Lecture 10: Summary

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.