Math & Kinematics

Reachability

Reachability is the property of whether a robot can attain a given pose or state, and reachability analysis computes the set of attainable end-effector poses or system states. In manipulation, precomputed reachability or capability maps score how well regions of the workspace can be reached across orientations, guiding grasp selection and mobile-base placement. In safety-oriented control, reachable-set computation bounds where a system can end up under bounded inputs and disturbances.

Why it matters for physical AI

Reachability reasoning connects kinematics to decision-making: it tells a mobile manipulator where to stand before acting, and it gives formal safety methods the machinery to certify collision and constraint avoidance.