Reduction (mathematics)

Related papers: 20

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Reduction in mathematics refers to the process of simplifying a complex problem, system, or model into a more tractable form while preserving its essential properties. In robotics and AI, reduction techniques appear across numerous domains: model order reduction compresses high-dimensional dynamic models of soft robots or flexible mechanisms into computationally efficient representations suitable for real-time control; dimensionality reduction collapses high-dimensional configuration spaces—such as human hand grasping postures—into lower-dimensional subspaces that simplify planning and control; and parameter reduction identifies the minimum set of inertial parameters needed to describe robot dynamics, cutting computational overhead in identification and simulation. Reduction also underpins deadlock prevention in flexible manufacturing, chattering suppression in sliding-mode controllers, and geometric simplification in motion planning for legged robots. The concept matters because robotics problems are inherently high-dimensional and computationally demanding; systematic reduction transforms otherwise intractable models and controllers into forms that can run reliably on physical hardware, enabling faster computation, easier identification, and more robust real-time performance across manipulation, locomotion, and human-assistive systems.

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