According to the Frobenius theorem, SBMS has been shown to be a nonholonomic system
Morse, "Logic-based switching control of a nonholonomic system
with parametric modeling uncertainty," Systems & Control Letters, vol.
Chang and Fu  proposed dynamic state feedback formation control for achieving the realization of the multirobot formation system with respect to the problem of dilation of a formation shape and stabilization issue in a nonholonomic system
During the past few years, the SMC strategy has been also applied to the nonholonomic system
In a leader/follower formation, the lead robot is controlled through a nonholonomic system
, meaning that the trajectory is set in advance, and the followers are tracing the same pattern that the leader takes by using sonar.
The first example is a unicycle model (nonholonomic system
) and the second is a two-link planar manipulator model (holonomic system).
If the Pfaff system (5.1) is not completely integrable (nonholonomic system
), then for any point a G D does exist some integral curves at a only and it is possible that integral manifolds of maximum dimension do not exist at certain points.
The purpose of tuning [b.sub.0] is to improve the robustness of nonholonomic system
and decrease the sensitivity for initial condition error at the expense of [d.sub.a] increase.
In the robot stabilization problem, according to , it is known that a nonholonomic system
cannot be asymptotically stabilized at an equilibrium point using a differentiable control law, despite the system's being completely controllable.
Mathematical Model of Nonholonomic System
. The kinematic model for a drift-free nonholonomic system
is given as
A Framework for the Stabilization of General Nonholonomic Systems
With an Application to the Plate-Ball Mechanism.