Mobile Robots with Wheeled Inverted Pendulum Base in Human Environments

Transcription

1 Mobile Robots with Wheeled Inverted Pendulum Base in Human Environments Undergraduate Thesis Proposal Presented to the Academic Faculty in Partial Fulfillment of Institute Requirements for the Undergraduate Research Option Ashish Katariya Undergraduate Student Prof. David G. Taylor Faculty Advisor Prof. Douglas B. Williams Associate Chair for Undergraduate Affairs School of Electrical and Computer Engineering College of Engineering Georgia Institute of Technology

2 Introduction In recent years, the usage of industrial robots by manufacturing companies has increased drastically but there hasn t been much progress in the usage of mobile robots in human environments. The human-machine interface is a key area of interest, particularly in the physical interaction between the robot and person. However, robotic arms and mobile robots used in industries are heavy and occupy much space i.e. they are position-controlled rather than force-controlled [1]. These heavy industrial robots cannot be accommodated in an environment occupied by humans due to their lack of dynamic agility. Therefore, it becomes necessary to build intelligent robots with dynamic stability that are safe, agile, and easy to maneuver in communities and building spaces occupied by humans [1]. One such system that can easily maneuver in a crowded environment is a wheeled inverted pendulum. Vehicles characterized as wheeled inverted pendulums have received recent attention in the robotics community [2]. A wheeled inverted pendulum is a body above two wheels with no balancing support. Another system for use in human environments would be a humanoid robot, but the dynamic motion of a humanoid robot is far too complex for initial consideration. A wheeled inverted pendulum is a non-linear system which can be controlled by a digital controller. The control system feedback loop needs to be non-linear for the system to behave more responsively and accurately. Also, accurate simulation results can be obtained only when the simulations are done considering a non-linear system. However, control systems for the wheeled inverted pendulum in previous works [2] [3] [7] [10] [11] have employed methods that involve linearizing the plant and control system during simulations. Due to linear feedback loops, control systems are not accurate, optimal systems cannot be designed and the system lacks efficiency. Also, most of the previous works assume that there are enough sensors available to measure every state variable. However, it is necessary to build a system that addresses the problems of having fewer sensors than required. To be able to build a wheeled inverted pendulum without any flaws, the most important step is to do the dynamical modeling correctly. There are two ways of deriving the equations of

3 motion of any mechanical system: the Newtonian and Lagrangian methods; the equations of motion from both approaches should be identical [4]. However, in previous works [2] [3] [7] [10] [11], only the Newtonian method has been applied to derive the equations of motion. Since, the equations of motion have never been cross-checked using two different methods, the validity of these equations seems questionable. Our initial research goal is to gain extensive knowledge about the dynamic and control system modeling of a complex system such as the wheeled inverted pendulum. Dynamic modeling of the system will be done using the Newtonian and Lagrangian methods. This project will build an observer based controller design that would require measurement of fewer state variables [6]. An observer based design estimates the unmeasured states and emulates full-state feedback for accurate control. Therefore, the usage of a reduced order observer based design addresses the problems of having fewer sensors than required. Also, it is possible to do an observability analysis to find the minimal set of sensors that can accurately control the non-linear system. An observability analysis for this system has not been done in any of the previous works mentioned earlier. All simulations will be done considering the wheeled inverted pendulum as a non-linear system; the feedback loop will be non-linear as well. Considering a non-linear system for all steps including simulations and building the actual physical system ensures that the simulation results and actual system would be more accurate than previous works. The eventual goal would be to use this maneuverable system to create a utility such as a robot for the benefit of humanity. Background The wheeled inverted pendulum has 3 degrees of freedom as seen in Figure 1 [3]. The 3 degrees of freedom are signified by the wheelbase being able to rotate around the z axis, a movement described by the angle θ p and the corresponding angular velocity ω p. The chassis is characterized by the position x RM and the speed v RM while moving linearly. Additionally, the wheelbase can rotate around its vertical axis with the associated angle δ and angular velocity δ. These six state-space variables fully describe the dynamics of the 3 degree of freedom system. Forces applied to the center of gravity (CG) of the vehicle, to the center of the left

4 wheel, and to the center of the right wheel are the disturbances that define the motion of this system from the equilibrium position. θ d describes a disturbance due to a change in location of the CG. The wheelbase is controlled by applying a torque C L and C R and to the corresponding wheels. This torque is contributed by the motors attached to each wheel. Other inputs that enable the control system to keep the robot upright at all times are signals from the gyroscopes and accelerometers. These sensors provide information about various state variables at any given time. Figure 1. A 3D model of the wheeled inverted pendulum base showing all relevant variables of motion [3]. The basic Newtonian equations of motion for the wheeled inverted pendulum have been derived in [3] but they fail to mention the non-linear equations explicitly and provide only the linearized model. This non-linear model will be derived first and the equations will be verified using the Lagrangian method as mentioned earlier.

5 Preliminary Research Figure 2. Schematic of cart-stick system showing all relevant variables of motion. The cart-stick system shown in Figure 2 is a simplified version of the wheeled inverted pendulum since it has only 2 degrees of freedom as opposed to 3 degrees of freedom in the wheeled inverted pendulum. In Figure 2, the pivot point of the inverted pendulum is mounted on to the cart which has one degree of freedom. Force F is the external force given to the system in order to maintain balance so that the rigid rod remains upright. Thus, force F in the cart-stick system is analogous to the torque given to the wheels in the wheeled inverted pendulum system. The dynamic modeling of this system is done using the variables shown in Figure 2 and the following equations of motion have been verified using the Newtonian and Lagrangian approach: F = m + M a mω 2 l sin θ + mαl cos θ & g sin θ αl a cos θ = 0 Control systems for the cart-stick system have been designed considering various scenarios such as linear system with full state feedback, non-linear system with full state feedback or regulator design and non-linear system with partial feedback or estimator design. Figure 3 shows the simulation results for the regulator design when initial condition on the vertical angle of stick is varied from 0.1 to 0.7 radians or 6 to 40.

6 Figure 3. Plot of vertical angle of stick versus time for various initial angles ranging from 0.1 to 0.7 radians or 6 to 40. Thus, it can be verified from the above plots that the non-linear cart-stick system is stabilizable and controllable for the set of system parameters (M, m and l) used in the above simulations. Similar simulation results are expected for the wheeled inverted pendulum system. Proposed Research The proposed research spanning two semesters of Fall 2009 and Spring 2010 can be categorized into the following three levels: Low Target Describe and model the dynamics of the inverted pendulum wheelbase using the Newtonian and Lagrangian approaches. The project will move forward only after exactly the same equations are obtained from both approaches. Successfully model the control system using state-space design method and simulate it in Matlab or Simulink.

7 Depending on the control system model and state-space variables, decide on the hardware components to be used in the robot. Build the inverted pendulum wheelbase in lab using wheels, motors, the microcontroller board, a battery, the DSP board, gyroscopes, accelerometers and other required components. The wheelbase will be able to balance on its own in a stationary position without any external feedback. Build the robot on top of the self-balancing wheelbase. For the purposes of this research project, the robot will be used as a mobile video conferencing system. This step will involve placing an onboard computer with a touch-screen LCD on the upper half of the robot. The robot will also bear 2-3 webcams connected to the on-board computer which will serve as a vision system for the user operating the robot remotely. Create a primitive application for the client computer to be able to control the robot remotely in real time over Wi-Fi. The on-board computer would be connected to Wi-Fi as well. Skype will be used to transmit the live video and audio from the on-board webcams to the screen of the client computer. This way the client will be able to control the robot remotely with the help of webcams and also perform live conversations with anyone near the robot. Ideal Target Create a GUI based application for the on-board computer as well as the client computer that would handle the audio, video and controls of the robot. This way the use of Skype can be eliminated entirely and the client would not have to deal with two applications at a time. A single application for conferencing and controlling the robot would provide a richer user experience. High Target Add limbs (1 or 2 motorized arms) to the robot. This would greatly enhance the functionality of the robot. Without limbs, the robot will be confined to just one building or maybe just one floor because it will not be able to open or close doors. Thus, adding motorized arms that are capable of opening doors and maybe carry some small things will increase the range of the robot.

8 Using the DSP board to add voice recognition and adding navigation by feeding in some maps can make it possible for the robot to do small autonomous tasks such as picking up a packet and delivering it to some other desired location. It can almost function as a personal assistant. Equipment Needed The following equipment will be needed for successful completion of the research project: Wheels Motors Microcontroller board Power electronics board Battery Gyroscope Accelerometer Steel/Aluminum body for the robot On-board computer with LCD screen Webcams Conclusion This research project is highly interdisciplinary and exposes us to several aspects of Electrical, Computer and Mechanical Engineering. While gathering all this knowledge, a marketable utility of tremendous usage to humans will evolve. Thus, this project is a great exercise in a product development setting.

9 Bibliography [1] Microdynamic Systems Laboratory, Carnegie Mellon University, Dynamically-Stable Mobile Robots in Human Environments. [Online]. Available: [Accessed: July 20, 2009]. [2] N. R. Gans and S. A. Hutchinson, "Visual Servo Velocity and Pose Control of a Wheeled Inverted Pendulum through Partial-Feedback Linearization," in International Conference on Intelligent Robots and Systems, Beijing, China, October 9-15, 2006, pp [3] F. Grasser, A. D Arrigo, S. Colombi, and A. C. Rufer, "JOE: A Mobile, Inverted Pendulum," IEEE Transactions on Industrial Electronics, vol. 49, pp , February [4] L. Meirovitch, Methods of Analytical Dynamics. Mineola, NY: Dover Publications, [5] G. F. Franklin, J. D. Powell, A. Emami-Naeini, Feedback Control of Dynamic Systems, 5 th ed. Upper Saddle River, NJ: Pearson Prentice Hall, [6] D. Choi and J.-H. Oh, "Human-friendly Motion Control of a Wheeled Inverted Pendulum by Reduced-order Disturbance Observer," in IEEE International Conference on Robotics and Automation, Pasadena, CA, USA, May 19-23, [7] S. W. Nawawi, M. N. Ahmad, and J. H. S. Osman, "Real-Time Control of a Two-Wheeled Inverted Pendulum Mobile Robot," World Academy of Science, Engineering and Technology, vol. 39, pp , [8] K. Pathak and S. K. Agrawal, "Band-Limited Trajectory Planning and Tracking for Certain Dynamically Stabilized Mobile Systems," Journal of Dynamic Systems, Measurement, and Control, vol. 128, pp , March [9] K. Pathak, J. Franch, and S. K. Agrawal, "Velocity Control of a Wheeled Inverted Pendulum by Partial Feedback Linearization," in 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, December 14-17, 2004, pp [10] S. Y. Seo, S. H. Kim, S.-H. Lee, S. H. Han, and H. S. Kim, "Simulation of Attitude Control of a Wheeled Inverted Pendulum," in International Conference on Control, Automation and Systems, Coex, Seoul, Korea, Oct , [11] A. Shimada and N. Hatakeyama, "High-Speed Motion Control of Wheeled Inverted Pendulum Robots," in International Conference on Mechatronics, Kumamoto, Japan, 2007.