How to create velocity control action models from pinocchio model #1131

Hi,

I see that when creating an action model using a Pinocchio model, the examples were doing something like this:

state = crocoddyl.StateMultibody(env.robot.model)
actuation = crocoddyl.ActuationModelFull(state)

Then the action model is created using

DAM = crocoddyl.DifferentialActionModelFreeFwdDynamics(state, actuation, runningCostModel)
Model = crocoddyl.IntegratedActionModelEuler(DAM, dt)

I believe, in this case, the action model's control is at the torque level. If I want to solve for the optimal joint velocities, how would I do it?

Thanks in advance!

@BolunDai0216 -- To understand Crocoddyl's formulations, it would be helpful if you read our papers before:

1. https://arxiv.org/pdf/1909.04947.pdf (forward dynamics)
2. https://arxiv.org/pdf/2209.05375.pdf (inverse dynamics)

None of these formulations take the joint velocities as a control input. However, you can extract the optimal generalised velocities from both of them's solutions. The optimal joint velocities are inside the optimal state, which is defined as $\mathbf{x} = [\mathbf{q}, \mathbf{v}]$. You can get them by

x_opt = solver.xs[I]
v_opt = x_opt[:state.nv] 

Moreover, it doesn't make sense to formulate an OP problem where its inputs are generalised velocities; what makes sense is generalised accelerations. Indeed, this is how the inverse-dynamics formulation works. In our implementation of the inverse-dynamics formulation, you can also disable the RNEA equality constraints, which in practice means "optimising for kinematics only". This seems to be what you need.