$3-$ Using the provided map and robot A which should go to position C $,$

a$.$ Perform and draw the Configuration Space Transform. Assume that the motion of the robot can be seen on the sheet as horizontal or vertical motions only $($i$.$e$.,$ only rotates $90)$

b$.$ Suggest a path on the transformed C$-$space that moves the robot from A to C$.$

c$.$ Repeat if the shape robot A is

${?}^A$

$4-$ For the given workspace in following figure, do the following:

a$-$ Sketch the free workspace and trapezoidate it $($using the sweeping trapezoidation algorithm$).$

b$-$ Sketch the dual graph for the trapezoidal partition and the roadmap $($i$.$e$.,$ the dual graph with centers and with connecting polygonal paths through midpoints$).$ Then sketch the continuous path from the start point to goal point that a robot would follow in the workspace. The path depends upon the decomposition and a search algorithm.