Lab04: Differentiable kinematics

The goal of this laboratory is to implement computation of Jacobian for planar manipulator and to generate null-space motion of the robot, i.e. motion where gripper remains stable while body is moving. Once you implement the Jacobian computation, you can generate following animations by using the scripts in the excersies/lab04 folder:

Planar RRRR

../../_images/lab04_jac_animation_RRRR.gif

Planar PPPR

../../_images/lab04_jac_animation_PPPR.gif

Spatial Panda

../../_images/lab04_jac_panda.gif

Tests

Mandatory HW:

  • robotics_toolbox/robots/planar_manipualator.py

    • implement numerical computation of the in the jacobian_finite_difference functions

    • implement analytical computation of in the jacobian function; you are not allowed to compute it by numerical difference!

If following tests will pass, your implementation is correct:

pytest tests/hw04/mandatory

At the end of the lab, you should be able to answer following questions:

  • how to compute Jacobian via finite difference

  • what is dimension of null-space? experiment with multi-dof planar robots

  • how to compute Jacobian analytically