Sphere world
Encyclopedia
A sphere world is a mathematical concept used in robotic motion planning. Essentially, if the environment is represented as a sphere, and the robot and obstacles within the environment are represented as spheres, then it is possible to construct navigation function
s which create paths from a start position to a goal position. Although the real world is rarely composed of spheres, sphere worlds are still useful for motion planning, as they are topologically equivalent to star world
s.
Navigation function
Navigation function usually refers to a function of position, velocity, acceleration and time which is used to plan robot trajectories through the environment...
s which create paths from a start position to a goal position. Although the real world is rarely composed of spheres, sphere worlds are still useful for motion planning, as they are topologically equivalent to star world
Star world
This article is about the robotic concept. For the TV channel, see STAR World.Star worlds are mathematical concepts used in robot navigation. Essentially, a star world is any n-dimensional shape that can be mapped to a sphere world of the same dimension...
s.
See also
- Navigation functionNavigation functionNavigation function usually refers to a function of position, velocity, acceleration and time which is used to plan robot trajectories through the environment...
- Sphere-worldSphere-worldThe idea of a sphere-world was constructed by Henri Poincaré who, while pursuing his argument for conventionalism , offered a thought experiment about a sphere with strange properties....
- Star worldStar worldThis article is about the robotic concept. For the TV channel, see STAR World.Star worlds are mathematical concepts used in robot navigation. Essentially, a star world is any n-dimensional shape that can be mapped to a sphere world of the same dimension...
- Forest of starsForest of starsA forest of stars is a set of star worlds whose adjacency matrix is a tree. This means that no intersecting star worlds create a cycle, or hole, in the overall space. If an object or space can be represented by a forest of stars, it can be mapped onto a sphere-world by mapping each star world...
- TopologyTopologyTopology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...