Math & Kinematics

Forward Kinematics (FK)

Forward kinematics is the computation of a robot's end-effector pose, or the poses of any of its links, from its joint positions using the kinematic model of the chain. It is evaluated by composing joint transforms, classically parameterized with Denavit-Hartenberg conventions or the product of exponentials formulation. FK is deterministic and unique for serial chains, in contrast to inverse kinematics, which may admit multiple or no solutions.

Why it matters for physical AI

Every layer of a robot stack, from Cartesian teleoperation to action-space design for learned policies, relies on fast, differentiable FK; it is the basic map between the joint space where motors live and the task space where goals live.