## Aircraft Trajectory Planning With Collision Avoidance Using Mixed Integer
Linear Programming

### Arthur Richards and Jonathan P. How

Presented at the IEEE 2002 ACC, May 2002, pp.1936-1941.

### This paper describes a method for finding optimal trajectories
for multiple aircraft avoiding collisions. Recent developments in spacecraft
path-planning have shown that trajectory optimization including collision avoidance
can be written as a linear program subject to mixed integer constraints, known
as a *mixed-integer linear program* (MILP). This can be solved using commercial
software written for the operations research community. In this paper, an approximate
model of aircraft dynamics using only linear constraints is developed, enabling
the MILP approach to be applied to aircraft collision avoidance. The formulation
can also be extended to include multiple waypoint path-planning, in which each
vehicle is required to visit a set of points in an order chosen within the optimization.

Download: Paper

Professor Jonathan
P. How

jhow@mit.edu

Arthur Richards

November 24, 2002