According to the Frobenius theorem, SBMS has been shown to be a
nonholonomic system.
Chang and Fu [11] 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 simultaneously.
During the past few years, the SMC strategy has been also applied to the
nonholonomic system control [18-21].
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 [3], 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.
A Framework for the Stabilization of General
Nonholonomic Systems With an Application to the Plate-Ball Mechanism.