Handling loop closures#

Understanding loop closures#

Robots with loop closures are robots containing loops in their kinematics chain. To understand better this concern, please refer to the loop closure section of the kinematics documentation. It will explain you how to model such closures within the URDF format.

Loop closure in dynamics: checklist#

Here is the checklist to handle loop closures within a dynamics solver:

  1. Add tasks to ensure loop closures, just like you would do for kinematics. Those tasks are typically relative position tasks

  2. Create a task contact associated with the loop closure task. This will adds internal forces to the system to enforce the loop closure.

  3. Make sure all passive degrees of freedom have zero-torque constraint, thanks to the torque task.

Breaking down planar 2DoF example#

Here is an example, that we will break down with details:

Planar 2DoF

In this example, a planar 2DoF parallel robot is controlled. The loop closure is handled with a relative position task, which is associated with a generic task contact.

Example code: dynamics/planar_2dof.py

In the source code, you will find the following lines:

# Adding a relative position task with contact at the effector
loop_closure = solver.add_relative_position_task(
    "closing_effector_1", "closing_effector_2", np.array([0.0, 0.0, 0.0])
)
loop_closure.mask.set_axises("xy")
loop_closure.configure("closure", "hard")

Here, the loop closure task is created as a constraint of the relative position for closing_effector_1 and closing_effector_2. The xy mask is added, because there are no way to compute the z axis of the loop closure. The task is configured as a hard constraint, meaning that the solver will strictly enforce this constraint.

The following line:

loop_closure_contact = solver.add_task_contact(loop_closure)

Creates a task contact associated with the loop closure task. Thanks to this, forces can be added by the solver to enforce the task.

Finally, the following line:

# Imposing zero torque on passive degrees of freedom
torque_task = solver.add_torque_task()
torque_task.set_torque("passive1", 0.0)
torque_task.set_torque("passive2", 0.0)
torque_task.configure("torque", "hard")

Ensure that the passive degrees of freedom have zero-torque constraint. This is done with a torque task, which is configured as a hard constraint.

Examples#

With a similar pattern, many loop closures are used un Megabot:

Megabot

Megabot is a giant quadrupedal robot using linear actuators. Many loop closures are present in its design.

Example code: dynamics/megabot.py

In this other example, gear tasks are used with task contact to simulate a differential gear system:

Differential

A differential gear system. At the end of the video, the torque is forced to zero to show the system’s behaviour when only subject to gravity.

Example code: dynamics/differential.py