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Hi,


Please solve the below.

Require on urgent basis.

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Q4.png

Formulate the mobile robot trajectory following problem as a control prob—
lem. A mobile robot position at time t is denoted as ($(t), y(t)) and its orienta-
tion at time t is denoted as 9(t), the velocity and turn rate are denoted as v(t) and w(t) respectively. The nonlinear motion model can be simplified as :i? = vcosfi', y = vsinfl, 9: w
Suppose the desired trajectory is
at) = not, at) = 0, at) = 0 Assuming v(t) is close to 1.10, w(t) is close to 0 and 9(t) is close to 0, define
the difference between the actual trajectory and the desired trajectory as the
state, ’U(t) — 110 and w(t) as control inputs, assume the output is the same as the
state, deriVe the state—space model of the lineariZed control system.

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