​​Suggestion on requirements.txt & A Question about Equation (26)​

[dazhongtu]

Dear lbusellato:
Hello! I've carefully reviewed your code and the referenced paper [1]. This GitHub project has been extremely helpful to me, and I'd like to express my sincere gratitude.
While using the project, I noticed the contents of the requirements.txt, which include many ROS 2 Foxy dependencies, such as:
ros2action==0.9.13 ros2bag==0.3.11 ros2cli==0.9.13 ros2component==0.9.13 ros2doctor==0.9.13 ros2interface==0.9.13 ros2launch==0.11.7 ros2lifecycle==0.9.13 ros2multicast==0.9.13 ros2node==0.9.13 ros2param==0.9.13 ros2pkg==0.9.13 ros2run==0.9.13 ros2service==0.9.13 ros2topic==0.9.13
These dependencies might be unnecessary for your GitHub project. I tested it on Ubuntu 22.04 and found that only three packages are actually required: matplotlib scipy scikit-learn. I'd like to suggest updating the requirements.txt accordingly.

Additionally, I have a question related to reference [1]. After examining the open-source code mentioned in the paper, I noticed the parameter λc in Equation (26). Does it actually affect the output trajectory? It seems to me that the output trajectory is only influenced by the mean of the KMP, whereas Equation (26) relates to variance. Is my understanding correct? How do you perceive the role of λc, which is represented as ’alpha‘ in your code?
Your code provides an implementation of Equation (26), which I couldn’t find in the original paper’s code. Thank you for expanding my knowledge in this regard. I’d greatly appreciate it if you could share your insights.
Looking forward to your response!

References

@Article{Huang19IJRR,
  Title = {Kernelized Movement Primitives},
  Author = {Huang, Y. and Rozo, L. and Silv\'erio, J. and Caldwell, D. G.},
  Journal = {International Journal of Robotics Research},
  Year = {2019},
  Volume={38},
  Number={7},
  Pages = {833--852},
}

[lbusellato]

Good catch on the requirements, as always I've got very messy workspaces and stuff gets mixed around.

As mentioned in another issue, this is an older project and some stuff is done in a different way wrt the original paper. I've essentially split eqn. 26 in two steps, one carried out in the fitting function, the rest handled by the predict function. The math is the same though.

Regarding alpha, it is the N/ λc term present in the paper. This was a suggestion by the author of the paper, supposedly helping in tuning the model. In a later project I switched back to using N/λc. In either case, that parameter influences only the predicted covariance, not the trajectory. Essentially it is a regularization term, if λc is low (or alpha is high) then the predicted covariance is tighter (with the risk of overfitting), while if λc is high (or alpha is low) the predicted covariance is wider. It basically regulates the tradeoff between the model's flexibility and generalization capabilities.

[dazhongtu]

Thank you for your reply. It took me some time to fully grasp your explanation, but I truly appreciate it. Your code is exceptionally clear and well-structured — I have great admiration for your work after reading through it.

Wishing you all the best!

[dazhongtu]

Now I understand that λc is a parameter that determines the ​variance​ of the KMP output trajectory — but it does ​not​ affect the trajectory itself. The shaded area in Figure 1d of reference [1] and the yellow region in your project's demo1 are exactly what is controlled by λc.

• When λc is small, the yellow region becomes narrower, since the covariance decreases.

• When λc is large, the yellow region widens, as the covariance increases.