MEAM 520. Mobile Robots

Transcription

1 MEAM 520 Mobile Robots Katherine J. Kuchenbecker, Ph.D. General Robotics, Automation, Sensing, and Perception Lab (GRASP) MEAM Department, SEAS, Universit of Pennslvania Lecture 22: December 6, 2012

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3 T 12/4 6:30-7:30pm W 12/5 12:30-1:30pm R 12/6 6:30-7:30pm T 12/11 4:00-5:00pm T 12/11 5:00-6:00pm W 12/12 12:30-1:30pm W 12/12 1:30-2:30pm R 12/13 6:30-7:30pm

4 Homework 6: Teleoperation MEAM 520, Universit of Pennslvania Katherine J. Kuchenbecker, Ph.D. December 3, 2012 This assignment is due on Frida, December 7,b 5:00 p.m. If ou don t finish b that time,ou ma turn it in with no penalt b 5:00 p.m. on Wednesda, December 12. After that deadline, no further assignments ma be submitted. Because it is short, this assignment is worth 30 points (half the value of homework assignments 1 through 5). You ma talk with other students about this assignment, ask the teaching team questions, use a calculator and other tools, and consult outside sources such as the Internet. To help ou actuall learn the material, what ou submit should be our own work, not copied from a peer or a solution manual. Teleoperation Controller (30 points) Your task is to write a good controller for a simple simulated teleoperation sstem. The image below shows asnapshotofthesimulatedteleoperator. Itincludesaone-degree-of-freedom master robot (left, in magenta) and an identical one-degree-of-freedom slave robot (right, in blue).each device consists of a single revolute joint, much like the pair of Immersion Impulse Engine 2000 josticks that Professor Kuchenbecker discussed in Lecture 18 (on November 20). Each robot s joint angle is measured in radians, with counterclockwise positive and straight up equal to zero. The stationar bracket to which the robots are attached is shown in dark gra. The robots can move freel through this region because the are not in the same plane. There are no obstacles in the master s workspace, and the robots are too short to touch each other directl. There is one obstacle in the slave s workspace; shown in green, it begins at obstacleangle and etends infinitel in the negative direction. You should move the obstacle around to test different environments; the controller that ou write should work for an obstacle location, so it should not use the variable obstacleangle in an wa. To simulate the presence of a human user holding onto the end ofthemasterrobot,themastermoves through a pre-determined trajector that ou select. Si trajectories are provided (mastermovement1.mat... mastermovement6.mat), and ou can also write our own. The slave has pre-programmed dnamics that are hidden from our view inside the function getslavetheta.p. Thesednamicsincludebutarenot limited to inertia, gravit, friction, actuator saturation, and encoder quantization. When ou first run the starter code, ou will see that the slave just falls into the obstacle and stas there, while the master robot follows the default pre-determined trajector. To help ou understand what is happening in the simulation, the starter code animates the entire interaction and graphs the resulting angles and commanded torques over time, as shown in the sample graph below. Commanded Torque (Nm) Angle (rad) Master Slave Obstacle Time (s) Master Slave Time (s) The simulated teleoperation sstem runs a servo loop at 1000 Hz, which ou should not change. At each time step, it obtains the new position of the master (mastertheta) andtheslave(slavetheta) in radians. Your job is to specif the torque to command to the master (mastertau) andtheslave(slavetau) in newton meters to ield good transparenc (good tracking and good feel in free space, good feel in contact with the obstacle) and good stabilit (no etraneous ongoing oscillations). There should be no motion scaling or clutching between the two devices. The slave torque that ou specif will directl affect the movement of the slave robot, while the master torque that ou specif will merel be graphed. Following standard robotics convention, a positive torque moves the joint in the positive direction. It is epected that our controller will include gravit compensation, a proportional term, and a derivative term on both devices. Download the starter code from this assignment s page on the class wiki, change the name of the provided script (teleoperation starter.m) toincludeourpennke,putournamewhereitsas PUT YOUR NAME HERE, andmakesurethestartercodeworkscorrectlbeforestarting to modif it. Near the top, ou can change the movement of the master, the initial position of the slave, the angle of the obstacle, and the speed of the animation. When ou re read, put our controller code between the two lines of stars, modif whatever other simulation settings ou want to elucidate the behavior of the sstem,and comment the final code ou write. Follow the instructions below to submit our Matlab files. Submitting Your Code Follow these instructions to submit our code: 1. Start an to meam520@seas.upenn.edu 2. Make the subject Homework 6: Your Name, replacing Your Name with our name. 3. Attach our correctl named MATLAB script (teleoperation ourpennke.m) to the ,along with an other files that ou created. You do not need to submit the provided mastermovement.mat or getslavetheta.p files. Please do not zip our files together before attaching them; just attach them as individual files. 4. Optionall include an comments ou have about this assignment. 5. Send the . You are welcome to resubmit our code if ou want to make corrections. To avoid confusion, please state in the new that it is a resubmission, and include all of our MATLAB files, even if ou have updated onl some of them. 1 2 Due b 5:00 p.m. on Wednesda 12/12

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7 Demo of a Penn MAGIC robot b James Yang

8 Magic 2010 Photo Galler These images are copright protected. You ma download, displa, print and reproduce this material in unaltered form onl (retaining this notice and imager metadata) for our personal, non-commercial use or use within our famil or organisation.

9 Mobile ground robots tpicall operate in a planar environment, so their movement is easier to describe than that of a manipulator.

10 Kinematics of Slides created b Jonathan Fiene Mobile Robots

11 Configurations & Degrees of Freedom configuration specification of all points on the robot configuration space set of all possible configurations degrees of freedom # of parameters to define the configuration θ

12 Constraints Inequalit Constraints : No two objects can occup the same space Inequalities C

13 Constraints Holonomic Constraints : Position is limited to a subset of the configuration space through a function equal to zero Free Configuration (pose) : q = θ Holonomic Constraints Constrained Configuration : q = [ θ ]

14 Constraints Non-Holonomic Constraints : an constraint that cannot be epressed as a function of the position coordinates, including limits on VELOCITY The robot can reach anwhere in the configuration space but it is under-actuated, and thus the velocit is constrained

15 Idealized knife-edge (non-holonomic) constraint e f C e l θ Single point of contact at C Velocit constrained to be along the knife edge v l =0

16 Idealized knife-edge (non-holonomic) constraint cos θ [ sin θ ] e f = sin θ e l = cos θ e f C e l θ Velocit at point C : v C = [ ẋ ẏ ] Single point of contact at C Velocit constrained to be along the knife edge v l =0 Constrained velocit : but the position is NOT constrained

17 Mobile Robot Drives Differential steering Co-aial wheels Independentl driven Two-dimensional Non-holonomicall constrained

18 Rigid Bod Kinematics B A

19 Planar : Instantaneous Center B A IC

20 Differential Steering : Forward Kinematics Given the robot geometr and wheel speeds, what is the robot s velocit? Wheel radius Bod width Right wheel ang. velocit φ R Left wheel ang. velocit φ L e f Forward velocit θ Angular velocit

21 Differential Steering : Instantaneous Center of Curvature IC

22 Differential Steering : Inverse Kinematics What wheel speeds are necessar to produce a desired robot velocit? e f θ

23 Differential Steering : Benefits Simple construction Zero minimum turning radius e f θ

24 Differential Steering : Drawbacks Small error in wheel speeds translates to large position errors Requires two drive motors Wheels-first is dnamicall unstable e f θ

25 Triccle : Forward Kinematics Steerable powered front wheel Free-spinning rear wheels Front wheel radius r e s Wheelbase d α e f Front wheel speed φ S Forward velocit v f = r φ S cos α θ Angular velocit θ = r d φ S sin α d

26 Triccle : Instantaneous Center of Curvature e s R ICC = d tan α = v f θ α e f θ d

27 Triccle : Inverse Kinematics What wheel speed and angle are necessar to produce a desired robot velocit? e s α e f α =tan 1 ( θd v f ) θ φ S = 1 r v 2 f + θ 2 d 2 d

28 Triccle : Benefits Doesn t require accurate speed matching e s α e f θ d

29 Triccle : Drawbacks Zero turning radius requires steering to 90 degrees More complicated drive train e s α e f θ d

30 Ackerman Steering ICC

31 Questions?

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34 Final Eam Wednesda, December 19 Noon to 2:00 p.m. Location to be announced Comprehensive, covering everthing through Tuesda s lecture Closed book Four single-sided pages of notes Calculator allowed

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36 SCARA Robot b PUT YOUR NAME HERE 2 t = s 1 Z (m) Y (m) X (m) 1 2

37 Thank ou for a great semester!