajectories, and is a majo... |

16 |
The Cornell Robocup team
- D’Andrea, Kalmár-Nagy, et al.
- 2001
(Show Context)
Citation Context ...e control problems. All files for generating the plots found in this paper are available online [10]. II. VEHICLE DYNAMICS We motivate our methods using the wheeled robots of the Cornell RoboCup Team =-=[6]-=-. In this section, we show how to 1552-3098/$20.00 © 2005 IEEEEARL AND D’ANDREA: ITERATIVE MILP METHODS FOR VEHICLE CONTROL PROBLEMS 1159 simplify their nonlinear governing equations using a procedur... |

15 |
E.: Spacecraft Trajectory Planning with Avoidance Constraints Using Mixed-Integer Linear Programming
- SCHOUWENAARS
(Show Context)
Citation Context ...te efficient MILP problem formulations, we have developed several iterative techniques that require fewer binary variables than standard MILP methods. The MILP obstacle-avoidance methods from [9] and =-=[19]-=- specify a uniformly distributed set of discrete times at which obstacle avoidance is enforced. We call this approach uniform gridding. In this approach, there is no avoidance guarantee between time s... |

11 |
Low observability path planning for an unmanned air vehicle using mixed integer linear programming
- Chaudhry, Misovec, et al.
- 2004
(Show Context)
Citation Context ...lems is described in [3]. MILP methods have been used for cooperative reconnaissance [16], air traffic management [17], coordinated robot motion [1], [18], unmanned aerial vehicle (UAV) path planning =-=[5]-=-, and cooperative control [2], [9]. Powerful software packages such as CPLEX [14] can solve MILPs efficiently for problems in which the number of binary variables is of reasonable size. However, a maj... |

10 |
AMPL–A Modeling Language for Mathematical Programming . The Scientific
- Fourer, Gay, et al.
- 1993
(Show Context)
Citation Context ...by solving randomly generated problem instances. Each instance is generated by randomly picking parameters from a uniform distribution over the intervals defined below. Each MILP is solved using AMPL =-=[11]-=- and CPLEX [14] on a PC with Intel PIII 550 MHz processor, 1024 KB cache, 3.8 GB RAM, and Red Hat Linux. For comparison, we solve the same instances using uniform gridding with sample time . This samp... |

9 |
Multi-vehicle cooperative control using mixed integer linear programming. Preprint available at http://arxiv.org/abs/cs.RO/0501092
- Earl, D’Andrea
(Show Context)
Citation Context ...ng equations are given by (5) where , , , and . The coefficients and are functions of , because we have allowed for nonuniform time discretizations. They can be calculated explicitly in the usual way =-=[7]-=-. Because there will be several different time discretizations used in this paper, we use subscripts to differentiate them. In this section, we use the subscript to denote variables associated with th... |

7 | Coordinating the Motions of Multiple Robots with Kinodynamic Constraints.
- Peng, Akella
- 2003
(Show Context)
Citation Context ...lly. The use of MILP for modeling and control problems is described in [3]. MILP methods have been used for cooperative reconnaissance [16], air traffic management [17], coordinated robot motion [1], =-=[18]-=-, unmanned aerial vehicle (UAV) path planning [5], and cooperative control [2], [9]. Powerful software packages such as CPLEX [14] can solve MILPs efficiently for problems in which the number of binar... |

6 |
Numerical Synthesis of the Time Optimal Nonlinear State Controller via Mixed Integer Programming,” ACC
- Rothwangl
- 2001
(Show Context)
Citation Context ...planning problems with avoidance constraints is described in [19]. Next, we consider the minimum-time trajectory-generation problem using MILP. The MILP approach to this problem presented in [20] and =-=[21]-=- generates an approximate solution. Time is discretized uniformly, and an auxiliary binary variable and a set of inequality constraints are added for each discrete time. This approach gives an estimat... |

5 |
Establishing optimal trajectories for multi-vehicle reconnaissance
- Ousingsawat, Campbell
- 2004
(Show Context)
Citation Context ...g capability and because powerful solvers are available commercially. The use of MILP for modeling and control problems is described in [3]. MILP methods have been used for cooperative reconnaissance =-=[16]-=-, air traffic management [17], coordinated robot motion [1], [18], unmanned aerial vehicle (UAV) path planning [5], and cooperative control [2], [9]. Powerful software packages such as CPLEX [14] can ... |