Topological Mapping using Visual Landmarks

1
Topological Mapping using Visual Landmarks

• The work is based on the "Team Localization A
  Maximum Likelihood Approach" paper.
• To simplify the problem, assume
• Landmarks are directional (In Player-Stage
  simulation, landmarks are represented as pairs of
  color boxes.)
• Each episode of motion consists of an in-place
  rotation by ?. Followed by moving straight
  forward by d. ? and d are corrupted by zero-mean
  Gaussian noises.
• The motion and observation forms a directed
  graph.
• When a cycle was detected, use maximum
  likelihood to update graph nodes.

2
Problem One Cycle Detection

• Unlike team localization, in which each Robot can
  be identified correctly, Landmarks with the same
  visual cues (color pairs) are indistinguishable.
• Cycle Detection, when observing a landmark the
  robot has seen before
• Backup old map.
• Assume a cycle is detected, update map
  accordingly.
• After updating the map, compute the average
  negative-log-likelihood of updated graph edges.
  If the average is below a threshold, keep the new
  map.
• Otherwise, restore the old map and add a new
  landmark.
• The problem is setting the threshold, which
  depends on the motion model parameters.

3
Problem Two Gradient Descent

• The project uses the simplest Steepest Descent
  algorithm to update the map. Which poses the
  problem of slow converging.
• Each node in the graph update itself to maximize
  the total local likelihood of connecting edges.
  The global maximum then is slow to reach.
• Exploiting the algorithm
• When update motion nodes, ignore landmark nodes
  that is newly observed and have not been updated
  before, except the on which forms the cycle.
• Applying better gradient descent algorithmmay
  improve the result.

4
Result

• Cycle Detection
• Can detect cycles when observed a landmark the
  robot have seen before.
• Can distinguish similar landmarks that are placed
  not too close to each other.
• Map Updating
• Not very good due to Steepest Descent algorithm.