There are four knights on a $3$ x $3$ chessboard. The two white knights are at the two bottom corners, and the two black knights are at the two upper corners of the board. Find the shortest sequence of moves to achieve the position shown on the right, below; or$,$ prove that no such sequence exists. Note that no two knights can ever occupy the same square on the chessboard. Develop the sequence using diagrams, and then translate these into written statements and implementable MATLAB code.