Grisetti 2011 - Tutorial graph-based SLAM

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Backlinks: What is SLAM?

Abstract

• formulate SLAM using a graph
  • nodes: poses of the robot (as well as landmark postiions) at different points in time
  • edges: constraints between poses
    • come from
      • sensor measurements/observations
      • robot movement/control input
    • constraints can contradict each other, due to effect of noise in sensor readings
• solve the graph, i.e. compute the map: find the spatial configuration of the nodes that best satisfy the constraints/edges
• tutorial for back-end (optimisation) part of graph-based SLAM

:: Navigation task: requires a map and knowledge of current position relative to locations in the map

The need for an accurate map

• systems navigating the map don’t have to rely on external reference systems like GPS sensors
  • GPS isn’t suitable for indoor environments
• can operate in complex environments while relying only on their on-board sensors

Filtering vs. smoothing Filtering: on-line state (robot pose, map) estimation; “on-line” because incremental in nature Smoothing: full trajectory estimation, typically rely on LSQ minimisation

History of graph-based formulation

• initially unpopular due to high solving complexity (high dimensional state spaces)
• later:
  • use structure of SLAM problem
    • static world assumption
    • Markov assumption
  • advancements in sparse linear algebra
• now: graph-based SLAM is state-of-the-art (w.r.t. accuracy, speed)

Modelling the probabilistic SLAM formulation

• DBN (shows temporal structure)
• Graph-based (shows spatial structure)

Temporal vs spatial pose graphs

Graph-based SLAM

• node:
  • robot pose, labelled according to location (as opposed to time as in DBN)
  • measurement acquired at that position
• edges: spatial constraints (in the form of probability distributions) between poses
  • from odometry/observations
  • :: g2o edges are constraints, which are the optim. function terms
  • edges are like an abstraction of raw measurements into ‘virtual measurements’ (using probability distributions, observation model etc.)
• main tasks of graph-based SLAM:
  • [graph construction] constructing the graph from raw measurements
    • front-end
    • data association
    • very sensor-dependent
    • “How to interpret sensor data to obtain the graph constraints?”
  • [graph optimisation] finding best pose configuration from graph
    • back-end
    • relies on abstract representation of data, is sensor agnostic
    • “How to compute the map given the constraints?”
• front- and back-end executions are interleaved (front end requires prior term which comes from back-end)

Observation model

• The observation model is usually multimodal:
  • a single observation may result in multiple edges (in the spatial graph)
  • “a feature can be observed from multiple view points/camera poses”
  • the graph connectivity
• Due to this multimodality, the Gaussian assumption does not hold