Develop a MatLab simulation of a 2-DOF RR Planar manipulator

Develop a MatLab simulation of a 2-DOF RR Planar manipulator. The end-effector of the manipulator has to follow a reference trajectory given in Lab#05.

Additionally, you have to consider the velocity (xa, ya) and acceleration (a,d) along the trajectory. The position, velocity and acceleration of end-effector along the desired trajectory can be transformed to desired joint variables, joint velocities and joint accelerations using following relations,

Use the computed torque is last step to drive the manipulator joints. Simulate the dynamic model of the manipulator using forward dynamic equation for small time step for computed input torque and current state of joint angles, and joint velocities.

Hint: You can represent the 2nd order differential equation as 1st order differential equations using state space representation as follows;

You can integrate the differential equation using 4th order Range-Kutta method.

Deliverables:

Simulate the manipulator for one cycle of the circular reference trajectory. Plot the history of following variables at the end of simulation.
End Effector position, velocity and acceleration along reference trajectory

• Desired Joint angles, joint velocities and joint accelerations
• Actual Joint angles, joint velocities and joint accelerations
• Error in position, velocity and acceleration of joint variables Joint Torques along the reference trajectory.

Consider following parameters
m₁ = m₂ = 1 unit  l₁=l₂= 3 unit, g=10
For reference circular trajectory center = (2,2) and radius = 1unit

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