Path Planning of Unmanned Aerial Vehicles using B-Splines and Particle Swarm Optimization

Abstract

Military operations are turning to more complex and advanced automation technologies for minimum risk and maximum efficiency. A critical piece to this strategy is unmanned aerial vehicles. Unmanned aerial vehicles require the intelligence to safely maneuver along a path to an intended target and avoiding obstacles such as other aircrafts or enemy threats. This paper presents a unique three-dimensional path planning problem formulation and solution approach using particle swarm optimization. The problem formulation was designed with three objectives: 1) minimize risk owing to enemy threats, 2) minimize fuel consumption incurred by deviating from the original path, and 3) fly over defined reconnaissance targets. The initial design point is defined as the original path of the unmanned aerial vehicles. Using particle swarm optimization, alternate paths are generated using B-spline curves, optimized based on the three defined objectives. The resulting paths can be optimized with a preference toward maximum safety, minimum fuel consumption, or target reconnaissance. This method has been implemented in a virtual environment where the generated alternate paths can be visualized interactively to better facilitate the decision-making process. The problem formulation and solution implementation is described along with the results from several simulated scenarios demonstrating the effectiveness of the method. Nomenclature C total cost function for a path C T , C L , C R threat, fuel, and reconnaissance components cost for a path c 1 , c 2 first and second confidence parameters for PSO K T , K L , K R weighting factors for threat, fuel, and reconnaissance components cost L length of path M number of control points for B-spline curve N number of line segments that define the B-spline curve N(u) bernstein basis function for B-spline curve p • u parametric equation for B-spline curve u set of line segments for B-spline curve V velocity vector for particle swarm optimization (PSO) w inertia weight for particle swarm optimization X i ith design variable in an optimization objective function in PSO x knot vector for B-spline curve Z T , Z R threat zone and reconnaissance zone λ w decay factor for inertia weight for PSO

Path Planning of an Autonomous Mobile Multi-Sensor Platform in a 3d Environment Using Newtonian Imperialist Competitive Optimization Method

“…In related research, Bezier curve technique is used for paths (Foo et al, 2009). For computing smooth, dynamically feasible trajectories for UAVs, we used Bezier curves.…”

“…Zhang et al (2006) used a algorithm based on Voronoi and B-spline. Genetic algorithm (GA) (Ruan et al 2008), ant colony optimization (ACO) (Wang et al 2008), and particle swarm optimization (PSO) (Foo et al 2009) were applied for solving UAV-PP problem.…”

Collision-free Multiple Unmanned Combat Aerial Vehicles Cooperative Trajectory Planning for Time-critical Missions using Differential Flatness Approach

“…The original state x and control u can be recovered from the flat outputs and their derivatives as follows 13 ( , ), ( ), ( ) ′ ξ = = ϕ ξ = α ξ z z x u (27) According to the kinematics equations in Eqn (14), the remaining three states using the flatness outputs in virtual time domain can be easily described as below …”

“…To generate feasible trajectories in a finite parameter space, flatness outputs are parameterized in terms of B-spline curves, which have been used to represent the trajectory of UCAV to minimize computation loads and successfully applied to path/ trajectory planning 14 . Without loss of generality, to decrease the computational time, the 3-degree B-spline curves are chosen to represent the trajectory, whose order equals to 4.…”

Particle Swarm Optimization of Non Uniform Rational B-Splines for Robot Manipulators Path Planning

“…It depends on complex mathematical model, and suffers from common drawbacks such as the limitation to simple two-dimension space, local minima, incompleteness and high computational time, produces long and rough paths resulting from a compilation of straight line which cannot be executed by the robot. On the other hand, the meta-heuristic class that group neural network [5,6], fuzzy logic [7], evolutionary algorithms [8] (i.e., genetic algorithm, genetic programming, evolutionary programming and evolution strategy), ant colony [9] and particle swarm [10][11][12][13][14] emerge to overcome the shortcomings of the conventional class. These algorithms are generally population based that make a multi exploring search; deals with the problem of local minima and the high class of configuration space; do not call for gradient, high order derivatives or initial estimation of solution.…”