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A robot’s environment often restricts its motion. A hand grasping a door handle must move with the door, while a pen tip must remain on the paper. You can express these restrictions as Pfaffian velocity constraints A(θ)θ˙=0A(\theta)\dot\theta = 0. This is the same form used for the TurtleBot’s wheels in configuration space. Assuming that the constraints do no work, you will add the constraint forces A⊤(θ)λA^\top(\theta)\lambda to the equations of motion. You will then solve for the motion and constraint forces together. The treatment follows section 8.7 of Lynch and Park (book page 299) (Kevin M. Lynch, 2017) and builds on forward dynamics.

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References

  • Kevin M. Lynch, F. (2017). Modern Robotics.
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