Autonomous Robot Navigation

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Autonomous Robot Navigation

• Panos Trahanias
• e-mail trahania_at_csd.uoc.gr

??475 Fall 2007
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Mobile Robots - Examples
The museum tour-guide Minerva
The Mars rover Sojourner
The museum tour-guide Lefkos
The RHex Hexapod
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Typical Mobile Robot Setup
Sensors Stereo vision Sonars Bump
sensors Infrared sensors Laser scanner Bump
sensors Sonars Odometry
Interaction Processing Power Motors
Communications
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Scope of the Course

• Mobile Robots How to move and achieve motion
  target goals in (indoor) environments
• Hence

• Localization (where am I?)
• Mapping, simultaneous localization and mapping
  SLAM (what is my workspace?)
• Path planning (how to get there?)
• Obstacle avoidance ( get there safely)

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Autonomous Navigation- Research Directions

• Given
• An environment representation - Map

• Knowledge of current position C

• Target position G

• A path has to be planned and tracked that will
  take the robot from C to G

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Autonomous Navigation- Research Directions

• During execution (run-time)
• Objects / Obstacles O may block the robot

• The planned path is no-longer valid

X

• The obstacle needs to be avoided and the path may
  need to be re-planned

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Navigation Issues

• Important questions (Levitt et al 91)

• Important navigation issues

Where am I
Robot localization
Where are other places relative to me
Map building
How do I get to other places from here
Path/motion planning
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Navigation Issues Underlying HW
Sensors Stereo vision Sonars Bump
sensors Infrared sensors Laser scanner Bump
sensors Sonars Odometry
Interaction Processing Power Motors
Communications
Laser Scanner
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Range Sensor Model

• Laser Rangefinder
• Model range and angle errors.

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Need for Modeling
Robot
Environment

Need for Appropriate Modeling
Extremely Complex Dynamical System
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Markov Assumption

• State depends only on previous state and
  observations
• Static world assumption
• Hidden Markov Model (HMM)

Bayesian estimation Attempt to construct the
posterior distribution of the state given all
measurements
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A Dynamic System

• Most commonly - Available
• Initial State
• Observations
• System (motion) Model
• Measurement (observation) Model

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Inference - Learning

• Localization (inference task)Compute the
  probability that the robot is at pose z at time t
  given all observations up to time t (forward
  recursions only)

• Map building (learning task)Determine the map m
  that maximizes the probability of the observation
  sequence.

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Belief State
How is the prior distribution represented?
How is the posterior distribution calculated?

• Discrete representation
• Grid (Dynamic) (Dynamic) Markov localization
  (Burgard98)
• Samples Monte Carlo localization (Fox99)
• Continuous representation
• Gaussian distributions Kalman filters (Kalman60)

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Example State Representations for Robot
Localization
Discrete Representations
Continuous Representations
Grid Based approaches (Markov localization)
Particle Filters (Monte Carlolocalization)
Kalman Tracking
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• LOCALIZATION

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Markov Assumption

• Localization determine the likelihood of robots
  state

Given a sequence of observations
Determine the probability
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Markov Assumption

• In practice too difficult to determine the joint
  effect of all observations up to time K.
• Common assumption hidden states obey the Markov
  assumption (static world assumption), so as we
  can factor as

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Markov Assumption
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Markov Assumption
Integrate over all possible states

• All information about past history is represented
  in

Different approaches in this representation lead
to different treatments of the problem.
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Kalman Filtering

• Probabilistic estimation
• Simultaneously maintain estimates for both the
  state x and error covariance matrix P
• Equivalent to say output of a Kalman filter is a
  Gaussian PDF (other methods can handle more
  general distributions)

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Kalman Filtering
Crude localization method integrate robot
velocity commands
Problem info continuously lost, no new info
added. Solution add info from exterioreceptive
sensors.
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Kalman Filtering
Sensor measurements add new info PDF in sensor
space. Localization knowledge (prior to sensor
measurement) is a PDF in state space. Probabilist
ic Estimation merge the 2 PDFs
Two step process prediction update
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Kalman Filtering
Simple observer update
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Kalman Filtering
Prediction
Update
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Kalman Filtering
Observing with probability distributions
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Kalman Filtering
Prediction
Update
where
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Kalman Filtering
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Kalman Filtering
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Kalman Filtering
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Kalman Filtering
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Bayesian Methods
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Bayesian Methods Discrete Approximations
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Bayesian Methods Discrete Approximations
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Bayesian Methods Discrete Approximations
Results
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Bayesian Methods Discrete Approximations
Results
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Bayesian Methods Particle Filters
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Bayesian Methods Particle Filters/Resampling
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Bayesian Methods Particle Filters
Motion Model
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Bayesian Methods Particle Filters
State Belief
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Bayesian Methods Particle Filters
Global Localization
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Bayesian Methods Particle Filters
Global Localization - Results
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Bayesian Methods Sensor Models
Typical Sonar Scan
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Bayesian Methods Sensor Models
Histograms
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• PATH PLANNING

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Bug Algorithms
Bug1
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Bug Algorithms
Bug1
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Bug Algorithms
Bug2
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Bug Algorithms
Bug2
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Bug Algorithms
Bug2
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• POTENTIAL FUNCTIONS

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Potential Field
Attractive Repulsive Forces
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Potential Field
Potential Function
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Potential Field
Attractive Potential
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Potential Field
Repulsive Potential
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Potential Field
BrushFire Algorithm
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Potential Field
Local Minima Problem
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Potential Field
Wavefront Planner
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Navigation Functions
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Navigation Functions
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Value Iteration

• Value Iteration Algorithm
• Dynamic programming (fast)
• Creates potential field (run only once per
  target)
• Initialization rule
• Update rule

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Value Iteration - Results
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• OBSTACLE AVOIDANCE

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Certainty Grid Representation
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VFF Virtual Force Field
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VFF Virtual Force Field
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Polar Histogram
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Polar Histogram
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Motion Candidate Directions
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Traveling Alongside an Obstacle
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Steering Reference
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VFH Example Course
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• CONFIGURATION SPACE

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Two-link Manipulator - Workspace
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Two-link Manipulator Configuration Space
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Obstacles Configuration Space
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Obstacles Configuration Space
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Obstacles Configuration Space
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Obstacles Configuration Space
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Workspace Configuration Space
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Workspace Configuration Space
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Workspace Configuration Space
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Planar Parallel Mechanism