1. Pure Topological Mapping in Mobile Robotics Authors ： Dimitri Marinakis Gregory Dudek Speaker ：李宗明 M99G0103 IEEE TRANSACTIONS ON ROBOTICS, VOL. 26, NO. 6, DECEMBER 2010 The Centre for Intelligent Machines, McGill University. 2016/3/151

2. Outline Introduction Problem specification Exploration strategies Hypotheses management Results Conclusions 2016/3/152

3. Introduction Given this limited sensing capability and without the use of any markers or additional information, we will show that the construction of a topological map is nevertheless feasible. The topological mapping problem we consider in this paper can be considered a subclass of the simultaneous localization and mapping (SLAM) problem in robotics, which considers mapping an unknown environment using imperfect sensory data. 2016/3/153

4. Robot Graph Exploration Errors of type OLD-LOOKS-NEW, in which the current vertex is assumed to be newly explored but was actually visited earlier; Errors of type MIS-CORRESPONDENCE, in which the current vertex is thought to be a certain previously visited vertex but is actually a different previously visited vertex; 2016/3/154

5. Robot Graph Exploration Errors of type NEW-LOOKS-OLD, in which a vertex is assumed to have been previously visited but is actually new. These error types are called correspondence errors. 2016/3/155

6. Contributions and Paper Organization The new exploration strategies that attempt to reduce correspondence errors, where possible. The incorporation of arbitrary feature vectors into the problem formulation. A new method to maintain consistent models in the exploration tree in which only a bounded set of likely hypotheses are stored based on the principle of Occam’s Razor. 2016/3/156

7. Problem Specification ψ(v i, e l,i, r) = v j 2016/3/157

8. Problem Specification This is especially true during the early part of the exploration in which not enough observations have been gathered to prove some models inconsistent. The size of the complete tree quickly becomes intractable for all but trivially small observation sequences. The goal of paper is to manage the growth of the exploration tree so that only those world models that appear of relatively high likelihood are retained. 2016/3/158

9. Exploration Strategies Breadth-First Traversal (BFT) Breadth-First Ears Traversal(BFET) 2016/3/159

10. Exploration Strategies 2016/3/1510

11. Breadth-First Ears Traversal(BFET) 2016/3/1511 1) For an edge from the vertex, the robot explores the path p1, beginning in one direction for some number of steps (until, for example, a node with the same degree as v is encountered). 2) The robot then backtracks to vertex v and explores the path p2 in the opposite direction for the same number of steps, that is appropriately located with reference to e1. 3) Steps 1 and 2 are repeated of steps taken in both directions until the degree trace for the path taken in two directions matches up, i.e., path p1 visits its vertices in the reverse order of those in p2.

12. Loop-Based Exploration 2016/3/1512 The intent of the revisiting portion of the strategy is to slow the growth of the hypothesis tree by showing the inconsistency of some of the currently maintained hypotheses. The approach has no coverage guarantees but shows good performance in practice.

13. Loop-Based Exploration 2016/3/1513 If the robot is currently visiting a vertex of degree three or higher, then it selects, with a probability p, the first edge from the incoming reference edge for its next traversal. This corresponds to choose r = 1. Otherwise, it takes, with probability (1-p), the second edge r = 2 from the incoming reference edge.

14. Hypothesis Assessment Using Topology 2016/3/1514 Hypothesis Assessment Using Topology Hypothesis Assessment Using Feature Vectors ◦ How to use this feature vector in evaluation of the “simplicity” of a candidate hypothesis. Hypotheses Management Algorithm(HMA)

15. Hypotheses management 2016/3/1515

16. Hypotheses management 2016/3/1516

17. Hypotheses management 2016/3/1517

18. Results 2016/3/1518

19. Results 2016/3/1519

20. Conclusions  Combines an exploration strategy that attempts to eliminate inconsistent models with a HMA that bounds the number of models maintained at each step based on the principle of Occam’s razor  In future work will consider the effect of dynamically adapting the exploration strategy to the region being explored and the current hypotheses maintained.  A criteria for halting the exploration process would also be of use. 2016/3/1520