Inverse kinematics

Inverse kinematics is the computation of joint angles required to achieve a desired end-effector pose. The forward problem (joints → pose) is trivial via the kinematic chain; the inverse problem (pose → joints) is generally over-determined for redundant manipulators (>6 DOF) and admits multiple solutions or none.

In modern humanoid control, classical inverse kinematics is largely subsumed by whole-body control and model-predictive optimization, which solve for joint commands directly against task objectives plus balance, joint-limit, and collision constraints. IK as a standalone routine survives in motion-planning pipelines, simulation tooling, and low-DOF industrial arms — but a 2026-vintage humanoid arm controller probably isn't running it as a separate step.