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 algorithm may 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.