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A. Richards and J. How, “Aircraft Trajectory Planning with Collision Avoidance Using Mixed Integer Programming,” Proceedings of the IEEE American Control Conference, Anchorage, Alaska, 2002.

has been cited by the following article:

• TITLE: A Measure Theoretical Approach for Path Planning Problem of Nonlinear Control Systems

  AUTHORS: Amin Jajarmi, Hamidreza Ramezanpour, Mohammad Dehghan Nayyeri, Ali Vahidian Kamyad

  KEYWORDS: Path Planning, Optimal Control, Measure Theory, Linear Programming

  JOURNAL NAME: Intelligent Control and Automation, Vol.2 No.2, June 3, 2011

  ABSTRACT: This paper presents a new approach to find an approximate solution for the nonlinear path planning problem. In this approach, first by defining a new formulation in the calculus of variations, an optimal control problem, equivalent to the original problem, is obtained. Then, a metamorphosis is performed in the space of problem by defining an injection from the set of admissible trajectory-control pairs in this space into the space of positive Radon measures. Using properties of Radon measures, the problem is changed to a measure-theo- retical optimization problem. This problem is an infinite dimensional linear programming (LP), which is approximated by a finite dimensional LP. The solution of this LP is used to construct an approximate solution for the original path planning problem. Finally, a numerical example is included to verify the effectiveness of the proposed approach.