The Surprising Effectiveness of Linear Models for Visual Foresight in Object Pile Manipulation

In this paper, we tackle the problem of pushing piles of small objects into a desired target set using visual feedback. Unlike conventional single-object manipulation pipelines, which estimate the state of the system parametrized by pose, the underlying physical state of this system is difficult to observe from images. Thus, we take the approach of reasoning directly in the space of images, and acquire the dynamics of visual measurements in order to synthesize a visual-feedback policy. We present a simple controller using an image-space Lyapunov function, and evaluate the closed-loop performance using three different class of models for image prediction: deep-learning-based models for image-to-image translation, an object-centric model obtained from treating each pixel as a particle, and a switched-linear system where an action-dependent linear map is used. Through results in simulation and experiment, we show that for this task, a linear model works surprisingly well -- achieving better prediction error, downstream task performance, and generalization to new environments than the deep models we trained on the same amount of data. We believe these results provide an interesting example in the spectrum of models that are most useful for vision-based feedback in manipulation, considering both the quality of visual prediction, as well as compatibility with rigorous methods for control design and analysis.