1. Minds and Computers 3.1 LEGO Mindstorms NXT l Atmel 32-bit ARM processor l 4 inputs/sensors (1, 2, 3, 4) l 3 outputs/motors (A, B, C) l 256 KB Flash Memory l 64 KB RAM l USB 2.0 Communication l 4 programmable buttons l 100x64 b/w LCD Display l Sensors ä Active: Old light and rotation ä Passive Touch, sensors for NXT ä Digital Ultrasonic l Motors ä 170 RPM ä 360 RPM for old motors, why?

2. Minds and Computers 3.2 Preview Spin left motor Spin right motor Wait until the motors have spun two rotations Stop left motor Stop right motor What five steps would the robot have to take in order to go forward for 2 rotations?

3. Minds and Computers 3.3 Preview Now lets examine what that would look like in the NXT Educational Programming Software. 1.Spin left motor2. Spin right motor 3. Wait for 2 rotations 4. Stop left motor5. Stop right motor

4. Minds and Computers 3.4 Preview While programming your motor blocks, make sure you select the proper output ports, and set both motors to the same direction and power level.

5. Minds and Computers 3.5 Preview l Don’t forget, the comments you include in your program don’t actually have any effect on what your robot will do. l Comments simply act as reminders for you when you edit your program. Here, the “wait for 1440 degrees” won’t do anything because the actual Wait Block is set to wait for 720 degrees.

6. Minds and Computers 3.6 Opening Activity Many things affected how far your robot traveled. The number of degrees your Wait For block is set to wait for The size of your tires

7. Minds and Computers 3.7 Wheels and Distance In this activity we’re going to program our robot to move an exact distance. To do so we must understand a few things about circles. STARTFINISH

8. Minds and Computers 3.8 Review Let’s start with the basics. Answer the following: 1. What is a radius of a circle? 2. What is a diameter of a circle? 3. What is the formula for the circumference of a circle? The distance from the center to the outside of a circle. The distance, through a circle’s center, from one edge to another. Circumference= diameter * π rd

9. Minds and Computers 3.9 Preview With our knowledge of circumference, we can start figuring out how to control the distance our robot goes.

10. Minds and Computers 3.10 Preview Finally, be sure to save frequently. That way, if anything happens to your computer you don’t have to start over.

11. Minds and Computers 3.11 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

12. Minds and Computers 3.12 Connector pegs l Black pegs are tight-fitting for locking bricks together. l Grey pegs turn smoothly in bricks for making a pivot

13. Minds and Computers 3.13 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

14. Minds and Computers 3.14 Drivetrain l LEGO Gears 8T 16T 24T 40T 24T Crown 1T Worm Bevel

15. Minds and Computers 3.15 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

16. Minds and Computers 3.16 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!

17. Minds and Computers 3.17 Differential drive Most common kinematic choice All of the miniature robots… Khepera, Braitenberg - difference in wheels’ speeds determines its turning angle VRVR VLVL

18. Minds and Computers 3.18 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?

19. Minds and Computers 3.19 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?

20. Minds and Computers 3.20 1) Specify system measurements Differential drive VRVR VLVL (assume a wheel radius of 1) x y  l - consider possible coordinate systems

21. Minds and Computers 3.21 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.

22. Minds and Computers 3.22 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

23. Minds and Computers 3.23 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 

24. Minds and Computers 3.24 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

25. Minds and Computers 3.25 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

26. Minds and Computers 3.26 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

27. Minds and Computers 3.27 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

28. Minds and Computers 3.28 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,

29. Minds and Computers 3.29 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