Differential Transformation for Kinematic Modeling of Autonomous Bicycle

Control for an Autonomous Bicycle

The control of nonholonomic and underactuated systems with symmetry is illustrated by the problem of controlling a bicycle. We derive a controller which, using steering and rear-wheel torque, causes a model of a riderless bicycle to recover its balance from a near fall as well as converge to a time parameterized path in the ground plane. Our construction utilizes new results for both the deriva...

On the discrete bicycle transformation

The motivation for this paper comes from the study of a simple model of bicycle motion. The bicycle is modeled as an oriented segment in the plane of fixed length `, the wheelbase of the bicycle. The motion is constrained so that the segment is always tangent to the path of the rear wheel; this non-holonomic constraint is due to the fact that the rear wheel is fixed on the frame, whereas the fr...

DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING FUZZY FRACTIONAL HEAT EQUATIONS

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...

Differential transformation method for solving a neutral functional-differential equation with proportional delays

In this article differential transformation method (DTMs) has been used to solve neutral functional-differential equations with proportional delays. The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. Exact solutions can also be obtained from the kno...

Differential transformation method for solving fuzzy differential inclusions by fuzzy partitions