Group: Do Lab 10 (70%)

Individual (30%) :

• Show that the cart can achieve full (x, y, theta) degrees of freedom using Lie Bracket analysis.
  • State the constraint vector w1(q)
  • State the allowable motion vectors g1(q) and g2(q)
  • Compute the Lie Bracket of g1 and g2

  

• Compute the inverse kinematics for the following system: a mobile robot
  with a two link manipulator on board. The location of the mobile base is (x,y), with an orientation alpha. The two link manipulator is attached such that the axes of rotation are perpendicular to the page in the Side View image. The first joint of the two-link manipulator is a height h from the floor.
  • Given a desired X, Y, Z, and Omega, determine the x,y position for the mobile robot, as
    well as its orientation alpha and the angles tau1 and tau2.