Math & Kinematics
Newton-Euler Dynamics
Newton-Euler dynamics is a formulation of rigid-body dynamics that applies Newton's second law and Euler's rotational equations to each link of a robot. The recursive Newton-Euler algorithm (RNEA) computes inverse dynamics, the joint torques required for a desired motion, in time linear in the number of joints, making it a workhorse of real-time controllers. It is the standard alternative to the Lagrangian formulation.
Why it matters for physical AI
Fast, exact inverse dynamics underpins computed-torque control, whole-body controllers, and the physics engines used to train locomotion and manipulation policies in simulation.
Build physical AI
Put these concepts to work on real hardware
Axol is a dual-arm robot built for physical AI — teleoperate it, collect demonstrations, and deploy learned policies out of the box.