IK manifold flows | Ken-Joel Simmoteit

Goal: Learn a generative model, that predictes the closest joint states given a current seed configuration and a target pose.

Idea: Leverage manifold flows (Normalizing flows + zero padding) to learn a latent nullspace state given target pose and project current joint state into it

Schematic representation of the projection into the nullspace and (b) generation of a target configuration (a).

First, the given seed configuration $\mathbf{q}$ (current joint state) is projected on a latent nullspace state $\mathbf{z}$ conditioned on target pose $\mathbf{x}$ using a manifold flow $$f(\mathbf{q}

\mathbf{x})$. This flow is designed via conditioned Affine Coupling Layer. From this latent nullspace state we can generate a target configuration in null space using the inverted manifold flow$f^{-1}$$ and zero padding.

Schematic relation of the manifold flow model.

Experiments: Generate target joint state given seed configurations

The model is trained with $125000$ sampled joint states from an 3 DOF robot arm. For testing $100$ seed configurations and one target position (not in training set) are sampled from the robot simulator. Then the target configuration is predicted. For reference the IK solution using Levenberg-Marquardt (LM) algorithm is calculated. The resulting target pose has currently a position error of approx. $1\text{cm}$.

Predicted target configuration (orange) and calculated IK solution (green).

Experiments on a 7 DOF robot will follow soon.