fuzzy control in robotics

Robots and Virtual Robots I Agents in Physical and Virtual Environments Lecture 4: Fuzzy Control in Robotics Gal A. Kaminka galk@cs.biu.ac.il Fall 2002 © Gal Kaminka, 2 Previously, on Robots I…  Fuzzy set theory, fuzzy logic  Generalizations of set theory and logic  Probability versus Fuzziness (a productive discussion?)  Fuzzy control  IF … THEN … rules where LHS, RHS refer to fuzzy sets  All rules matched, all matching rules combined  Three stages: Fuzzification, inference, defuzzification  Useful when mathematical model of plant unavailable Fall 2002 © Gal Kaminka, 3 This week, on Robots I….  Fuzzy Logic basics  A crash course in Fuzzy Control  Fuzzification, Inference, Defuzzification  Applications of Fuzzy Control in robotics  Simple skills: avoid obstacles, greedy navigation  Issues and challenges to fuzzy control  Curse of dimensionality  Real-time responses  Incomplete controllers Last Week Fall 2002 © Gal Kaminka, 4 But first…. םיפד איצוהל .1 םיאתמ רלורטנוקב דחא קוחמ רתוי רשאכ הרוק המ ?רוסנס תאירקל .2 םהמNegative Rules? Fall 2002 © Gal Kaminka, 5 Fuzzy Control  When plant model unavailable  A set of rules associating sensor readings with action IF Close-by(right-sensor) THEN Left IF Clear(forward-sensor) THEN Forward IF Right(goal-location) THEN Right  All rules fire in parallel, and their results are combined Fall 2002 © Gal Kaminka, 6 Three stages  Fuzzification (each rule):  Sensor reading are matched with the IF side  LHS: Left-Hand Side  Inference (each rule):  As a function of matched LHS, THEN part is operationalized  RHS: Right-Hand Side  Defuzzification (all rules together)  The operationalized RHS of all rules are combined  A crisp result is extracted Fall 2002 © Gal Kaminka, 7 Fuzzification  Determine degree of membership of sensor reading  IF Close-by(right-sensor) AND FAR(goal-location) THEN Left  IF Close-by(forward-sensor) THEN Left OR Right  Get value of sensors right, forward, goal-location  Find membership value of value in fuzzy sets Close- by  This value determines activation of this rule Fall 2002 © Gal Kaminka, 8 Inference (see blackboard)  Each rule’s LHS activation determines RHS activation  Two common types of inference:  Cut RHS set(s) to LHS activation value  Scaling: Multiply RHS function by LHS activation value Fall 2002 © Gal Kaminka, 9 Defuzzification (see blackboard)  Aggregation: Combine all RHS sets  Approaches:  Non-additive: Multiple contributions count as one (e.g., max)  Additive: Multiple contributions strengthen result (sum)  Now we have a combined output of the system  Pick a crisp value to send to actuators:  Max: Pick maximum value as representing set  COG: pick center-of-gravity as representing set  MOM: Mean-of-Maxima  … Fall 2002 © Gal Kaminka, 10 ?תולאש [...].. .Fuzzy Control in Robotics    Mathematical model of task, robot body unavailable Information from sensors is often imprecise, uncertain Good match with fuzzy control Fall 2002 © Gal Kaminka, 11 Case Study: Controller for YODA  Denning MRV-3 Robot     Old: ~20 years Massive: ~1m tall, ~75cm wide, ~30Kg 24 sonar sensors (distance), internal x, y, theta odometry Task:... heading=left IF small-posive(angle-to-goal) THEN heading=small-right … IF dead-on(angle-to-goal) THEN heading=zero-change Fall 2002 © Gal Kaminka, 17 Design alternative 2 summary   Add some pre-processing of sensor data Gain scalability, readability  Notice that we can do goal-seeking in about 10 rules! Sonar (x24) Speed Controller Curr X, Y, Theta Heading Change Goal X, Y Fall 2002 © Gal Kaminka,... rules to increase weight Add distance to goal into obstacle-avoidance rules Re-define fast to be slower Fall 2002 © Gal Kaminka, 27 A systematic method  There are essentially two sets of rules in our design    Goal-seeking Obstacle-avoiding Split controller into two, then merge their results Sonar (x24) Theta Avoid Obst Seek Goal Current X, Y Goal X, Y Fall 2002 Speed Heading Change Speed Heading Change... sensor readings again Treat sensors relative to heading:     IF obstacle-close(forward) THEN speed=stop IF obstacle-close(right30) THEN speed=slow, turn=left IF obstacle-close(left50) THEN speed=slow, turn=small-right …… Fall 2002 © Gal Kaminka, 21 Goal-relative sensing   Create virtual-sensors based on heading In principle, we can do this using rules        IF north(current-heading) THEN... north(current-heading) THEN left45=north-west IF north(current-heading) THEN right90=east … IF south(current-heading) THEN forward=south IF south(current-heading) THEN left45=south-west …… Fall 2002 © Gal Kaminka, 22 Goal-relative sensing  Note these are no longer fuzzy rules   Indeed, why do this with rules?     Only dynamically rename sensors, no inference Simple pre-processing algorithm Yet... this not work? What did we give up here? Fall 2002 © Gal Kaminka, 23 Controller: Complete Design Sonar (x24) Theta Curr X, Y Speed Controller Heading Change Goal X, Y Fall 2002 © Gal Kaminka, 24 From design to implementation   Requires assigning membership values There is significant literature on doing this   Including automated learning For our purposes, this can be done by hand    Pick trapezoid... combinations Raw heading   IF current-heading(theta0) AND current-at(x0,y0) AND goalat(xg,yg) THEN turn=D0 { some function of angle to goal } Fall 2002 © Gal Kaminka, 14 Problem: Too many rules    For each possible location And each heading in each location How is this ever going to scale? Fall 2002 © Gal Kaminka, 15 Design alternative 2    Let’s do some pre-processing of the sensors Instead... THEN obstacle-close=true …… Fall 2002 © Gal Kaminka, 29 Problems with fuzzy control   Avoid-obstacles controller needed to know the goal This may result in rule explosion   Would be much simpler to have negative rules    All combinations of sensor readings and goal state But these are not trivial in fuzzy Defuzzification, inference methods may or may not work Also, what do we do with multi-modal... north(current-heading) THEN speed=slow, turn=small-left IF object-close(north-east) AND south(current-heading) THEN speed=fast, turn=no-change … IF object-close(south) AND north(current-heading) THEN speed=fast, turn=no-change Fall 2002 © Gal Kaminka, 20 Alternative Design 2  Again, seems we consider all combinations    For each sensor and heading, consider obstacle distance Let’s try pre-processing the... location Angle from current heading to line pointing to goal Then controller looks very different Fall 2002 © Gal Kaminka, 16 Design Alternative 2 Rules  Distance difference     IF large(distance-to-goal) THEN speed=fast IF small(distance-to-goal) THEN speed=slow IF zero(distance-to-goal) THEN speed=zero Heading Difference      IF large-positive(angle-to-goal) THEN heading=right IF large-negative(angle-to-goal) . 2002 © Gal Kaminka, 3 This week, on Robots I….  Fuzzy Logic basics  A crash course in Fuzzy Control  Fuzzification, Inference, Defuzzification  Applications of Fuzzy Control in robotics  Simple. I Agents in Physical and Virtual Environments Lecture 4: Fuzzy Control in Robotics Gal A. Kaminka galk@cs.biu.ac.il Fall 2002 © Gal Kaminka, 2 Previously, on Robots I…  Fuzzy set theory, fuzzy. as representing set  COG: pick center-of-gravity as representing set  MOM: Mean-of-Maxima  … Fall 2002 © Gal Kaminka, 10 ?תולאש Fall 2002 © Gal Kaminka, 11 Fuzzy Control in Robotics  Mathematical