It is necessary to generate a smooth and feasible

path for an UAV. It must not take any sharp turn during its maneuvering.

In this section a smooth trajectory will be

generated by differential flatness when any obstacle is detected by the UAV

while it is moving through predefined path. So, the UAV will start movement

through the predefined path until it detects any obstacle. The path will be

generated using differential flatness. The definition of differential flatness according

to 13 is, a nonlinear system is differentially ?at, if there exists a

function A such that

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and the solution can be written as a function of output

z and its derivatives 13.

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The trajectory between two points, from initial

positionto final positionmust be generated in such a way so

that to ensure the smoothness of the function of the curve in a certain time

period using differentiable function. The

trajectory is defined for x(t) and y(t) as-

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is the basis function picked from Andrews’

curve, which helps to eliminate the effect of growing magnitude of time. andare all coef?cients used to generate

trajectory along with Andrew’s curve basis function. According to the

assumption of differential flatness to generate smooth and feasible trajectory

of virtual leader equation must be agreed when –

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Now we wish to generate trajectory using equation –

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If the agent is differentially flat then-

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and

we see that the initial and ?nal condition in the full state space depends on just

the output z x and z and its

derivatives at the initial and ?nal times.

Thus, any trajectory for z that satis?es

these boundary conditions will be a feasible trajectory for the system. We can parameterize the ?at output

trajectory using a set of smooth basis functions

?(t)-

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We seek set of

co-efficient a (t) satis?es the boundary conditions. The derivatives of the ?at

output can be computed in terms of the derivatives of the basis functions-

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The coefficient is picked from Andrew’s curve and

can be expressed as below-

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The

boundary condition of the system output z is described as –

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The coefficients a and v can be determined by

taking inverse of both the side of equ () as follows-

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Similarly, coefficient b can be determined as-

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