State space
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About
State space is a mathematical framework that represents all possible configurations or conditions a system can occupy at any given moment. In robotics and AI, it is typically defined as a multidimensional vector capturing every variable needed to fully describe a robot or system — such as joint positions, velocities, sensor readings, or probability distributions over uncertain quantities. Algorithms for motion planning, control, localization, and learning all operate by reasoning about trajectories, transitions, or policies within this space. Planning methods like RRT and DDP search for feasible or optimal paths through state space, while control approaches such as sliding-mode and feedback controllers drive a robot toward desired states. Probabilistic techniques like particle filters and POMDPs extend the concept to belief space, where uncertainty about the true state is explicitly modeled. State space representation matters because it provides a unified, rigorous language for formulating and solving diverse robotics problems — from trajectory optimization and simultaneous localization and mapping to reinforcement learning — making complex system behavior analyzable, predictable, and ultimately controllable.
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