3. Forward Kinematics<br />How does the robot move in world space given its actuator speed and geometry?<br />“Odometry”: forward kinematics for mobile platform<br />Example: from exercise 3<br />
4. Proportional Control<br />N.B.: zero error neq correct position!<br />
5. More on robot kinematics (arms)<br />John Craig<br />Introduction to Robotics<br />Mark Spong, Seth Hutchinson and M.Vidyasagar<br />Robot Modeling and Control<br />
6. Inverse Kinematics<br />How do we need to control the actuators to reach a certain position?<br />Inversion of forward kinematics<br />Examples: Differential wheel drive (Exercise 3)<br />
7. Feedback control<br />Use error between reference and actual state to calculate next control input<br />Change in speed proportional to error<br />Error zero -> speed zero<br />Problem: find stable controllers<br />Example: from exercise<br />K. Ogata<br />Modern Control Engineering<br />
8. Today <br />Perception: Basis for reasoning about the world<br />Understand how a sensor works before using it<br />Case studies<br />
15. Sensor performance<br />Dynamic range: lowest and highest reading<br />Resolution: minimum difference between values<br />Linearity: variation of output as function of input<br />Bandwidth: speed with which measurements are delivered<br />Sensitivity: variation of output change as function of input change<br />Cross-Sensitivity: sensitivity to environment<br />Accuracy: difference between measured and true value<br />Precision: reproducibility of results<br />Hokuyo URG<br />
16. Relation between sensor physics and performance (solutions)<br />Dynamic range: <br />Range: limited by power of light and modulated frequency, smallest wave-length difference measurable<br />Angle: limited by physical setup / trade-off between bandwidth and angular resolution<br />Resolution:<br />Range: Precision of phase-shift measurement<br />Angle: limited by bandwidth / encoder<br />Linearity:<br />Range: phase shift is linear -> signal is linear, but: weak reception makes determination of phase harder<br />Angle: depends on motor implementation<br />Bandwidth<br />Range: speed of light, calculating phase shift<br />Angle: motor speed<br />Sensitivity:<br />Range: Doppler effect -> not relevant in robotics, Confidence in the range (phase/time estimate) is inversely proportional to the square of the received signal amplitude<br />Angle: n.a.<br />Cross-Sensitivity:<br />Range: Glass / reflection properties, 785nm light <br />Accuracy:<br />Range: Precision of phase-shift measurement, strength of reflected light<br />Angle: motor quality<br />Precision: range / variance<br />
17. Infra-red distance sensors<br />Principle: measure amount of reflected light<br />The closer you get, the more light gets reflected<br />Digitized with analog-digital converter<br />Sharp IR Distance Sensor GP2Y0A02YK<br />20-150cm<br />Miniature IR transceiver<br />0-3cm<br />
18. Sensor performance<br />Dynamic range: lowest and highest reading<br />Resolution: minimum difference between values<br />Linearity: variation of output as function of input<br />Bandwidth: speed with which measurements are delivered<br />Sensitivity: variation of output change as function of input change<br />Cross-Sensitivity: sensitivity to environment<br />Accuracy: difference between measured and true value<br />Precision: reproducibility of results<br />Sharp IR Distance Sensor<br />
19. Relation between sensor physics and performance (solutions)<br />Dynamic range: limited by power of light<br />Resolution: limited by ADC, e.g. 10bit -> 1024 steps<br />Linearity: highly non-linear (intensity decays quadratically)<br />Bandwidth: limited by ADC bandwidth (sample&hold)<br />Sensitivity: varies over range due to resolution<br />Cross-Sensitivity: sun-light, surface properties<br />Accuracy: limited by ADC, varies over range<br />Precision: varies over range<br />
20. Infra-red distance sensors in Webots (Exercise 1)<br />Color of the bounding object affects sensor<br />Non-linear relation between distance and signal strength<br />Distance-dependent resolution and noise<br />Software linearization<br />Noise<br />
21. Exercise<br />Design a robot that can<br />Vacuum a room<br />Mow a lawn<br />Collect golf-balls on a range<br />Collect tennis balls on a court<br />Address<br />Sensors<br />Algorithm<br />Mechanism<br />
22. Scratchboard<br />
23. Homework<br />Read section 4.1.7 (pages 117 – 145)<br />Questionnaire on CU Learn<br />Midterm: October 11 (during class)<br />
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