The motion of the mobile robot is defined by a holonomic system
composed of three omnidirectional wheels, allowing it to perform complex maneuvers in narrow indoor areas .
Kashiwara, Kazhdan-Lusztig conjecture and holonomic system
The first example is a unicycle model (nonholonomic system) and the second is a two-link planar manipulator model (holonomic system
The Pfaff system (5.1) is called completely integrable (holonomic system
) if through the point a G D passes an integral manifold whose dimension is p - s (maximal integral manifold).
Adopting a holonomic system
meant refining the control systems to ensure that the robot utilized all its new-found maneuverability:
These constraints make kinematic and dynamic analyses more difficult than those of holonomic systems
. Therefore, significant effort in a variety of solutions to the problem of mobile robot control has been investigated by the robotics research community.
Among the topics are real and complex singularities, the topology of differentiable maps, openings of differential map-germs, the relationship between free divisors and holonomic systems
, effective computational methods of invariants of singularities, the application of singularity theory to differential geometry, the deformation theory of CR structures, and differential equations with singular points.
between the derived categories of [D.sub.X]-modules and of ind-sheaves on X x P, provide a RiemannHilbert correspondence for holonomic systems.
There, we will also describe some of the properties of the essential image of holonomic systems by the functor [PHI] Such a category is related to a construction of .
One recalls that holonomic systems
involve an agreement of the degrees of freedom with the number of independent variables.
In holonomic systems
, the control input degrees are equal to total degrees of freedom, whereas, nonholonomic systems have less controllable degrees of freedom as compared to total degrees of freedom and have restricted mobility due to the presence of nonholonomic constraints.