A new classification of non-holonomic constraints

A new class of non‐holonomic constraints is proposed, namely, completely non‐holonomic, partially non‐ holonomic, and truly non‐holonomic. The classification is mainly based on the Frobenius condition and the existence of the integral surfaces of the constraints. The intrinsic properties of non‐holonomic constraints, such as the reachability property, vary with respect to different classes. In fact, some non‐holonomic constraints do not have the reachability property. The path‐planning problems for different classes of non‐holonomic constraints also become quite delicate. The paths from a point on one side of the critical surface to a point on the other side must pass through the singular points on the critical surface. The observation made in this paper gives a new outlook of non‐holonomic constraints, and may lead to a deeper understanding of the behaviour of systems with non‐holonomic constraints.