Subspace Planning

[chongwilliam]

Hi @thowell,

I wanted to ask about a feature addition to the planners, which is to plan within a subspace of the robot's control space. The subspace would be defined by a basis V, with the orthogonal projection matrix VV^{T}. I would be mainly interested in the derivative-based approaches for this purpose.

Thanks!

[Tadinu]

@chongwilliam may it be related to #370

[thowell]

@yuvaltassa do you think a plugin would make sense for this type of application?

[yuvaltassa]

The way I would do this depends on the answer to two questions. Let's call the size of your subspace nw, so the matrix $V$ is nu x nw.

1. Is nw fixed or varying? If varying, would it vary between episodes, planner iterations or timesteps within a rollout? Obviously these three options correspond to "easy", "hard" and "forget about it" 🙂
2. Now assuming nw is fixed or mostly fixed, how often do you imagine $V$ itself varying?

[chongwilliam]

In my application, I want to impose motion constraints given by geometric constraints between a manipulated object and the environment, for instance. Here, nw would vary based on the current interaction, so I would assume this means per planner iteration? Similarly, V would vary based on the interaction (maybe every few seconds or so).

[yuvaltassa]

Oh wow. This does not sound like a good idea at all. If you like, I can explain why this is a bad idea and/or provide examples of ideas that I think are good.

To do that I need to understand if you are

1. Interested in subspace planning and looking for an application.
2. Interested in imposing motion constraints and think that subspace planning might be a good solution.
3. Interested in this specific combination of problem and solution approach.

[chongwilliam]

I'm interested in 2. My goal is to compute online path modifications based on state estimation (object poses, force information, ...) for a nominal motion plan, where the modifications exist in a subspace. For example, in assembly tasks, there might be instances of jamming, where some constrained perturbations can be performed to un-jam the manipulated piece. I'm interested in hearing about your thoughts about the applicability of Mujoco MPC for this type of application.