Topology

Study of geometric properties preserved under continuous deformations.

What is Topology?Open and Closed SetsContinuous Functions
Topological InvariantsCompactness and ConnectednessManifolds and Higher Dimensions
Computer Graphics and AnimationRobotics and Path PlanningData Analysis and Machine Learning
Visualize and DrawUse Analogies and Stories
What is Topology?Open and Closed SetsContinuous FunctionsTopological Invarian...Compactness and Conn...Manifolds and Higher...Computer Graphics an...Robotics and Path Pl...Data Analysis and Ma...Visualize and DrawUse Analogies and St...
Practical Applications

Robotics and Path Planning

Navigating the World: Topology in Robotics

Robots need to figure out how to get from one place to another without bumping into things. Topology helps by describing the space the robot moves in and finding paths that avoid obstacles.

How It Works

  • Robots model their environment as a topological space.
  • Algorithms use connectedness and holes to find safe routes.

Examples

  • A robot vacuum finds its way around furniture using a map of open and blocked areas.

  • Drones navigate through buildings by understanding which spaces are connected.

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Data Analysis and Machine Learning