Develop a MATLAB script for determining the position of a Universal Robotics UR-10 to locate the end effector link called "tool0" in a specific position and orientation as defined below. Determine the UR-10 configuration using both BFGS and LM algorithms. Answer the following questions. Start each algorithm at the UR-10 home configuration.

For each of the following tool configurations

1. position = [0 0.5 1]^T, orient tool z axis in the base y direction
2. position = [2 3 0]^T, orient tool z axis in the base x direction
3. position = [0 0.0 0]^T, orient tool z axis in the base y direction
4. position = [0 0.5 1]^T, orient tool z axis in the base z direction
5. position = [1 1 1]^T, orient tool z axis in the base z direction

for each of the above 5 tool targets, answer the following

1. does the BFGS algorithm converge
2. does the LM algorithm converge
3. is it possible for the robot to achieve this configuration? why or why not?
4. include a isometric view picture of the robot using the show command for BFGS
5. include a isometric view picture of the robot using the show command for LM
6. compare and contrast the pictures. Same configuration or different configurations?