1. Using Incomplete Online Metric Maps for Topological Exploration with the Gap Navigation Tree Liz Murphy and Paul Newman Mobile Robotics Research Group, Oxford University, UK

2. Oxford Mobile Robotics Group The Problem Path Planning: How to get from A->B? Navigation: Knowing where you are when going from A to B Exploration: Deciding what B is. Possible Approach: Gap Navigation Tree –B. Tovar, R. Murrieta and S. M. LaValle, Distance-Optimal Navigation in an Unknown Environment without Sensing Distances, IEEE Transactions on Robotics (2006) –Very lightweight representation of space Uses a minimalistic sensor (gap sensor) based on a simple range scanner to detect gaps and build a tree structure –Returns a complete topological map of a simply-connected 2D region –Idea of using such a lightweight process to ‘drive’ an underlying SLAM system is appealing

3. Oxford Mobile Robotics Group Summary of Gap Navigation Tree Gap = discontinuity in depth information in the robot’s field of view GNT requires a Gap Sensor to identify and recognize gaps as robot moves –Ideal, infinite range sensor –Returns cyclical order of gaps as seen from the robot, no metric representation required Gaps correspond to regions of free space –Lie at the boundary between visible region and the shadow region not visible to robot Tree structure encodes the relationship between these regions in a topological map –Each gap is a node in the tree –Reflects combinatorial changes in the visibility region of the robot –Reflects how the environment appears relative to the position of the robot

4. Oxford Mobile Robotics Group Overview Summary of Gap Navigation Tree operation Highlight the difficulties with practical implementation of the gap sensor Present a probabilistic Gap Sensor to detect and track gaps Present an architecture to enable online exploration and map building using an existing SLAM system, the probabilistic gap sensor and the Gap Navigation Tree algorithm

5. Oxford Mobile Robotics Group Critical Gap Events Gaps appear or disappear as robot crosses an inflection ray Gaps split or merge as the robot crosses a bitangent ray Update tree in accordance –Appear/disappear add or remove node from root of tree –Merge add or remove Children of root node are those gaps currently seen by Gap Sensor All other gaps in the tree were once seen by sensor but have merged Differentiate between gaps which have been completely explored and those which represent unseen areas Can be used to drive exploration by chasing down branches of the tree until all regions have been seen Appear abcab Disappear abcdc ab Split Merge Above figure: http://planning.cs.uiuc.edu

6. Oxford Mobile Robotics Group GNT Operation

7. Oxford Mobile Robotics Group But in reality … Issues with adopting the GNT Predicated on existence of perfect gap sensor –Capable of tracking gaps perfectly even as the robot moves across non-smooth points in the boundary and the gaps jump discontinuously Predicated on ability to observe world with infinite resolution –In reality sensor range limitations produce gaps (may or may not be real gaps) at the end of corridor walls Not immediately applicable to integration with discrete laser based SLAM system: –Map is discrete –Sensor is discrete

8. Oxford Mobile Robotics Group Why complicate things with a map? Laser generates samples from continuous surfaces. –Naïve policy and common pathologic sensing geometry can produce faux gaps. Motivates use of accumulation of data to mitigate this –Precisely what SLAM does for us Idea: Use SLAM map to generate a superior Gap Sensor, not “ideal”. –Take a probabilistic approach so that we can still track gaps even when the range sensor fails to find correct gaps Encapsulate the uncertainty in sensing by representing gap location at time=k by a probability distribution g k Faux Gap

9. Oxford Mobile Robotics Group Gap Detection Decide on angular resolution Allocate each laser data point to an angular bin Take the closest point from each bin to compute the visibility map –Gives an approximation to the visible region Differentiate to find gap location g k –Test for gaps against threshold –Resolve to an [x,y] location (with associated covariance) –Location is a Tangent Point as line between robot and TP is tangential to the corner

10. Oxford Mobile Robotics Group Gap Tracking in a Sampled Representation Using pose-based SLAM Map is dense aggregate of individual points Local shape of map can be used to generate a probabilistic model of gap motion across time steps –Helps us to cope with the addition of a chunk of point cloud data to the SLAM map t=kt=k+1t=k-1

11. Oxford Mobile Robotics Group Formulation of Gap model from SLAM Map Gap Motion Model –Given the location of the gap at t=k-1 and the current state of the map, model the distribution of its current location as a 1 st order Markov process Prediction –Integrate out the last estimate of the gap’s location to come up with the predicted location at t=k Prediction gives us p(g k pred ) –Used to reconcile against p(g k detect )

12. Oxford Mobile Robotics Group Gap Motion Model Is a gaussian: Γ is a function –D is a diagonal scaling matrix –Used to exaggerate the covariance of the nearest neighbours to encompass potential gap movement where

13. Oxford Mobile Robotics Group Data Association Reconcile detected and predicted g k Mimic the operation of the ideal angular gap sensor by converting our g k =[x k,y k ] locations to bearing measurement –Do this for both detected and predicted g k Χ 2 test used to determine associations Multiple associations show that splitting or merging is occurring –Set relatively wide threshold for the Χ 2 test to allow these to be captured g k (detected) g k (predicted) Two new associations to the same old gap indicates split t k-1 tktk

14. Oxford Mobile Robotics Group Integration SLAM mapping generates dense aggregate map Map allows implementation of virtual gap sensor Tracking of gaps over time substantially increases performance and stability of GNT implementation SLAM System Gap Navigation Tree Map informs Gap Tracking GNT drives Navigation process

15. Oxford Mobile Robotics Group Conclusions GNT can be driven by data from a far from GNT- ideal sensor Good use can be made of the metric structure of the local map to aid in the understanding of the perception of apparent gap behaviour. SLAM map need not be global –so we can still hold onto a light weight exploration formulation Future work –Further improve virtual gap sensor by using Gaussian Processes to model discrete sensor data or add policy to actively increase local metric map sample density

16. Oxford Mobile Robotics Group Questions Questions?

17. Oxford Mobile Robotics Group Results