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Given a quadruped standing on all fours, or trotting with 2 legs down/2 up, I've seen a few methods of computing inverse dynamics. All derive from centroidal momentum physics, and I think all distill down to the same conservation of linear and angular accelerations, but the formulations vary significantly. A common equation of motion, :  , can be manipulated to solve for tau.
Another form directly utilizes summation of torques from the ground reaction forces and linear/angular forces about the center of mass and ends up with a set of underdetermined set of linear (I hope) equations that are solved as a QP optimization problem with constraints dependent up frictional forces and feet on the ground.

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And another approach is Recursive Newton-Euler modified for a floating-base robot.

While all seem to give either forces multiplied by the Jacobian for torque or torque directly, I can understand systems of linear equations, though the constraints can be complex. Reading Featherstone's articles it seems that RNEA produces torque results without complexities of other approaches, but there must be limitations to RNEA, otherwise why resort to optimization approaches. My goal is to calculate either torque for a PD controller or for better tracking, feed-forward torque control, but am not sure of the better approaches and their potential limitations.

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