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.
This paper presents the application of genetic algorithms in the solution of motion planning problem in mobile robots for a two-dimensional environment without uncertainties and with a model of mobile three-wheeled robot with characteristics than classify it like a nonholonomic system
. It is intended to demonstrate the effectiveness of application of one belonging to techniques of artificial intelligence in the solution of problems of robotics and desired then evaluating the performance and validity of the tool implemented and proposed model.
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.