Computing the jacobian of a constrained quadruped

[edoardopanichi]

I am Edoardo a Robotics master's student at TU Delft and I am currently doing my thesis about "Robust and Complaint Landing for Quadrupeds".

I am using Pinocchio to compute the mass matrix of the robot (I have a urdf of its model) and also the jacobians. But now I am facing a problem.

I would like to compute the jacobian with respect to the trunk (body of the quadruped) when the robot has its leg on the ground. Just to be clear, J_trunk is the jacobian that maps a force applied at the COM to the leg joints. Basically, in my work, I am computing a desired force that should be generated at the COM level, and I want to map it to the leg joint torques with J_trunk, such that I can generate the equivalent torques.

For the moment I was computing this matrix like this:

# Using Pinocchio Library to compute the Jacobian of the robot for the current joint configuration

# Compute all joint Jacobians
pin.computeJointJacobians(pinocchio_model.model, pinocchio_model.data, robot_state)

# Get the Jacobian for the "root_joint", a fixed joint that is the parent of the trunk frame.
root_joint_id = pinocchio_model.model.getJointId("root_joint")

J_root = pin.getJointJacobian(pinocchio_model.model, pinocchio_model.data, root_joint_id, pin.WORLD)

# J_root is J_trunk in the world frame
self.J_trunk_w = J_root

But I realize that the result is probably not what I need. Indeed J_trunk_w is a 6x18 matrix and the result that Pinocchio gives has the last 6x12 elements equal to zero. This means that any force applied to the COM has no effect on the leg joints. This is correct (I think) only if the legs are not constrained by the ground. So I tried really hard to find an example or some documentation about how to compute the Jacobians when the system is constrained but I was not able to find anything. I came across pinocchio3, which I think might help me, but I did not understand how to install it.

Can you give me some advice?
(either on how to install Pinocchio3 and how to use it to solve my problem, or how to use normal Pinocchio to solve my problem)