Difference between Denavit-Hartenberg and Rodrigues formulas/conventions

I am trying to compute the forward kinematics for a 6 DOF robot arm.

I've found two methods : the Denavit-Hartenberg (original and modified) and the product of exponentials with the Rodrigues formula.

This methods are very similar because we define the axis lengths and twist angles but how are they different?

Thanks a lot for your explanations.

• I don’t think they are similar. They are quite different actually. DH relies on homogeneous transformation and the second is based on screw theory. Jun 24 at 1:36

The DH method requires you to carefully specify local frames attached to each link and calculate linear and angular offsets between those frames in a very specific way in order to reduce the effective transformation from 6 variables down to 4. You then have to plug in your joint angle/positions and multiply the resulting transformation matrices to determine the end effector transformation (orientation & position). Computing the differential kinematics and dynamics using this formulation is challenging and can lead to numerical errors.

The Product of Exponentials formulation uses matrix exponentials for each joint and a transformation from the base to the end effector, all defined based on the zero-configuration (constants). The joint variables are then inserted into the exponentials to find the overall transformation resulting from the changes due to the joint motions. It makes the resulting differential kinematics and dynamics far easier and faster to compute.