Development of an Experimental Testbed for Multiple Vehicles Formation Flight Control

Transcription

1 Proceedings of the IEEE Conference on Control Applications Toronto, Canada, August 8-, MA6. Development of an Experimental Testbed for Multiple Vehicles Formation Flight Control Jinjun Shan and Hugh H. T. Liu Abstract This paper presents the development of an experimental testbed for multiple vehicles formation control. This four -DOF helicopter-testbed in the Flight Systems and Control (FSC) Laboratory of University of Toronto can be applied to validate the effectiveness of formation flight and cooperative (coordination) control strategy. Each helicopter has three degrees of freedom, in elevation, pitch and travel motion respectively. Two experimental schemes and results of the classical leader-follower and cooperative configurations are presented and discussed. I. INTRODUCTION Recently, multiple vehicles formation flight (flying) has become very active research topic. Many formation contol applications have been proposed, such as formation or coordination of spacecraft [], [], aircraft [], [] and robotics [], [6]. In order to evaluate the effectiveness of the proposed control strategies, some experimental testbeds have been developed [7], [8], [9]. The Flight Systems and Control (FSC) Laboratory at University of Toronto has been in the field of multiple vehicles formation flight for several years. This paper presents the development of multiple vehicles formation flight experimental testbed. The remainder of this paper is organized as follows. Section II introduces the architecture of -DOF helicopter testbed for formation flight and helicopter s attitude dynamics. Section III gives the experimental schemes and results. Section IV concludes this paper. II. ARCHITECTURE OF TESTBED FOR FORMATION FLIGHT The Flight Systems and Control (FSC) Laboratory, of the University of Toronto, facilitates four Quanser s -DOF helicopters ( see Fig.. Each - DOF helicopter system consists of a computer, a Q8 terminal board, the support base and arm, two propellers (Fig. ), one Universal Power Module (UPM, Fig. ), the joystick (Fig. ) and one optional active disturbance system (ADS, Fig. ). The front and back propellers are the actuators of the - DOF helicopters. The elevation motion is controlled by the sum of forces generated by the two propellers. Meanwhile, the difference between these two forces controls both the pitch motion and the travel motion. The Q8 terminal board connects the control computer with the -DOF helicopter and provides interface functions such as A/D, D/A. The trajectory for the -DOF helicopter can be programmed using MATLAB/Simulink or generated using joystick. Jinjun Shan and Hugh H. T. Liu are with The Institute for Aerospace Studies, University of Toronto, 9 Dufferin St., Toronto, Canada MH T6 shan,liu@utias.utoronto.ca Fig. : Four -DOF helicopters setup Fig. : Propellers Fig. : Universal Power Module (UPM) //$. IEEE 6

2 Fig. : Joystick (a) Helicopter without ADS Fig. : Active disturbance system (ADS) Two -DOF helicopters without/with ADS are shown in Fig. 6. The ADS can be used to simulate the disturbance on system or controller. The ADS consists of a lead screw driven by a DC motor. Attached to the lead screw is a mass that can be made to travel along the arm. The position can be measured by the installed encoder. The measurements show that the effective masses for the -DOF helicopter in Fig. 6(b) are. kg,.7 kg, and. kg when the ADS is at the points farthest away, middle, and nearest from propellers, respectively. The -DOF helicopter can be modeled individually for three axes: elevation, pitch, and travel. Elevation axis The elevation motion can be described by the following differential equation: J e α = K f l a cos (β)(v f + V b ) mgl a sin (α + α ) = K f l a cos (β)v s mgl a sin (α + α ) () where α is the elevation angle, α is the angle between helicopter arm and its base, β is the pitch angle, J e is the moment of inertia of the system about the elevation axis, K f is the force constant of the motor/propeller combination, 6 l a (b) Helicopter with ADS Fig. 6: Photograph of -DOF helicopters is the distance from the pivot point to the helicopter body, V f and V b are the respective voltages applied to the front and back motors, V s is the sum of V f and V b, m is the effective mass about the elevation axis, g is the gravity constant. For -DOF helicopter with ADS, the effective mass m is adjustable. Pitch axis The pitch axis is controlled by the difference of the forces generated by the propellers: J p β = Kf l h (V f V b )=K f l h V d () where J p is the moment of inertia of the system about the pitch axis, l h is the distance from the pitch axis to either motor, V d is the difference between the voltage applied to the front and back motors. If the force generated by the front motor is higher than the force generated by the back motor, the helicopter body will pitch up (positive). It should be noted that the pitch angle is limited among ( π, π )

3 mechanically during experiment. Travel axis The only way to apply a force in the travel direction is to pitch body of the helicopter. The corresponding dynamic equation of travel axis is: J t γ = K f l a sin β sin (α + α )(V f + V b ) +K f l h cos (α + α )(V f V b ) () [ ] = K f l a sin β sin (α + α )V s + l h cos (α + α )V d where γ is the travel angle, J t is the moment of inertia about the travel axis. Moreover, if (α + α )=π/, i.e.thearmis in horizontal position, the above travel motion becomes J t γ = K f l a sin β sin (α + α )V s () III. EXPERIMENTAL SCHEMES AND RESULTS The developed testbed is mainly used for validation of multiple vehicles formation flight controller design. The experiments will be conducted in two ways: classical leaderfollower configuration and cooperative configuration. Figure 7 shows the control flowchart of the leader-follower configuration. Here, the attitude commands are designed only for. The attitude outputs of will be fed into I as its commands. Analogical process applies to and IV. In this way, every helicopter with its anterior helicopter form a classical leader-follower configuration and the controller for each helicopter is related to itself only. Commands I V Fig. 7: The leader-follower configuration The cooperative configuration is given in Fig. 8. The attitude commands are designed for all -DOF helicopters in formation. In this configuration, every helicopter has its own attitude controller. In addition, all helicopters attitude information will enter into the formation flight controller and the control will be fed back to the corresponding attitude controller for formation flight. Using the above two schemes, we have finished some experiments with three -DOF helicopters in formation, as shown in Figs. 9 and. Fig. gives the position trajectory of ADS system for all experiments. In our experiments, we employ the traditional PID controller for elevation axis and Commands I V Fig. 8: Cooperative configuration Formation Flight Controller Quanser-provided LQR controller for travel axis of each helicopter. The systematic parameters and controller gains for our experimental setup are given in Table I. The quintic polynomial trajectory in Eq.() is chosen for the elevation motion and attitude motion for the travel axis. α d (t) =.89 t.99 t +. t () TABLE I: Parameters and controller gains for three -DOF helicopters Parameters/gains I J ei,kg m...7 J pi,kg m... m i, kg..8. K fi, N/Volt l ai, m l hi, m ADS Yes No No [K P,K I,K D ] [, 6, ] Value measured when ADS at the farthest position from propellers,.7 for the middle position in the slide bar,. for the nearest position from propellers. For the leader-follower and the cooperative configurations, the controllers for these three helicopters elevation axes are V s = K P (α d α )+K I (α d α ) and +K D ( α d α ) V s = K P (α α )+K I (α α ) (6) +K D ( α α ) V s = K P (α α )+K I (α α ) +K D ( α α ) V s = K P (α d α )+K I (α d α ) +K D ( α d α ) V s = K P (α d α )+K I (α d α ) (7) +K D ( α d α ) V s = K P (α d α )+K I (α d α ) +K D ( α d α ) 6

4 respectively. From experimental results in Fig. 9 we can know that there are some time delays between the leader and follower helicopters. This is because each helicopter follows its leader s trajectory, as in Eq.(6). Another point for this leader-follower configuration is that all helicopters move at a synchronized way. For example, the first helicopter tracks its desired trajectory under the ADS disturbance, under this configuration, other two helicopters move at the same way so that the synchronized tracking errors between all helicopters are small. Comparing with the leader-follower configuration, the experimental results in Fig. show that the time delays between all the helicopters with cooperative configuration (without interconnection) are much smaller. However, the synchronized tracking errors between three helicopters are much bigger when the ADS disturbance works on the first helicopter because there is no interconnection among these helicopters and other helicopters will not response to the disturbance. Trajectory of elevation angle of three helicopters(deg) I (a) Elevation trajectory tracking IV. CONCLUSIONS This paper presents the development of multiple vehicles formation flight control testbed in the Flight Systems and Control (FSC) Laboratory of University of Toronto. This testbed consists of for -DOF helicopters, which have elevation, pitch, and travel three motion axes. This testbed can be used to verify the formation flight controller design, cooperative/coordination strategies of multiple vehicles in formation, and synchronization control of multiple vehicles. Some experimental are given and discussed. Our future work will be focused on the study of cooperative formation flight control with interconnection strategy. Trajectory of travel angle of three helicopters(deg) I REFERENCES [] M. S. de Queiroz, V. Kapila, and Q. Yan, Adaptive nonlinear control of multiple spacecraft formation flying, Journal of Guidance, Control and Dynamics, vol., no., pp. 8 9,. [] S. R. Vadali, S. S. Vaddi, and K. T. Alfriend, An intelligent control concept for formation flying satellites, International Journal of Robust and Nonlinear Control, vol., no. -, pp. 97,. [] S. N. Singh, R. Zhang, P. Chandler, and S. Banda, Decentralized nonlinear robust control of UAVs in close formation, International Journal of Robust and Nonlinear Control, vol., no., pp. 7 78,. [] P. Binetti, K. B. Ariyur, M. Krstic, and F. Bernelli, Formation flight optimization using extremum seeking feedback, Journal of Guidance, Control and Dynamics, vol. 6, no., pp.,. [] T. Balch and R. C. Arkin, Behavior-based formation control for multirobot teams, IEEE Transactions on Robotics and Automation, vol., no. 6, pp , 998. [6] J. R. T. Lawton, R. W. Beard, and B. J. Young, A decentralized approach to formation maneuvers, IEEE Transactions on Robotics and Automation, vol. 9, no. 6, pp. 9 9,. [7] L. Cremean, W. B. Dunbar, D. van Gogh, J. Hickey, E. Klavins, J. Meltzer, and R. M. Murray, The caltech multi-vehicle wireless testbed, in The st IEEE Conference on Decision and Control, Las Vegas, Nevada, Dec. -, pp [8] E. King, Y. Kuwata, M. Alighanbari, L. Bertuccelli, and J. How, Coordination and control experiments on a multi-vehicle testbed, in American Control Conference, Boston, MA, Jun -Jul, pp.. [9] T. W. McLain and R. W. Beard, Unmanned air vehicle testbed for cooperative control experiments, in American Control Conference, Boston, MA, Jun -Jul, pp. 7. Control voltages for front motors of three helicopters(v) (b) Travel trajectory tracking I (c) Control voltages for front motors 6

5 Control voltages for back motors of three helicopters(v) I (d) Control voltages for back motors Fig. 9: Experimental results of three -DOF helicopters in leader-follower configuration Trajectory of elevation angle of three helicopters(deg) I (a) Elevation trajectory tracking Control voltages for front motors of three helicopters(v) Control voltages for back motors of three helicopters(v) (c) Control voltages for front motors I (d) Control voltages for back motors I Fig. : Experimental results of three -DOF helicopters in cooperative configuration without interconnection Trajectory of travel angle of three helicopters(deg).... I (b) Travel trajectory tracking ADS position(m) Fig. : ADS position trajectory 6