Due: Mo 05/04/2009

1. Use the Newton-Euler algorithm to find the closed-form dynamic equations for the planar, RP robot shown below. Assume the links are symmetric about the center of mass, so that only principal moments of inertia are present.
   
2. Find the inertia tensor for each link given m₁ = 5 kg, m₂ = 4 kg, l₁ = 0.4 m is half the length of link one, distance from link two's center of mass to either end is 0.5 m, and that links 1 and 2 can be represted as solid squares of width 10 cm and 8 cm, respectively.
3. Generate smooth trajectories (with zero end velocities) for the end effector such that it moves from o₂ = [-1.2, 1.2, 0] m to o₂ = [0.8, 0.8, 0] m in 4 s.
4. Use inverse kinematics to compute the joint variables and velocities that would yield the desired end-effector motion.
5. Design and implement a controller from chapter 8 such that your robot tracks the joint variables determined from the inverse kinematics.
6. Simulate your robot and controller using an ODE solver and demonstrate its performance in joint space and task (end-effector) space. You should also be able to visualize the movement.