Amortized NeuralSDF-Mesh Collision Detection for Robotic Contact Simulation

Abstract

Collision detection is a fundamental problem in robotics, but handling collisions between non-convex objects remains challenging. A common approach for representing non-convex geometry is a signed distance function (SDF). Voxel-based SDF (VoxelSDF) enables fast distance queries but suffers from discretization artifacts and high memory costs. Neural implicit SDF (NeuralSDF) provides a continuous and memory-efficient representation with generalization, yet their slow query speed has limited their use in collision detection. To overcome these limitations, this paper proposes a novel amortized NeuralSDF–mesh collision detection framework. NeuralSDF–mesh collisions are formulated as a constrained optimization problem at the triangle level, and the Karush–Kuhn–Tucker conditions are derived to enable the amortization. A learning-based amortized optimization directly predicts collisions in a single forward pass, eliminating iterative optimization procedures. The amortized model adopts an auto-decoder architecture, extending the advantages of NeuralSDF in memory efficiency and category-level generalization to collision detection. Experiments demonstrate substantial speedups over baseline methods while maintaining comparable contact quality and reduced memory usage. The proposed approach also exhibits category-level generalization to unseen objects and can be applied to various robotic simulation scenarios.