# $2$: Path planning: $(30\%)$ Given the following manipulator with frames, $D$&$H$ table, and inverse kinematics solution, define a continuous, second order smooth path from the points: $P_1=(200,0,200{)}^T,P_2=(0,200,500{)}^T,V1=0,V2=0($Undergraduates$),$ GRADUATES$),$ over the time step $tl=0$ seconds to $t2=1$ second. $($give joint variables as equations that are functions of time.$)$ Use cubic splines for the trajectory and show all your work.

$\backslash$table$[[i,a_i,{}_i,d_i,{}_i$