• (70%) Group: Lab 10: Final Contest
• (30%) Individual

• Supplement the lecture material of non-holonomic motion
• Boost the concepts of lie brackets and allowable motions of non-holonomic robots

1. Show that the cart can achieve full (x, y, θ) degrees of freedom using Lie Bracket analysis.
   1. State the constraint vector w₁(q)
   2. State the allowable motion vectors g₁(q) and g₂(q)
   3. Compute the Lie Bracket of g₁and g₂

   

    

2. Compute the inverse kinematics for the following system:
   • A mobile robot with a two link manipulator on board.
   • The location and orientation of the mobile base is (x,y,α).
   • 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 Ω, determine the (x,y) position for the mobile robot, as well as its orientation alpha and the angles τ₁ and τ₂.

 

Turn in:

Submit a PDF named [andrewID]HW12.pdf to Gradescope by 11:59 PM, April 25.