Transcript
Introduction to RoboticsCourse Summary
…or all you need to know in 75min
December 6, 2011
Retrospective
• Introduction• Locomotion• Kinematics• Sensors
– Overview– Vision-based ranging– Features & Uncertainty
• Localization and Mapping– Overview– Markov Localization– Kalman filter
Midterm
Ratslife
Locomotion: Control
• Actuators are controlled by a periodic signal
• Think about the desired phase difference, not about the desired angle
Locomotion: Stability
• Dynamically stable: has to keep moving in order not to fall
• Statically stable: does not fall when resting
3-Point rule
3 legs : static stability6 legs : static walking
Kinematics
• Forward kinematics– Calculate impact of
actuators on world coordinates
• Inverse kinematics– Calculate actuation
based on desired change in world coordinates
Wheel kinematic constraints
• Wheel cannot slide (in this class)
• Exception: Castor, swedish and spherical wheels
Recipe: Forward and Inverse Kinematics
• Start with forward kinematics
• Focus on actuated wheels
• Check constraints• Keep all but one wheel
fixed• Add wheels up• Inverse kinematics: solve
equation system
Exam preparation: Kinematics
• Solve differential wheel drive (textbook) on paper
• Revisit Midterm example (tricyle)
Sensors
• What can be sensed?• How can be sensed?• Navigation– Distance– Position
• Vision
Laser Range Scanner
• Measures phase-shift of reflected signal
• Example: f=5MHz -> wavelength 60m
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
Example: Position Sensing
Odometry
GPS
Gyroscope
Control input
Landmarks
Exam preparation: Sensors
• Get an overview over robotic sensors• Reason about what the different sensor
properties, e.g. bandwidth mean for this specific sensor
Uncertainty: The Gaussian Distribution
Key concept: Error Propagation
• Intuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weighted
Covariance matrixrepresenting input
uncertainties
Covariance matrixRepresenting output
uncertainties
Function relating sensor inputto output quantities
Differential Wheel Robot Odometry
How does the error build up?
• Ingredient 1: variance on wheel-speed / slip
• Ingredient 2: variance on previous position estimate
• Relation between wheel-speed and position– Derivative wrt error– Derivative wrt position
Error propagation
Wheel-Slip
f=
Localization
p(A^B) =p(A|B)p(B)=p(B|A)p(A)
p(loc|sensing)=p(sensing|loc)p(loc)
Example 1: topological map
• Detect open/close doors using sonar
p(n|i)=p(i|n)p(n)
Example 1: topological map
Kalman Filter: Intuition
1. Predict2. Update
Basics: Fuse two Measurements
• Multiple measurements
• Actual value• Mean-square error• Weights 1/
• Optimal error
Kalman FilterMeasurement
Kalman Filter Gain
Exam preparation
• No need to derive any of the equations• Understand what they mean and what the
intuition is• Understand Bayes formula and how it maps to
localization
A* Shortest Path Routing
• Heuristic path cost biases search toward goal• Heuristic here: Manhattan distance• Extra rule: Always start from cell with lowest
cost
Organization
• Wednesday: Q&A in the CSEL• Final exam: Wednesday, December 15, 7:30
p.m. - 10:00 p.m, CAETE classroom.
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