Simulation and Experimental Works of Quadcopter Model for Simple Maneuver

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1 Siulation and xperiental Works of Quadcopter Model for Siple Maneuver Rafiuddin Sya Mechanical ngineering Departent, Hasnuddin University, Jl. P. Keerdekaan K Makassar - Indonesia (corresponding author phone: ; e-ail: Abstract This study ais to create a siulated and experiental of aircraft oveents for ultirotor quadcopter. The research ethod is theoretical and experiental ethods. For theoretical ethod consists of calculating the dynaics and kineatics. While the experiental ethod consists of the aircraft testing and processing of GPS data recorded aircraft. The results showed that the acceleration acting on the aircraft is large enough that x =.75 /s, y =.8 /s =.67 danz / s, () the value of the axiu error between the theoretical and the actual oveent is ex =.68 ; ey and ez =.5 =.56. Theoretical oveent pattern already resebles the actual oveent Mustari Mechanical ngineering Departent, Dayanu Iksanuddin university, Baubau-Indonesia (phone: ; e-ail: Mustari@gail.co). the sae value. This oveent produces a vertical force U (N) to the body frae which will be up or down the quadcopter. Roll otion is obtained by increasing or reducing the rotor speed of the left and at the sae tie reducing or increase the right rotor speed. Pitch otion is obtained in the sae way on both the other otors. Front and rear otors turn to the the anti-clockwise direction while the two other otor turn to the clockwise, so that the direction of the yaw otion/ anti-clockwise obtained if the front-rear speed propeller increase/ decrease and the left and right speed of propeller decrease/ increase. Keywords: odel siulation, quadcopter, dynaic control, kineatics control I. INTRODUCTION One type robots attract uch attention is a ini unanned aerial aircraft UMAVs ( Unanned Mini Aerial Vehicles ), because of its ability to perfor rescue tasks in hazardous locations and difficult to reach. This type of helicopter flying robot has the advantage over other flying vehicle that can aneuver in craped areas and perfor takeoff and vertical landing that it is called vertical take off landing (VTOL). Figure. Fraework configuration of Quadcopter To design a dynaic quadcopter odel, first, defined two fraes (coordinate axes) as shown in Figure, condition of an aircraft that explains the position and a vector velocity defined in a state of X H. ach vector consists of linear and angular position and linear velocity and angle. Figure. Quadcopter with rotors The research will discuss an unanned aircraft ini type with rotating wing type RUMAV ( Rotary wing Unanned Mini Aerial Vehicle ) is called quadcopter. Shown at Figure, the quadcopter which is a flying robot that has four blades independent rotor propeller ounted at each end of a cross frae. II. DYNAMICS MODL In general, a quadcopter described siply as four rotors that are in a cross configuration. Vertical oveent is obtained by adding or reducing the speed of the rotor with all If X LIN is linear position vector consisting of the coponents in the direction of the x,y,z (x,y,z) and X ANG angular position vector consisting of the coponents of the angular position x,y,z (ϕ,θ,ψ) then Quadcopter position vector X H [] is X H = [X LIN X ANG ] T = [x y z ϕ θ ψ] T () If LIN is the linear velocity vector consisting of coponents B of velocity of the x,y,z (x,y,z ) and ANG is the angular velocity vector consisting of the coponents of the angular velocity on the x, y, z (p, q, r) then velocity vector,

2 International Journal on Sart Material and Mechatronics Vol. No. 5 Rafiuddin Sya, Mustari pp 9- ISSN: 56-5 H = [ LIN B ANG] T = [x y z p q r] T () Subscript, B and H indicates that the variable relative to the frae-, B-frae and H-frae. It will be distinguished initial state vector and the state vector after acceleration in a given tie t, respectively notated X H, H, X Ht dan Ht, X H = [x y z ϕ θ ψ ] T () H = [x y z p q r ] T () Subscript H indicates that the variable corresponding relative to the H frae. If [kg] is ass of quadcopter and I [N s ] is oent inertia atrix, the the inertia syste could be described as, I x M H = [ O x O x I I xx I yy [ I zz ] (8) ω F ω F y ψ F g ω z. ẋ F ω F Φ θ It appears that MH is a diagonal atrix and a is a constant. Centripetal Coriolis atrix, O x O x C H = [ B I zz r I yy q O x S(I. ANG) I zz r I yy I xx p [ I yy q I xx p ] (9) Figure. Freebody diagra of quadcopter with four rotors. Figure, shows the dynaics of the oveent of a quadcopter. If the aircraft is given an acceleration of the aircraft will change its position and velocity. If X is äcceleration vector consisting of coponents (x,y, z, p, q, r ), the new velocity vector at tie t is obtained by the acceleration vector engintegral quadcopter against t. While the new position vector at tie t is obtained by integration of the velocity vector respect to tie t. Percepatan yang bekerja pada pesawat diakibatkan oleh gaya yang diberikan pada pesawat. Then, the equilibriu of the dynaics odel of quadcopter will be shown in this part. Then it is iportant for analyzing the dynaic equilibriu in the plane so it will know the forces and oents that can work on the plane. Furtherore, of the forces and oents acting on the aircraft will be known acceleration occurs. If the oent of inertia atrix M H, X H acceleration atrix X H, Centripetal Coriolis atrix CH, velocities atrix H, GB gravitational vector and the action vector Λ of the general oveent of an aircraft dynaics odel of quadcopter can define in the following atrix for [],[]: M H.X H + C H. H G H = Λ (5) If the action of the oveent vector UH, OH propeller gyroscopic atrix and propeller angular velocity Ω, then the action vector is a general oveent Λ = U H + O H. Ω (6) Both equation above can be written in the following for Gravitational vector, G H = [ F G O x -g [ ] () If JTP [N s] is the total rotational oent of inertia of the propeller axis and Ω [rad / s] is the angular velocity of the propeller whole, then the propeller gyroscopic atrix, O H Ω = J TP q q q q Ω () p p p p [ ] If lift force factor b [N s] and d [N s] is the drag factor, then the oveent atrix can be shown below, H = b b b b b l b l b l b l [ d d d d ] () If U [N], U [N ], U [N ] and U [N ] are the lift force, roll torque, torque pitch and yaw torque respectively, then lift factor b [N s] and the drag factor d [N s ] then action vector relative to frae-b, M H.X H = C H. H + G H + O H. Ω + U H (7)

3 International Journal on Sart Material and Mechatronics Vol. No. 5 Rafiuddin Sya, Mustari pp 9- ISSN: 56-5 U B = B Ω = U U U [ U ] = b (Ω + Ω + Ω + Ω ) b l (Ω Ω ) b l (Ω Ω ) [ d (Ω + Ω Ω Ω ) ] () If R Θ rotation atrix then relative action vector respect to frae-h, R Θ O x U H = [ ] U B = O x I x [ (s ψ s ϕ +c ψ s θ c ϕ )U ( c ψ s ϕ +s ψ s θ c ϕ )U (c θ c ϕ )U U U U ] If c k = cos k, s k = sin k then atriks atrix, R θ = c ψ c θ s ψ c ϕ +c ψ s θ s ϕ s ψ s ϕ +c ψ s θ c ϕ s ψ c θ c ψ c ϕ +s ψ s θ s ϕ c ψ s ϕ +s ψ s θ c ϕ [ s θ c θ s ϕ c θ c ϕ ] () (5) III. DYNAMICS MODL OF QUADCOPTR This section will be calculated dynaics of the oveent of aircraft with specifications as shown in Table, the calculation process will be assisted with Matlab progra. Tabel.Spesification Paraeters Description Value L ar b lift coefficient 7,8. -6 Ns² d drag coefficient,. -6 Ns² ass of quadcopter,576 kg I xx body inertia oent for axis-x 5,9. - Ns² I yy body inertia oent for axis-y 5,9. - Ns² I zz body inertia oent for axis-z,7. - Ns² J TP rotational oent inertia,. -6 Ns² An exaple of output progra using atlab progra: Action Vector, U_H = Inertia Matrix of the Syste, M_H, If t k = tan k then transfer atrix, s ϕ t θ c ϕ t θ T θ = c ϕ s ϕ [ s ϕ /c θ c ϕ /c θ] (6) = centripetal-coriolis Matrix C_H (.^-) Acceleration vector of quadcopter relative to frae-b could be described as, X H = [x y z p q r ] (7) = ( C H H + G B + O H Ω + U H ) M H In the siple equation is described as (7): x = (sin ψ sinϕ + cosψ sinθ cosϕ) U y = (-cos ψ sinϕ + sinψ sinθ cosϕ) U z = g + (cosθ cosϕ) U p = I yy I zz I xx q = I zz I xx I yy q r J TP q Ω + U I xx I xx p r J TP q Ω + U I yy I yy r = I xx I yy I zz p q + U I zz (8) On equation (8) shows the atheatical odel of quadcopter = Gravitational Vector G_H =... Gyroscopic Propeller Matrix O_H (.^-) = Angular velocities vector of each propeller, Oega = Angular velocities of quadcopter, Ω = -.7

4 z () y () x () International Journal on Sart Material and Mechatronics Vol. No. 5 Rafiuddin Sya, Mustari pp 9- ISSN: 56-5 Acceleration Vector for aircraft, XDDot_H = Translation B-F Translation L-R Vertical Translation L-R In Figure 5, shows the graph of the trajectory of aircraft oveent in three diensions obtained fro the calculation of dynaics and kineatics using atlab progra 6 5 tie (s) tie (s) tie (s) Rotation L-R Rotation B-F Rotation Bjj-Sjj tie (s).5.5 tie (s) tie (s) tie (s).5.5 Figure. Acceleration and Tie for vertical and horizontal oveents Figure shows the acceleration (/s ) and angular accelration (rad/s ) respect to tie tie (s) 6 5 a x s i z a xis y axis x Figure 5.Siulation of aircraft oveent IV. QUADCOPTR SIMULATION This section will show a siulation of oveent quadcopter both theoretically and experientally. Moveent of the experiental results obtained fro the GPS data attached to Quadcopter. Furtherore, the results of calculations using the odel dynaics and kineatics will be deonstrated in this section. For illustration, the oveent in the x direction is planned to reach a distance of 5. As for the otion in the y direction is planned to reach a distance of.5. For otion in the z direction is planned and aintained at a height of tie (s) Figure 6. Position () vs tie t(s) In Figure 6, shows the graph plane distance () and tie (s) in the x, y and z both theoretical and experients using atlab progra. V. CONCLUSIONS Acceleration due to the thrust plane is large enough that x =.759 / s, y =.77 / s and z =.67 / s for each ileage is x =.5565, y =.67 and z =.97. Thus indicating that the aircraft is quite agile in aneuvering. Quadcopter oveent siulation shown that the axiu error position between the theoretical and the actual oveent is ex =.68 ; ey and ez =.5 =.56. Moveent patterns and the theoretical value of the error is influenced by the control liit ebership function of the fuzzy logic control design. The theoretical of oveent pattern is siilar to the actual oveent.

5 International Journal on Sart Material and Mechatronics Vol. No. 5 Rafiuddin Sya, Mustari pp 9- ISSN: 56-5 RFRNCS [] Bresciani,T. 8.Modelling, Indentification and Control of a Quadcopter Helicopter. Departent of Autoatic Control, Lund University. [] Rodić Aleksandar, Mester Gyula..The Modeling and Siulation of an Autonoous Quad-Rotor Microcopter in a Virtual Outdoor Scenario, University of Belgrade, Institute Mihajlo Pupin, Robotics Laboratory, Belgrade. [] Matilde Santos, Victoria Lopez. Intelligent Fuzzy Controller o\f a Quadcopter. Facultad de Inforatica Universidad Coplutense, 8 Madrid, Spain. []. Abbasi, M. J. Mahjoob, R. Yazdanpanah.Controlling of Quadcopter UAV Using a Fuzzy Syste for Tuning the PID Gains in Hovering ModeCenter for Mechatronics and Autoation, School of Mechanical ngineering College of engineering, University of Tehran Iran. [5] Birkan Tunç, K. Oytun Yapıcı.Fuzzy Logic Control Of A Four Rotor Unanned Air Vehicle, Quadcopter Istanbul Technical University Mechanical ngineering Departent, Syste Dynaics & Control Unit