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Fuzzy Logic

Fuzzy Logic and Robot Control. Fuzzy Logic. Mundhenk and Itti , 2007. Problem: . We have a robot and we want it to move around obstacles based on how close we are to them. How do we do this? . Current Path. Ideal New Path. Current Path.

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Fuzzy Logic

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  1. Fuzzy Logic and Robot Control Fuzzy Logic Mundhenk and Itti, 2007

  2. Problem: • We have a robot and we want it to move around obstacles based on how close we are to them. How do we do this? Current Path

  3. Ideal New Path Current Path Your course adjustments are minimally proportional to the distance to an obstacle and your current speed and heading. The closer you are to an obstacle, the harder you need to turn to avoid it. Ideal New Path Current Path

  4. Very Basic Control Theory • Your speed towards a goal or away from an object should be proportional to the distance from it. • If you want to get to a goal in an optimal amount of time you want to move quickly. • However, you need to decelerate as you grow near the target so you can have more control. • Speed µ distance-to-target

  5. Very Basic Control Theory • In systems with momentum (i.e. the real world) we have to worry about more complex acceleration and deceleration. • We can overshoot our target or stop short! • You increase your rate of deceleration based on how close you are to a goal or obstacle. • You can also integrate over the distance to a goal to create a steady state. • This is the basic idea behind a PID controller. • Proportional Integral Derivative • The physical derivation of PID can be tricky, we will avoid it for now. • However this part of an extremely interesting topic!

  6. IDEA! • Lets just hack a fuzzy controller together and avoid some math. • The gods will curse us…. • But if it works, that may be all that matters! • Derive rule of thumb ideas for speed and direction • If I’m 6 meters from the obstacle, am I far from it?

  7. Ideal New Path Far? In addition to a change in speed, we may need to turn to avoid hitting an obstacle. If we are near, our course correction may need to be more abrupt. Ideal New Path Near?

  8. Try some fuzzy rules… • Lets look at adjusting trajectory first then we will look at speed… • If an obstacle is near and center, turn sharp right or left. • If an obstacle is far and center, turn soft left or right. • If an obstacle is near, turn slightly right or left, just in case. • Etc…

  9. Distance Trajectory Turn Hard Right Near Center Soft Right AND THEN IF Near Center Far A very simple example... Yes the robot only turns right. 0 M 20 M 90° 0° -90° -25° 0°

  10. El mal de plantas Distance Trajectory Turn HardRight Near Center Soft Right AND THEN IF Near 10 ° 10 M Center Far We have a robot and an obstacle we want to avoid. We create some fuzzy rules about how much to steer in any direction to avoid hitting the obstacle based on how far we are from it and to what degree it’s in our way. Happy Robot (幸せなロボット) 0 M 20 M 90° 0° -90° Translations by Google. Are they any good?

  11. El mal de plantas Distance Trajectory Turn HardRight Near Center Soft Right AND THEN IF Near 10 ° 10 M Center Far Implication of the rules: RULE 1. “Near” is less than “Center” we take the min since we are using “AND” RULE 2. We are getting near so we do a “Soft Right” RULE 3. We center to a certain degree since the obstacle is still kind of far away. Happy Robot (幸せなロボット) 0 M 20 M 90° 0° -90°

  12. Distance Trajectory Turn HardRight Near Center Aggregation Soft Right AND THEN IF Near 13 ° 9 M Far Defuzzification: Center of gravity – Turn -10 ° We can see that the second rule gives us a slight right turn much of the time. Thus, it’s not a very good rule! Lets get rid of it… 0 M 20 M 90° 0° -90°

  13. Distance Trajectory Turn HardRight Near Center 13 ° 9 M Center Far Center of gravity – Turn -10 ° The second rule turned out to not be very helpful anyways… 0 M 20 M 90° 0° -90°

  14. Distance Trajectory Turn HardRight Near Center 10 ° 6 M Center Far Center of gravity – Turn -17 ° Thus, as we get closer and the obstacle is more centered in our trajectory, we will tend to turn more to the right. 0 M 20 M 90° 0° -90°

  15. The robot works in continuous time • The fuzzy rules should change slightly at each time step. • We don’t want the robot to jerk to a new trajectory too quickly. Smooth movements tend to be better. • How often we need to update the controller is dependant on how fast we are moving. • For instance: If we update the controller 30 times a second and we are moving < 1 kph then movement will be smooth. • Ideally, the commands issued from the fuzzy controller should create an equilibrium with the observations.

  16. Our robot has momentum • We have somewhat implicitly integrated the notion of momentum. • This is why we would slow down as we get closer to an obstacle • What about more refined control of speed and direction? • Use the derivative of speed and trajectory to increase or decrease the rate of change. • Thus, if it seems like we are not turning fast enough, then turn faster and visa versa.

  17. Distance Trajectory Turn Hard Right Near Center AND THEN IF Center Far DTrajectory Soft Left Far-ish? 0 M 20 M 90° 0° 10° -90° -25° Change in Trajectory Prevent over steering with our robot

  18. Distance Trajectory Speed Slow Near Center AND THEN IF Fast Far 0 M 20 M DDistance Very Slow Quick 0 mps 10 mps 90° 0° 10 kph -90° 0 kph Possible Rules to define speed

  19. Demo 

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