Math & Kinematics
Nonholonomic Constraint
A nonholonomic constraint is a constraint on a system's velocities that cannot be integrated into a constraint on configuration alone. The rolling-without-slipping condition of wheels is the canonical example: a differential-drive robot cannot translate sideways, yet can still reach any planar pose through maneuvering. Such systems require specialized motion planners, since feasible paths must respect the velocity constraints at every point.
Why it matters for physical AI
Wheeled bases, cars, and steerable platforms dominate mobile robotics, so planners and learned navigation policies must produce trajectories that respect nonholonomic kinematics to be executable.
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.