Hello Stephan,

Thank you for your effort in maintaining this nice repo!

While using pink, I get the following two questions for you.

1. I've installed pink on my mac which is intel OSX Monterey 12.5.1 and I am using anaconda virtual environment (python version 3.8). When I tried to run the upkie_crouching.py example, it kept complaining there is no module named pink.models. So, instead of running the script, I manually tried opening the python interpreter(python version 3.8) in the same anaconda environment and typed the code in upkie_crouching.py line by line, and it successfully imported all the modules. I don't know how this could be possible. Do you have anything in your mind?

2. Other than the aforementioned software issue, I have another question regarding the inverse kinematics solver interface (API). I have a 7-DoF robotic manipulator which has a holonomic constraint (q_1 = q_2) so it has 6 active joints with one passive joint. Given any cartesian tasks, I would like to solve the inverse geometry problem to get the joint positions satisfying the holonomic constraint. In this case, I think one way to solve the problem is by setting the holonomic constraint as a task in the cost function and giving the larger task gain compared to the cartesian task. Another way to solve the problem is using projected jacobian (J_cartesian_task * N_holonomic_constraint) with N = I - JJ_pseudo_inverse. Do you think those two methods sound okay to obtain the solution that I want? If so, can you point out which API in pink I should use to set the holonomic constraint as a cost in the QP (I think I could try the latter one by myself)?

Thank you, Seung Hyeon

Dear Caron: I found this repo by using Pinocchio when I tried to learn more about Meshcat, and thanks a lot for your code, I get some inspiration for drawing a TF tree for a robot model. My understanding of this code in pink

meshcat_shapes.frame(viewer["left_contact_target"], opacity=0.5)

is that we will replace the old object with a new frame. My question is if we could just add the frame by using addGeometryObject?

Thanks for your help! heaty

Continuous joints have nq=2, whereas the posture task assumes nq=1 for revolute joints so that the tangent twist between two joint configurations is simply their difference. This will need to be generalized.

• Example: see WIP_kinova_gen2_arm.py in the examples folder.
• Related: https://github.com/stack-of-tasks/pinocchio/issues/1751
• Related: https://github.com/stack-of-tasks/pinocchio/issues/794

When there is no velocity bound on a joint, Pink currently sets inequality constraints as $-\infty < v_i < \infty$. But with CVXOPT this approach yields ValueError: domain error.

Possible solutions:

• Trim large values (might not generalize well)
• Add some post-processing to remove redundant inequalities for CVXOPT specifically
• Avoid such inequalities altogether

The omnidirectional three-wheeled robot added by https://github.com/tasts-robots/pink/pull/14 does not work yet because of joint limits for its root planar joint.

This issue will be fixed by https://github.com/tasts-robots/pink/pull/12.

Performance increase is 5x as of 3f2feae3396bbc847a843b34c9ce162f75e55596 (on Upkie model):

In [1]: from pink.limits import compute_velocity_limits_2, compute_velocity_limits             

In [2]: %timeit compute_velocity_limits(configuration, dt)                                     
68.1 µs ± 5.7 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)

In [3]: %timeit compute_velocity_limits_2(configuration, dt)                                   
13.4 µs ± 596 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)