A manipulator is performing a task during which the end-effector (treated as a point for this problem) is moving on the plane z = 1 with circular obstacles of radii 2.5 units centered at (2.5,7.5,1) and (7.5,2.5,1) as shown in the figure below. The end-effector needs to move from start position (4, 1, 1) shown by o to target position (5, 10, 1) shown by while avoiding the obstacles. 10 9 8 7 6 LO 5 4 3 O 2 1 0 0 2 3 4 5 6 7 8 9 10 You are given the following minimum requirements that must be satisfied by the end-effector: (a) the manipulator begins its motion at rest; (b) the manipulator comes to rest at the end of the motion; (c) the total duration of motion is 6 seconds; (d) velocity at the via point is continuous. You have the freedom to choose any additional requirements as needed, for example: (a) location of an intermediate via point; (b) time step between start to via point and between via point to target as long as the total duration equals 6 seconds; (c) slope of the trajectory dy at start, via point or target position. dx Use piece-wise cubic polynomials to generate the trajectory from the starting point to the via point and from the via point to the end point. In your solution, (a) clearly list all the requirements that were selected; (b) generate a plot of the trajectory showing that your chosen parameters result in the end-effector successfully avoiding the obstacles; (c) generate a plot of the end-effector x and y positions as a function of time; (d) attach a printed copy of the code to your homework PDF file. You may use software of your choice for calculations and plots, such as Matlab or numpy + matplotlib. Hint: In order to generate a unique solution for piece-wise cubic polynomials with one via point we need 16 conditions as we have 16 unknowns.