High-dimensional Winding-Augmented Motion Planning with 2D topological task projections and persistent homology

2016 ◽  
Author(s):  
Florian T. Pokorny ◽  
Danica Kragic ◽  
Lydia E. Kavraki ◽  
Ken Goldberg
Keyword(s):  
Motion Planning ◽  
Persistent Homology ◽  
High Dimensional

scholarly journals Online, Interactive User Guidance for High-dimensional, Constrained Motion Planning

2018 ◽  
Author(s):  
Fahad Islam ◽  
Oren Salzman ◽  
Maxim Likhachev
Keyword(s):  
Motion Planning ◽  
Domain Knowledge ◽  
High Dimensional ◽  
Constrained Motion ◽  
Significant Progress ◽  
Planning Framework ◽  
Planning Algorithm ◽  
Speed Up ◽  
User Guidance ◽  
Intermediate Configuration

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration q^, which is used to bias the planner to go through q^. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafted domain-dependent heuristics.

scholarly journals Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

2021 ◽  
Vol 15 ◽  
Author(s):  
Louis Kang ◽  
Boyan Xu ◽  
Dmitriy Morozov
Keyword(s):  
Topological Structure ◽  
Spatial Representation ◽  
Persistent Homology ◽  
High Dimensional ◽  
Head Direction ◽  
Representation System ◽  
Topological Structures ◽  
Neural Recordings ◽  
Persistent Cohomology ◽  
Low Dimensional

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

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