Math & Kinematics

Inverse Kinematics (IK)

Inverse kinematics is the problem of finding joint configurations that place a robot's end-effector at a desired pose, the inverse of forward kinematics. Solutions may be analytic for specific geometries such as 6-DOF arms with spherical wrists, or numerical, using Jacobian-based iteration or nonlinear optimization as in solvers like TRAC-IK; redundant arms admit infinitely many solutions, and singularities and joint limits complicate solving.

Why it matters for physical AI

IK is the translation layer between task-space intent, whether from planners, teleoperators, or learned policies, and the joint commands hardware executes, running inside nearly every manipulation stack.