Integrating Symmetry into Differentiable Planning with Steerable Convolutions
Linfeng Zhao,Xupeng Zhu,Lingzhi Kong,Robin Walters,Lawson L.S. Wong
To achieve this, we draw inspiration from equivariant convolution networks and model the path planning problem as a set of signals over grids. We demonstrate that value iteration can be treated as a linear equivariant operator, which is effectively a steerable convolution. Building upon Value Iteration Networks (VIN), we propose a new Symmetric Planning (SymPlan) framework that incorporates rotation and reflection symmetry using steerable convolution networks. We evaluate our approach on four tasks: 2D navigation, visual navigation, 2 degrees of freedom (2-DOF) configuration space manipulation, and 2-DOF workspace manipulation. Our experimental results show that our symmetric planning algorithms significantly improve training efficiency and generalization performance compared to non-equivariant baselines, including VINs and GPPN.
