Planar
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Planar, in robotics and AI, refers to systems, motions, or analyses constrained to a two-dimensional flat surface or plane. A planar robot or mechanism operates within a single plane — typically defined by two spatial axes — simplifying the mathematical modeling of kinematics, dynamics, and control compared to fully three-dimensional systems. This constraint appears across many robotic domains: planar biped walkers that stride in a vertical plane, planar manipulator arms modeled with flexible links, cable-suspended planar robots, and mobile robots whose motion is analyzed as a rigid body on a flat surface. Planar assumptions also appear in sensor calibration (using flat calibration grids), environment mapping (extracting planar surface patches from 3D point clouds), and motion planning with potential functions. The planar simplification matters because it reduces computational complexity while preserving essential dynamic and geometric properties, making systems far more tractable for formal stability proofs, closed-form equations of motion, and real-time control. It also serves as a critical stepping stone — insights and controllers developed for planar systems frequently generalize to full three-dimensional implementations in advanced robots.
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