1. Minds and Computers4.1 Today's Topics l Braitenberg Vehicles l Art of Lego Design ä Notes from Jason Geist, Carnegie Mellon University l Differential Drive ä Notes from Zachary Dodd, Harvey-Mudd College l ROBOLAB ä Control structures ä Data & containers

2. Minds and Computers4.2 Goals: l Build better robots ä Minimize mechanical breakdowns ä Build robots that are easy to control ä Encourage good design strategy ä Strive for elegant, clever solutions l Know your materials ä Plastic bricks since 1949 (wooden blocks prior) ä On average, 2100 different parts each year ä Manufacturing tolerance: 1/1000 of an inch ä Number of ways of combining six 8-stud bricks: 102,981,500 ä Widely used by scientists and engineers as a rapid prototyping tool

3. Minds and Computers4.3 Geometry l 1-stud brick dimensions: exactly 5/16” x 5/16” x 3/8” (excluding stud height 1/16”), l This is the base geometry for all LEGO components l Three plates = 1 brick in height

4. Minds and Computers4.4 Structure l The right way:

5. Minds and Computers4.5 Connector pegs l Black pegs are tight-fitting for locking bricks together. l Grey pegs turn smoothly in bricks for making a pivot

6. Minds and Computers4.6 Structure l LEGO bricks are finicky: ä They HATE duct tape. ä They HATE hot glue. ä They HATE s uper glue. ä They HATE epoxy. l You should never need adhesives to build reliable LEGO structures

7. Minds and Computers4.7 Braitenberg Vehicles l How do people ascribe behavior? ä The inferred properties may be more more complicated than known structure ä Emergent behavior of interacting pieces l Fear and Agression ä Excitatory connections ä 2 sensors ä 2 motors

8. Minds and Computers4.8 Drivetrain l LEGO Gears 8T 16T 24T 40T 24T Crown 1T Worm Bevel

9. Minds and Computers4.9 Worm Gears l Pull one tooth per revolution 1 2 3 4 Result is a 24:1 gearbox Not back driveable!

10. Minds and Computers4.10 Design Strategy l Incremental design ä Test components parts as you build them Drivetrain Sensors, sensor mounting Structure ä Don’t be afraid to redesign ä KISS l Testing ä Don’t wait until you have a final robot to test Interaction of systems Work division (work concurrently) ä Develop test methods ä Repeatability

11. Minds and Computers4.11 Philosophy l Build for accurate, precise control ä Slow vs. fast? ä Gear backlash ä Stability ä Skidding l Have fun l Be creative, unique l Strive for cool solutions, that work! l Aesthetics: it’s fun to make beautiful robots!

12. Minds and Computers4.12 Differential drive Most common kinematic choice All of the miniature robots… Khepera, Braitenberg - difference in wheels’ speeds determines its turning angle VRVR VLVL

13. Minds and Computers4.13 Differential drive Most common kinematic choice All of the miniature robots… Khepera, Braitenberg - difference in wheels’ speeds determines its turning angle VRVR VLVL Questions (forward kinematics) Given the wheel’s velocities or positions, what is the robot’s velocity/position ? Are there any inherent system constraints?

14. Minds and Computers4.14 1) Specify system measurements 2) Determine the point (the radius) around which the robot is turning. 3) Determine the speed at which the robot is turning to obtain the robot velocity. 4) Integrate to find position. Differential drive Most common kinematic choice All of the miniature robots… Khepera, Braitenberg - difference in wheels’ speeds determines its turning angle VRVR VLVL Questions (forward kinematics) Given the wheel’s velocities or positions, what is the robot’s velocity/position ? Are there any inherent system constraints?

15. Minds and Computers4.15 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) x y  l - consider possible coordinate systems

16. Minds and Computers4.16 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) x y  l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning.

17. Minds and Computers4.17 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) x y  l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning. ICC “instantaneous center of curvature” - to minimize wheel slippage, this point (the ICC) must lie at the intersection of the wheels’ axles - each wheel must be traveling at the same angular velocity

18. Minds and Computers4.18 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) x y  l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning. ICC “instantaneous center of curvature” - to minimize wheel slippage, this point (the ICC) must lie at the intersection of the wheels’ axles - each wheel must be traveling at the same angular velocity around the ICC 

19. Minds and Computers4.19 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning. ICC - each wheel must be traveling at the same angular velocity around the ICC R robot’s turning radius 3) Determine the robot’s speed around the ICC and its linear velocity   R+l/2) = V L  R- l/2) = V R x y

20. Minds and Computers4.20 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning. ICC - each wheel must be traveling at the same angular velocity around the ICC R robot’s turning radius 3) Determine the robot’s speed around the ICC and then linear velocity   R+d) = V L  R-d) = V R Thus,  = ( V R - V L ) / l R  = l ( V R + V L ) / ( V R - V L ) x y

21. Minds and Computers4.21 1) Specify system measurements Differential drive VRVR VLVL l - consider possible coordinate systems 2) Determine the point (the radius) around which the robot is turning. ICC - each wheel must be traveling at the same angular velocity around the ICC R robot’s turning radius 3) Determine the robot’s speed around the ICC and then linear velocity   R+d) = V L  R-d) = V R Thus,  = ( V R - V L ) / l R  = l ( V R + V L ) / 2( V R - V L ) x y So, the robot’s velocity is V  =  R = ( V R + V L ) / 2

22. Minds and Computers4.22 4) Integrate to obtain position Differential drive VRVR VLVL l ICC R(t) robot’s turning radius  (t)  = ( V R - V L ) / l R  = l( V R + V L ) / ( V R - V L ) V  =  R = ( V R + V L ) / 2 What has to happen to change the ICC ? V x = V(t) cos(  (t)) V y = V(t) sin(  (t)) with x y

23. Minds and Computers4.23 4) Integrate to obtain position Differential drive VRVR VLVL l ICC R(t) robot’s turning radius  (t)  = ( V R - V L ) / l R  = l ( V R + V L ) / 2( V R - V L ) V  =  R = ( V R + V L ) / 2 V x = V(t) cos(  (t)) V y = V(t) sin(  (t)) with x y x(t) = ∫ V(t) cos(  (t)) dt y(t) = ∫ V(t) sin(  (t)) dt  (t) = ∫  (t) dt Thus,

24. Minds and Computers4.24 4) Integrate to obtain position Differential drive VRVR VLVL l ICC R(t) robot’s turning radius  (t) Thus,  = ( V R - V L ) /l R  = l ( V R + V L ) / 2( V R - V L ) V  =  R = ( V R + V L ) / 2 What has to happen to change the ICC ? V x = V(t) cos(  (t)) V y = V(t) sin(  (t)) x(t) = ∫ V(t) cos(  (t)) dt y(t) = ∫ V(t) sin(  (t)) dt  (t) = ∫  (t) dt with x y Kinematics

25. Minds and Computers4.25 Questions l For each of the following, describe what the sequence of ROBOLAB commands should do?

26. Minds and Computers4.26 Control structures l Forks l Loops l Tasks

27. Minds and Computers4.27 Sharing resources l Sensors l Motors