Simulation and Control of an Unmanned Surface Vehicle

Transcription

1 Paper ID #26 Simulation and Control of an Unmanned Surface Vehicle Dr. Lifford McLauchlan, Teas A&M University, ingsville Dr. Lifford McLauchlan completed his Ph.D. at Teas A&M University, College Station. After spending time in industry, he has returned to academia. He is an associate professor at Teas A&M University- ingsville in the Electrical Engineering and Computer Science Department. His main research interests include controls, rootics, education, adaptive systems, intelligent systems, signal and image procesg, iometrics and watermarking. He is the current chair of the ASEE Ocean and Marine Engineering Division and is a senior memer of IEEE. c American Society for Engineering Education, 24

2 Simulation and Control of an Unmanned Surface Vehicle Astract Academic eercises that demonstrate the theory give students an understanding of the concepts ut generally without real world concerns and constraints. Prolem ased learning (PBL) has een shown to ecite students and get them more involved in discussions and the course. Students generally ecome ecited when they design solutions for real world or realistic prolems that are ased upon applications and prolems as they can visualize how their solutions work or do not work for the given prolem. With the continued reduction in resources availale to otain large scale vehicles as well as the high t of equipment, simulations ecome ever more important for illustrating control system designs to students. At Teas A&M University- ingsville a new la eercise for an unmanned underwater vehicle has een created for students. The la eercise steps the students through the development of the physics ased model for the system. This allows the students to etter understand the vehicle s movements in 3D as they eplore the vehicle s model. The students analyze the staility of the open loop system ug methods they have learned during the lecture and then develop the control for the closed loop system. The model is then simulated in MATLAB, Octave or another similar software program. With the developed model and closed loop control system, the model (physics ased equations) can then e ported to simulation environments such as Autonomous Unmanned Vehicle (AUV) Workench, which was developed as a modeling tool to study and utilize physics ased real time unmanned vehicle simulation operating in realistic environments. The la demonstrates how this model can e incorporated into AUV Workench. Different controllers for the unmanned vehicle can also e implemented in AUV Workench. AUV Workench then acts as a visual demonstration of how the vehicle moves in the three dimensional (3D) simulation environment giving the students more feedack on how the controllers would ehave on a real system. The new realistic la eercise s efficacy is demonstrated through each of the student s increased understanding of control system concepts.. Introduction Autonomous Unmanned Vehicle (AUV) Workench []-[5] was developed as a modeling and simulation environment to enale physics ased real time simulation of autonomous vehicles, such as surface, underwater, land and air [6]. This or similar software allows a lower t prolem ased learning (PBL) capaility as compared to the high t of large scale underwater, land and air vehicles [6]. PBL has een shown to engage students more therey increag student involvement and understanding of lecture materials [7]-[]. MATLAB is utilized in this assignment to study the closed loop system staility and to design controllers for an unmanned surface vehicle (USV) known as a Sea Fo. The rest of the paper is organized as follows: the Proposed Method is descried in the rest of Section, the Student Design is discussed in Section 2, the esults are in the Section 3, and the Conclusions are in Section 4.

3 . Proposed Method An unmanned surface vehicle such as the Sea Fo depicted in Figure can e modeled with a si degree of freedom (DOF) model []. The mathematical model is developed ug the relationships illustrated in Figure 2 [6], []-[2]. (surge), y (sway) and z (heave) directional motions are depicted. otations around the ais (roll) y ais (pitch) and z ais (yaw) are also taken into account. Velocities are given as u, v and w for the, y and z ais. Angular velocities are given as p, q and r., y Figure Unmanned Surface Vehicle and z define positions while the roll, pitch and yaw Sea Fo Shown in AUV Workench [] are, and [6], []-[2]. In this assignment, students will step through the development of the physics ased model for the unmanned surface vehicle system. This allows the students to etter understand the vehicle s movements in 3D as they eplore the vehicle s model. The students will analyze the staility of the open loop system ug methods they have learned during the lecture and then develop the control for the closed loop system [6]. First the student assignment steps through the various relationships starting with the rotational matrices. Once the model is developed the students will utilize the control theory they have learned in class to control the sys- Figure 2. USV Model [6], []-[2] tem given various constraints. The students net will implement a Proportional Integral Derivative (PID) controller for a linearized model for the Sea Fo. The three general rotation matrices are given elow in the following equations. z, y,, The net step in the model is to calculate the rotation. The rotation is then calculated y the following equation [6], []-[2] z, y,,

4 Linearizing the system model around small angles one can make and. The rotation matri will then e given y. The angular velocity transformation matri T can e found y the following matri [6], []- [2] / / tan tan T. Again linearizing the system model around small angles results in the transformation matri. T. If one assumes no currents and realizing that the following relationships hold [6], []-[2] r q p T w v u z y, the si degree of freedom model can e written y the following matri equation r q p w v u T z y The students can then model the si degree of freedom equations in MATLAB, Octave or another software program as long as the program can simulate differential equations or transfer function responses. Since the la is simulating and controlling an unmanned surface vehicle (USV) the roll, pitch, and heave can e ignored if one assumes relatively calm marine conditions

5 resulting in simulation of the USV only in a horizontal plane. This would reduce the si equations to three and reduce the angles to one that changes [6]. Since the students will e controlling the USV they will need the course angle χ, heading angle and sideslip angle. The three equation model, simplified horizontal plane model, assuming relatively calm conditions is given y the following equation [6], []-[2]. r v u y The course angle χ, heading angle and sideslip angle are depicted in Figure 3 [6], []-[2] where Figure 3. Heading, Sideslip and s [6], []-[2] equations for the velocity U, course angle χ, heading angle and sideslip angle are given y 2 2 tan v u U u v If one assumes that the USV has no sideslip then the equations ecome [6], []-[2] r U y

6 A negative unity feedack control system can then e utilized to control as seen in Figure 4 the Sea Fo modeled y a horizontal plane model descried previously. The PID for the model can e implemented for the simulation. 2. Student Design Figure 4. Feedack Control System for Horizontal Plane Model [6] modified from [] If one assumes in the simulation that the USV s speed is V m/s and is assumed constant, then the Sea Fo model can e further simplified for the simulations [6]. The controller that is utilized y the students in the assignment was a PID controller that can e discrete or analog depending on the simulation environment choice. The PID controller parameters are determined ug techniques, such as design ug root locus the students have learned previously in the class. The students then simulated the controller in the system ug MATLAB and Simulink. In the first case, the students were given the following design constraints and conditions for the control system utilizing a PID controller [6]: ) Sea Fo is traveling at a constant speed of m/s, 2) There is no sideslip, thus course angle χ= heading angle 3) Commanded = rad for 2 seconds, 4) Followed y Commanded = rad for seconds, 5) < % overshoot (% OS) for each commanded angle, 6) Zero steady state error (e ss ) for each commanded angle, and 7) A settling time T s of less than 3 sec for each commanded angle. The students then plotted the trajectory of the USV. In the second case, the students then repeated the simulation ut this time the following assumptions and conditions were given [6]: ) Sea Fo is traveling at a constant speed of m/s, 2) There is no sideslip, thus course angle χ= heading angle 3) Commanded =.2 rad for seconds, 4) Followed y Commanded = -.2 rad for seconds, 5) Followed y Commanded = -.6 rad for seconds, 6) < % overshoot (% OS) for each commanded angle, 7) Zero steady state error (e ss ) for each commanded angle, and 8) A settling time T s of less than 3 sec for each commanded angle.

7 The transfer function G PID of a PID controller is given y one of the following G PID D s 2 D s prop s I D prop s I s D prop sti st D where prop is the proportional constant, I is the integral constant, D is the derivative constant, and T I integration time and T D rate time are related y T I prop D TD. I prop 3. esults Assuming the simplified horizontal plane model for the Sea Fo and with the assumptions previously mentioned, Tale I. shows eamples of the PID parameters and the corresponding transient response values for the commanded angle changes for the first case that are ased upon the student groups determined PID parameters: Tale I First Case - Eample PID Parameters and Time esponse Characteristics POP I D First Second % OS e ss T s % OS e ss T s As can e seen the first two eamples of PID parameters otained meet all of the desired transient characteristics for oth commanded angles, the third was a set one student group determined efore redesigning the controller and otaining a set that met all specifications. The groups generally went through an iterative process retuning the parameters ased on a root locus design at least two or three times. All of the other groups succeeded in meeting the design requirements as well. Figures 5-7 show the output and commanded course angles for the first row PID values of Tale I. Figures 8- show the output and commanded course angles for the second row PID values of Tale I. In Figure, the output and commanded course angle simulations corresponding to the third row of Tale I are shown.

8 Angle (radians) Angle (radians) Angle (radians) Figure 5. First Case Given Two s, One at and One at 2 Seconds prop =, I =2, D = Figure 6. First Case Close-up of After First rad at Seconds prop =, I =2, D = Figure 7. First Case Close-up of After Second rad at 2 Seconds prop =, I =2, D =.

9 Angle (radians) Angle (radians) Angle (radians) Figure 8. First Case Given Two s, One at and One at 2 Seconds prop =8, I =5, D = Figure 9. First Case Close-up of After First rad at Seconds prop =8, I =5, D = Figure. First Case Close-up of After Second rad at 2 Seconds prop =8, I =5, D =.

10 y y Angle (radians) Figure. First Case Given Two s, One at and One at 2 Seconds prop =.9, I =.9, D = Assuming the simplified horizontal plane model for the Sea Fo and with the assumptions previously mentioned, Tale II. shows eamples of the PID parameters and the corresponding transient response values for the commanded angle changes for the second case. Tale II Second Case - Eample PID Parameters and Time esponse Characteristics First Second Third % OS e ss T s % OS e ss T s % OS e ss T s USV Trajectories USV trajectory 2 USV trajectory USV trajectory USV Trajectories USV Trajectory USV Trajectory 2 USV Trajectory Figure 2. First Case Comparison of USV Trajectories Figure 3. Second Case Comparison of USV Trajectories The only trajectory in Figures 2 and 3 to not closely follow the commanded course angles was the third row in the Tales I and II. This corresponds to USV trajectory 3 in Figures 2 and 3 oth of which have the greatest overshoot and error for the displayed trajectories.

11 4. Conclusions The student la groups succeeded in meeting all of the design requirements after performing redesigns to ensure their controller designs met the constraints. After performing this la, the student groups appeared more confident in their ailities to design PID controllers. The students have followed the development of the USV model. In addition, the students were shown how the controller could then e implemented in AUV Workench which includes the Sea Fo as one of the models. The file controlcoefficients can e modified to implement their designed PID controllers. AUV workench though considers the full 6 DOF model in order to include movements in 3D not just the horizontal plane. The students net used the model in a follow on la on path planning. Acknowledgements The author acknowledges the students and their feedack concerning this assignment. Biliography. AUV Workench, accessed January 5, D. Brutzman, Presentation "NPS AUV workench: rehearsal, reality, replay for unmanned vehicle operations," NPS Technical eview and Update (TAU), 25 April 27, accessed Decemer 3, D. Davis and D. Brutzman, "The Autonomous unmanned vehicle workench: mission planning, mission rehearsal, and mission replay tool for physics-ased X3D visualization," 4 th International Symposium on Unmanned Untethered Sumersile Technology (UUST), Autonomous Undersea Systems Institute (AUSI), Durham New Hampshire, 24 August J. Weekley, D. Brutzman, A. Healey, D. Davis and D. Lee, "AUV workench: integrated 3D for interoperale mission rehearsal, reality and replay," 24 Mine Countermeasures & Demining Conference: Asia-Pacific Issues & Mine Countermeasures (MCM) in Wet Environments, Australian Defense Force Academy, Canerra Australia, 9- Feruary D. Brutzman, "Autonomous unmanned vehicle workench (AUVW) rehearsal and replay: mapping diverse vehicle telemetry outputs to common XML data archives," 5 th International Symposium on Unmanned Untethered Sumersile Technology (UUST), Autonomous Undersea Systems Institute (AUSI), Durham New Hampshire, 9-22 August L. McLauchlan, Control of an Unmanned Surface Vehicle (USV) Sea Fo La Assignment for the Senior Course Linear Control Systems, Teas A&M University-ingsville, L. McLauchlan, Design-oriented course in microprocessor ased controls, Proc. of the 27 ASEE Annual Conference and Eposition, AC27675, Honolulu, HI, pp. -, June 247, M. Prince, Does Active Learning Work? A eview of the esearch, Journal of Engineering Education, pp. 2233, July Pucher, A. Mense, and H. Wahl, How to Motivate Students in Project Based Learning, 6 th IEEE Africon Conference in Africa, vol., pp , Oct. 2-4, 22.. L. McLauchlan, M. Mehrueoglu, and J. Durham, Prolem Based Learning Through Modeling and Simulation of Unmanned Vehicles, ASEE Annual Conference, Atlanta, GA, June 236, 23.. C. Sonnenurg, A. Gadre, D. Horner, S. rageland, A. Marcus, D. Stilwell and C. Woolsey, Control Oriented Planar Motion Modeling of Unmanned Surface Vehicles, Technical eport, Virginia Center for Autonomous Systems, T. Fossen, Lecture Notes TT 49 Guidance and Control of Vehicles, Norwegian University of Science and Technology.