Using MILP for UAVs Trajectory Optimization under Radar Detection Risk

Abstract

This paper presents an approach to trajectories optimization for Unmanned Aerial Vehicle (UAV) in presence of obstacles, waypoints, and threat zones such as radar detection regions, using Mixed Integer Linear Programming (MILP). The main result is the linear approximation of a nonlinear radar detection risk function with integer constraints and indicator 0-1 variables. Several results are presented to show that the approach can yields trajectories depending on the acceptable risk of detection.

UAV Trajectory Planning for Static and Dynamic Environments

“…For each pop-up the system generates at planning-time several feasible evasion manoeuvres, qualified by a set of route parameters (fuel consumption, assumed risk and spent time) used at flight-time as decision variables to optimize the route. The work extends our preliminary results on trajectory generation over static environment (Ruz et al, 2006), taking into account the knowledge about pop-ups in the trajectory design. The route planner that is proposed in this work allows the UAV to make a decision among several alternative routes considering both, current state of the UAV and probabilities of pop-up threats appearance in future time.…”

“…In the arrival constraints, (x f ,y f ,z f ) is the target location, λ t is a binary indicator variable to enable/disable each constraint, and t arrival is the time to be included as a term of the objective function to be minimized (Ruz et al, 2006).…”

Evolutionary path planner for UAVs in realistic environments

“…Finding the optimal solution to the route planning problem is NPcomplete ( [14]) and so the problem has been approached with different heuristics such as A* [17], [15], MILP [10], [6], [11], nonlinear programming [9] and others. The planners based on those techniques deal with a simplified version of the original problem (point-mass dynamics, discretising the solution space, and, in some of them, linearizing the objective function and the constraints) where the addition of new constraints or objective indexes is a difficult task.…”

Path Planning for Single Unmanned Aerial Vehicle by Separately Evolving Waypoints

“…In the literature, UAV path planning problems have attracted a large variety of optimization applications, including A* [10], [11], Mixed-Integer Linear Programming [12], [13], Nonlinear Programming [14], Voronoi Diagram [15], [16] and Evolutionary Algorithms (EAs) [1], [4], [9], [18]- [29], [35]. One of the difficult problems in the field of the UAV path planning is to plan a feasible path in a scenario with obstacles.…”