Learning State Conditioned Linear Mappings for Low-Dimensional Control of Robotic Manipulators

TL;DR

Results suggest state-conditioned linear maps outperform conditional autoencoder and PCA baselines on a pick-and-place task and perform comparably to mode switching in a more complex pouring task.

Abstract

Identifying an appropriate task space that simplifies control solutions is important for solving robotic manipulation problems. One approach to this problem is learning an appropriate low-dimensional action space. Linear and nonlinear action mapping methods have trade-offs between simplicity on the one hand and the ability to express motor commands outside of a single low-dimensional subspace on the other. We propose that learning local linear action representations that adapt based on the current configuration of the robot achieves both of these benefits. Our state-conditioned linear maps ensure that for any given state, the high-dimensional robotic actuations are linear in the low-dimensional action. As the robot state evolves, so do the action mappings, ensuring the ability to represent motions that are immediately necessary. These local linear representations guarantee desirable theoretical properties by design, and we validate these findings empirically through two user studies. Results suggest state-conditioned linear maps outperform conditional autoencoder and PCA baselines on a pick-and-place task and perform comparably to mode switching in a more complex pouring task.

Figures (9)

• Figure 1: A user controls a 7-DOF robotic manipulator through low dimensional actions of a 2-DOF joystick. The state-conditioned linear mapping $h(\mathbf{q}) \in \mathbf{R}^{7 \times 2}$ transforms the joystick inputs $\mathbf{a}$ to high dimensional motor commands $\dot{\mathbf{q}}$.
• Figure 2: State conditional linear maps are trained as autoencoders. At deployment, the encoder is replaced with the appropriate control policy. In our teleoperation user study, the control policy $\pi(o_h)$ is embodied by a human.
• Figure 3: Empirical results from an experiment demonstrating proportionality and soft reversibility of SCL maps on the Kinova Gen-3 lite robot. The line and shaded area show the mean and one-half standard deviation from 100 runs (10 trained models, 10 random states), respectively. Note $||\mathbf{q}^{fwd}-\mathbf{q}_0||_2$ for SCL and PCA overlap.
• Figure 4: The number of trials in which participants successfully completed the Table Cleaning and Pick and Place tasks.
• Figure 5: Violin plots of euclidean distances across human prior loss combinations for training. Experiments were on simulated 5-DOF planar reaching task. Reported in log scale for visualization.

Theorems & Definitions (2)

• Theorem 1: Soft Reversibility
• proof