A nonholonomic constraint limits how a robot can move without limiting where it can ultimately go — the reason a car can reach any parking spot but can't slide sideways into it, and a core idea in wheeled-robot planning.
A nonholonomic constraint restricts the directions you can move right now, but not the places you can eventually reach. A car can't move sideways, yet with enough back-and-forth it can park anywhere — that's nonholonomic.
Why is parallel parking hard? Because a car is nonholonomic — it can go anywhere, just not directly. This distinction shapes how wheeled robots must plan every move.
The idea
A nonholonomic constraint restricts your instantaneous motion — the directions you can move right now — without restricting the configurations you can ultimately reach. A car can't slide sideways at any instant, yet through a sequence of forward/backward turns it can reach any position and heading. The constraint is on velocity, not on where you can end up.
Contrast with a holonomic robot (like an omniwheel platform), which can move directly in any direction — its motion is unconstrained, so planning is far simpler.
Constrained motion, unrestricted goals
The instantaneous 'no sideways' rule never goes away, but clever maneuvers still reach every configuration — that gap is what makes nonholonomic planning tricky.
Why it matters for planning
A nonholonomic robot's planner can't just draw a straight line in configuration space — that line might command a physically impossible sideways slide. Planners must respect the motion model, generating only feasible paths: smooth curves a car can actually follow, often assembled from arcs and reversals. This is exactly why parking maneuvers involve shuffling, and why planners like Hybrid A* and RRT variants build in the vehicle's turning limits.
Where you'll see it
Cars and car-like robots — the classic example (can't move sideways or spin in place).
Differential-drive robots — can rotate in place but can't translate sideways.
Bicycles, tractors, boats, some manipulators — all nonholonomic.
Omnidirectional (mecanum/omniwheel) platforms are the holonomic exception that can strafe.
Why it matters
The holonomic/nonholonomic distinction determines how a mobile robot must plan and control its motion. Recognizing that a robot can reach anywhere but not move anywhere-instantly is fundamental to wheeled robotics.
