Tham khảo tài liệu 'innovations in intelligent machines 1 - javaan singh chahl et al (eds) part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | UAV Path Planning Using Evolutionary Algorithms 91 points located inside the solid boundary consequently non-feasible curves with fewer points inside the solid boundary show better fitness than curves with more points inside the solid boundary. Term f2 is the length of the curve non-dimensional with the distance between the starting and destination points used to provide shorter paths. Term f3 is designed to provide flight paths with a safety distance from solid boundaries nline nground f3 E E 1 di j dsafe 2 9 i 1 j 1 where nline is the number of discrete curve points nground is the number of discrete mesh points of the solid boundary di j is the distance between the corresponding nodes and curve points while dsafe is a safety distance from the solid boundary. Term f4 is designed to provide curves with a prescribed minimum curvature radius 23 . Weights Wi are experimentally determined using as criterion the almost uniform effect of the last three terms in the objective function. Term W1f1 has a dominant role in Eq. 8 providing feasible curves in few generations since path feasibility is the main concern. The minimization of Eq. 8 through the EA procedure results in a set of B-Spline control points which actually represent the desired path. Initially the starting and ending path-line points are determined along with the direction of flight. The limits of the physical space where the vehicle is allowed to fly upper and lower limits of their Cartesian coordinates are also determined along with the ground surface. The determined initial flight direction is used to compute the third fixed point close to the starting one its position is along the flight direction and at a pre-fixed distance from the starting point. The EA randomly produces a number of chromosomes to form the initial population. Each chromosome contains the physical coordinates of the free-to-move B-Spline control points. Using Eqs. 1 to 6 with a constant step of parameter u a B-Spline curve is calculated
