Target defense in $2$D$.$ In Figure $1,$ an adversarial robot k $($red$)$ is approaching target p$.$ The defense robot i aims to intercept the adversarial robot before it reaches the target. Both robots have differential

drive dynamics and the state is denoted by $($x$,$ y$,\backslash$theta $).$

$1$ point. What sensors$/$measurements are required for this task?

$4$ points. Using these measurements, estimate the velocity of the red robot, and then predict its trajectory. Write down the derivations in detail.

$3$ points. With the predicted trajectory, design a controller for the blue robot to intercept the red robot. Write down the derivations in detail.

You don$$t have to consider any uncertainties or noises and feel free to use any other notions.