Iterative MILP methods for vehicle control problems

Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this paper, we introduce two iterative MILP algorithms that address this issue. The first is for obstacle avoidance problems, and the second is for minimum time optimal control problems. The algorithms require fewer binary variables than standard MILP methods and on average require much less computational effort.

[1]  E. Campbell,et al.  Establishing Trajectories for Multi-Vehicle Reconnaissance , 2004 .

[2]  Srinivas Akella,et al.  Coordinating the motions of multiple robots with kinodynamic constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[3]  Jonathan P. How,et al.  Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming , 2002 .

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Antonio Bicchi,et al.  Conflict resolution problems for air traffic management systems solved with mixed integer programming , 2002, IEEE Trans. Intell. Transp. Syst..

[6]  Jonathan P. How,et al.  Cooperative path planning for multiple UAVs in dynamic and uncertain environments , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[7]  R. D'Andrea,et al.  Modeling and control of a multi-agent system using mixed integer linear programming , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  R. D'Andrea,et al.  Low observability path planning for an unmanned air vehicle using mixed integer linear programming , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  R. D'Andrea,et al.  A study in cooperative control: the RoboFlag drill , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[10]  Raffaello D'Andrea,et al.  Multi-Vehicle Cooperative Control Using Mixed Integer Linear Programming , 2005, ArXiv.

[11]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[12]  Seth Hutchinson,et al.  Coordinating the motions of multiple robots with specified trajectories , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[13]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[14]  Heinz Peter Rothwangl.  Numerical synthesis of the time optimal nonlinear state controller via mixed integer programming , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[15]  Hiroaki Kitano,et al.  RoboCup-2001: The Fifth Robotic Soccer World Championships , 2002, AI Mag..

[16]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[17]  Raffaello D'Andrea,et al.  Near-optimal dynamic trajectory generation and control of an omnidirectional vehicle , 2004, Robotics Auton. Syst..

[18]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[19]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[20]  Raffaello D'Andrea,et al.  The Cornell RoboCup Team , 2000, RoboCup.