sadET VS pinocchio

Then, each expression should carry enough information that you can call different member functions, such as derivative for their derivative, or conjugate to take its complex conjugate, etc. Now, the conjugate (and derivative) member function should somehow inherit its behaviour from the sub expressionss. You only need to define what conjugate means for the Number class, and then all other expressions, just apply this function to its sub expressions, until a Number is reached. I am not sure if this is detailed enough, but I apply this logic here. In this piece of code, I am using ETs to that define expressions, and then use these expressions to take their derivatives. This is an autodiff library (without dual numbers), which works well, but it suffers from the the problem; can't find a way to assign and reassign variables to expressions.

Open-loop walking + physics: (e.g. ZMP-based) one thing you can do (that does not imply adding an IMU to Kayra and going for feedback) is include some walking physics into your walking trajectory generation. To give you an idea, I've written a tutorial on doing that in Python a couple of years ago. The libraries in this tutorial are deprecated now, but I'm working on an equivalent stack at github.com/tasts-robots using more durable software like pinocchio. The libs are still WIP but if you are interested in exploring that dev path (i.e. making a ZMP-based trajectory generator for Kayra) I can support you and help adapt them (because I want that SW to be useful for a maximum number of people).

Drake and Pinocchio both use the Python interface to Meshcat as an option for visualizing robots, and they can both do the forward kinematics and have visualizer components that place the visual meshes properly relative to the computed frames, but both of those are full-fledged and complex kinematics and dynamics libraries for contact-rich interaction (and more), so the API calls to get a model set up are doing a lot more than providing a visual model you can feed joint angles to.

Pinocchio sounds like exactly what you need: https://github.com/stack-of-tasks/pinocchio