$\mathrm{SE}(3)$ Frame Equivariance in Dynamics Modeling and Reinforcement Learning

In this paper, we aim to explore the potential of symmetries in improving the understanding of continuous control tasks in the 3D environment, such as locomotion. The existing work in reinforcement learning on symmetry focuses on pixel-level symmetries in 2D environments or is limited to value-based planning. Instead, we considers continuous state and action spaces and continuous symmetry groups, focusing on translational and rotational symmetries.We propose a pipeline to use these symmetries in learning dynamics and control, with the goal of exploiting the underlying symmetry structure to improve dynamics modeling and model-based planning.