2. Review: Kinematics and Control Concepts Forward Kinematics “Odometry” Feed-back Control Inverse Kinematics
3. Forward Kinematics How does the robot move in world space given its actuator speed and geometry? “Odometry”: forward kinematics for mobile platform Example: from exercise 3
4. More on robot kinematics (arms) John Craig Introduction to Robotics Mark Spong, Seth Hutchinson and M.Vidyasagar Robot Modeling and Control
5. Inverse Kinematics How do we need to control the actuators to reach a certain position? Inversion of forward kinematics Examples: Differential wheel drive (Exercise 3
6. Feedback control Use error between reference and actual state to calculate next control input Change in speed proportional to error Error zero -> speed zero Problem: find stable controllers Example: from exercise K. Ogata Modern Control Engineering
7. Today Perception: Basis for reasoning about the world Understand how a sensor works before using it Case studies
12. Laser Range Scanner Measures phase-shift of reflected signal Example: f=5MHz -> wavelength 60m
13. Examples 2 D 3D (PR2 sweep) (after classification)
14. Sensor performance Dynamic range: lowest and highest reading Resolution: minimum difference between values Linearity: variation of output as function of input Bandwidth: speed with which measurements are delivered Sensitivity: variation of output change as function of input change Cross-Sensitivity: sensitivity to environment Accuracy: difference between measured and true value Precision: reproducibility of results Hokuyo URG
15. Relation between sensor physics and performance (solutions) Dynamic range: Range: limited by power of light and modulated frequency, smallest wave-length difference measurable Angle: limited by physical setup / trade-off between bandwidth and angular resolution Resolution: Range: Precision of phase-shift measurement Angle: limited by bandwidth / encoder Linearity: Range: phase shift is linear -> signal is linear, but: weak reception makes determination of phase harder Angle: depends on motor implementation Bandwidth Range: speed of light, calculating phase shift Angle: motor speed Sensitivity: 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 Angle: n.a. Cross-Sensitivity: Range: Glass / reflection properties, 785nm light Accuracy: Range: Precision of phase-shift measurement, strength of reflected light Angle: motor quality Precision: range / variance
16. Infra-red distance sensors Principle: measure amount of reflected light The closer you get, the more light gets reflected Digitized with analog-digital converter Sharp IR Distance Sensor GP2Y0A02YK 20-150cm Miniature IR transceiver 0-3cm
17. Sensor performance Dynamic range: lowest and highest reading Resolution: minimum difference between values Linearity: variation of output as function of input Bandwidth: speed with which measurements are delivered Sensitivity: variation of output change as function of input change Cross-Sensitivity: sensitivity to environment Accuracy: difference between measured and true value Precision: reproducibility of results Sharp IR Distance Sensor
18. Relation between sensor physics and performance (solutions) Dynamic range: limited by power of light Resolution: limited by ADC, e.g. 10bit -> 1024 steps Linearity: highly non-linear (intensity decays quadratically) Bandwidth: limited by ADC bandwidth (sample&hold) Sensitivity: varies over range due to resolution Cross-Sensitivity: sun-light, surface properties Accuracy: limited by ADC, varies over range Precision: varies over range
19. Infra-red distance sensors in Webots (Exercise 1) Color of the bounding object affects sensor Non-linear relation between distance and signal strength Distance-dependent resolution and noise Software linearization Noise
20. Exercise Design a robot that can Vacuum a room Mow a lawn Collect golf-balls on a range Collect tennis balls on a court Address Sensors Algorithm Mechanism
