Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopy-Aware RRT* : Toward Human-Robot Topological Path-Planning Daqing Yi Michael A. Goodrich Kevin D. Seppi Computer Science Department Brigham Young University
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Human-Robot Collaboration Instruct a robot executing a task
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Collaborative Path-Planning T opology space Metric space
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopy Definition A path can can be continuously deformed into another without encroaching any obstacle σ 1 ≃ σ 2 σ 1 �≃ σ 2 Homotopy Class A set of paths that are homotopic
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopy-based Path Planning Find the optimal paths of several homotopy classes σ (0) = x init σ (1) = x goal H ⊆ ❍ ( x init , x goal ) ∀ h i ∈ H , σ ∗ h i = arg max σ ∈ X free ∧ h ( σ )= h i Cost ( σ )
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Framework Map Topology Constraint Homotopy Classes Homotopic TrimREP Map Strings Paths DFA Homotopy HARRT* Optimal Paths Identification
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Spatial Semantic Hierarchy Kuipers , “The spatial semantic hierarchy,” Tech. Rep. AI99-281, 29, 1999.
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Approaches of Homotopic Path-Planning (a) Space-cut approaches 1 , 2 (b) Homology approaches 3 , 4 (c) Reference-frame approaches 5 , 6 (a) (b) (c) 1 Hershberger et al. , “Computing minimum length paths of a given homotopy class,” Computational Geometry, 1994. 2 Grigoriev et al. , “Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane,” ISSAC 98. 3 Bhattacharya , “Search-based path planning with homotopy class constraints,” AAAI 2010. 4 Florian et al. , “Multiscale topological trajectory classification with persistent homology,” RSS 2014. 5 Hernandez et al. , “A topologically guided path planner for an AUV using homotopy classes,” ICRA 2011. 6 Kim et al. , “Path planning for a tethered mobile robot,” ICRA 2014.
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Map Decomposition Sampling representative S1-1 point in each obstacle Sampling the center point Generating a radial structure S1-0 S4-0 S2-0 Reference frames separate S3-0 regions An ID for a reference frame S3-1 A string for a sequence of reference frames
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Topology of DFA S1-1 S1-0 S4-0 S2-0 Region ⇒ Node S3-0 Reference frame ⇒ Edge S3-1 Deterministic Finite Automata S1-1 Path ⇒ String S1-0 String block S4-0 S2-0 A set of paths that generates the S3-0 same string by DFA S3-1
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopic DFA S1-1 S1-0 S4-0 S2-0 S3-0 S3-1 S1-1 Homotopic equivalence in crossing the center point S1-0 S2-0 Merge regions that connect S3-0 S4-0 with the center point S3-1
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Hierarchy of Path Partition
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion REP String Definition A string made up of recursive embedded palindromic substrings Example A path crosses several reference frames and backtrack Example: ε ww R uvv R ww R u R REPTrim () Before deform After deform trim REP string
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopic Equivalence Identification Theorem Removing all the REP substrings of ▼ h ( σ ) yields the v ∗ i for which Γ ▼ h ( σ ) ≃ Γ v ∗ i . Corollary REPTrim ( ▼ h ( σ i )) = REPTrim ( ▼ h ( σ j )) iff σ i ≃ σ j .
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Homotopy-Aware RRT* Homotopic identification of each branch Bidirectional RRT* Reference Frame start goal goal Homotopic identification Bidirectional RRT*
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Flow Iteration Start Tree Sample Sample Goal Tree Add Vertex Add Vertex Paths of Homotopy Classes Rewire Vertices Rewire Vertices Find a Path Find a Path
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Human-Robot Interactive Path-Planning Quickly go from point A to point B through a Quickly go from point A to point B making sure to sequence of specific regions. visit some regions and avoid other regions. 1 2 3 4 In quickly going from point A to point B, I prefer some types of paths over others, but I recognize that tradeoffs may be needed.
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Single Homotopy Class
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Multiple Homotopy Classes Unidirectional Tree Bidirectional Tree
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Multiple Homotopy Classes
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Interactive Graphical Interface Sketch reference Planned path
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Nature Language Interface “Go between box 8 and box 6, and avoid the left of box 1”.
Introduction Related Work Homotopy Identification Homotopy-Aware RRT* Experiments and Application Conclusion Outline Introduction 1 Human-Robot Path-Planning Homotopy Related Work 2 Homotopy Identification 3 Map Decomposition Homotopic Equivalence Homotopy-Aware RRT* 4 Experiments and Application 5 Experiments Single Homotopy Class Multiple Homotopy Classes Application Conclusion 6
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