Nonholonomic Constraint

A constraint on velocity direction only, which can't be integrated into a position constraint — like a wheel that can't slide sideways.

A nonholonomic constraint restricts a system's velocity in a way that cannot be integrated into an equation involving position alone; the term 'holonomic' was introduced by Hertz in 1894. The most common source is a wheel rolling without slipping: a differential-drive cart at pose (x, y, θ) must satisfy ẋ·sinθ − ẏ·cosθ = 0, where x, y are position and θ is heading, meaning it can never move sideways at any instant. This narrows the velocity directions available at any moment, but it doesn't shrink the set of poses the vehicle can eventually reach — it can still park in any spot, just by maneuvering back and forth the way parallel parking does. So planning for wheeled bases can't simply interpolate straight lines between poses; it needs methods like hybrid A* that account for steering constraints. Escaping the constraint means switching to an omnidirectional base such as one with Mecanum wheels. Finger contacts that roll across an object's surface during grasping are this same type of constraint.

ExampleA vacuum-cleaning robot that wants to shift 20 cm directly to its left can't simply slide sideways — it has to either rotate 90° in place and then drive forward, or maneuver back and forth like parallel parking. That's the nonholonomic constraint at work.

Also called

Nonholonomic System, Nonintegrable Constraint

Related

Differential Drive Kinematics · Configuration Space (C-Space) · Generalized Coordinates · Hybrid A* · Mecanum Wheel · Kinodynamic Planning

Sources

Wikipedia: Nonholonomic system
Modern Robotics (Lynch & Park), Sec. 2.4 Holonomic and nonholonomic constraints