A differentially$-$steered robot is currently positioned at the origin of the global reference and is pointed in the direction of the $x_1$ axis. It is necessary to drive it to a goal whose range and bearing is $(70(m),30).$ The robot's construction requires that the maximum turn rate that it can be run at is $0\mathrm{.}25ra\frac{d}{s}($in magnitude$).$

a$)$ If the robot is required to follow a single circular path to the goal, what should the radius of this path be$?$

b$)$ Where is the ICC located with respect to the global axes?

c$)$ What is the shortest time that the robot will take to arrive at the goal?

d$)$ What will its orientation $($pose angle$)$ be when it gets to the goal?

e$)$ Reevaluate part $($a$)$ if the robot is required to have a pose angle of $90$ at the destination.

f$)$ In the situation presented in this problem, is there a way of determining $($even before you move$)$ whether the distance to the goal is shorter if you drive backwards rather than forwards?