Regularization

In the case of underconstrained tasks, there might be many solutions to the problem: a choice has to be made about the preferred solution. Regularization is the addition of a very low cost to the objective function, in order to favour some solutions over others. Do not hesitate to have a look at kinematics regularization.

Torque regularization

In the dynamics solver, the torque can be expressed as the other decision variables. The (squared) torque is regularized by default, meaning that \(\sum \tau_i^2\) will be minimized, with a default weight of \(10^{-3}\). This weight can be adjusted with solver.torque_cost:

# Weight for the torque regularization (1e-3 by default)
solver.torque_cost = 1e-2

Pose regularization

Another type of regularization is to use a joint task or a position, orientation or frame task to regularize the pose of the robot.

To do that, simply give a very low weight to the task, for example:

# Adding a task with a very low priority to take the DoFs back to 0
joints_task = solver.add_joints_task()
joints_task.set_joints({
    joint: 0.0
    for joint in robot.joint_names()
})
joints_task.configure("joints_regularization", "soft", 1e-5)