Landmark Selection for Vision-Based Navigation. Pablo L. Sala Joint work with Robert Sim, Ali Shokoufandeh and Sven Dickinson To be presented in IROS 2004 September 17 th , 2004. Robot Navigation. [Leonard and Durrant-Whyte] Where am I? Where am I going? How do I get there? .

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Landmark Selection for Vision-Based Navigation

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Landmark Selection for Vision-Based Navigation Pablo L. Sala Joint work with Robert Sim, Ali Shokoufandeh and Sven Dickinson To be presented in IROS 2004 September 17th, 2004

Robot Navigation • [Leonard and Durrant-Whyte] • Where am I? • Where am I going? • How do I get there?

Robot Navigation • [Leonard and Durrant-Whyte] • Where am I? Localization • Where am I going? • How do I get there?

Robot Navigation • [Leonard and Durrant-Whyte] • Where am I? Localization • Where am I going? Goal Identification • How do I get there?

Robot Navigation • [Leonard and Durrant-Whyte] • Where am I? Localization • Where am I going? Goal Identification • How do I get there? Path-planning

Robot Navigation • [Leonard and Durrant-Whyte] • Where am I? Localization • Where am I going? Goal Identification • How do I get there? Path-planning

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?)

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks?

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks? • Manually

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks? • Manually • Automatically

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks? • Manually • Automatically… but how?

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks? • Manually • Automatically • Store every landmark visible at each location (costly!)

Landmark-Based Navigation • What makes a good landmark? • Distinctiveness (does it tell me where I am?) • Wide Visibility • How do we select good landmarks? • Manually • Automatically • Store every landmark visible at each location (costly!) • Find smallest subset of landmarks that supports reliable navigation (optimal!)

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Collection of images acquired at known discrete points in pose space. Pose recorded and image features extracted and stored in database.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Collection of images acquired at known discrete points in pose space. Pose recorded and image features extracted and stored in database.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Collection of images acquired at known discrete points in pose space. Pose recorded and image features extracted and stored in database.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Collection of images acquired at known discrete points in pose space. Pose recorded and image features extracted and stored in database.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Collection of images acquired at known discrete points in pose space. Pose recorded and image features extracted and stored in database.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization Four features are needed in this set.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization Four features are needed in this set. Only two features needed. Our goal is to find this decomposition.

View-Based Robot Navigation Off-line Exploration Landmark Database Construction On-line Localization • Current pose is estimated using the locations of a small number of features in the current image, matched against their locations in two model views.

Outline • Problem Formulation • Complexity • Heuristic Methods • Results on Synthetic and Real Images • Conclusions

A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MOVRDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that:

A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MOVRDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that: Theorem 1: A -MOVRDP can be reduced to an equivalent 0-MOVRDP, and the solution to this latter problem can be extended to a solution for the original problem.

A Graph Theoretic Formulation Problem Definition: The -Minimum Overlapping Region Decomposition Problem (-MOVRDP) for a world instance <G=(V,E), F, {v}vV> consists of finding a minimum size -overlapping decomposition D = {R1, …, Rd} of V into regions such that: Theorem 1: A -MOVRDP can be reduced to an equivalent 0-MOVRDP, and the solution to this latter problem can be extended to a solution for the original problem. Theorem 2: The decision problem <0-MOVRDP, d> is NP-complete. (Proof by reduction from the Minimum Set Cover Problem.)

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms.

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region:

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 25

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 25

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 19

Heuristic Methods for 0-MOVRDP • 0-MOVRDP is intractable. • Optimal decomposition not needed in practice. • We developed and tested six greedy approximation algorithms. • Algorithm A.x: O(|V|2|F|) k = 4 Features commonly visible in region: 17