Novel Algorithms for Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Construction

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about the dynamics holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining useful gradients and Hessians, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that can address the collision detection part of the puzzle in a manner that is smoothly differentiable and massively vectorizable. This is achieved via two contributions: i) a highly expressive class of analytical SDF primitives that can efficiently represent complex 3D surfaces, ii) a novel contact manifold generation routine that makes use of this geometry representation.

Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Generation

Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation: representing the volume of intersection between two colliding geometries via a discrete set of properly distributed contact points. A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern, and thus rely on logic and control flow that hinder these goals. We instead propose a framework designed from the ground up with these goals in mind, by trying to strike a middle ground between: i) convex primitive based approaches used by common robotics simulators (efficient but not differentiable), and ii) mollified vertex-face and edge-edge unsigned distance-based approaches used by barrier methods (differentiable but inefficient). Concretely, we propose: i) a representative set of smooth analytical signed distance primitives to implement vertex-face collisions, and ii) a novel differentiable edge-edge collision routine that can provide signed distances and signed contact normals. The proposed framework is evaluated via a set of didactic experiments and benchmarked against the collision detection routine of the well-established Mujoco XLA framework, where we observe a significant speedup. Supplementary videos can be found at https://github.com/bekeronur/contax, where a reference implementation in JAX will also be made available at the conclusion of the review process.

Learning 3D-Gaussian Simulators from RGB Videos

Learning physics simulations from video data requires maintaining spatial and temporal consistency, a challenge often addressed with strong inductive biases or ground-truth 3D information -- limiting scalability and generalization. We introduce 3DGSim, a 3D physics simulator that learns object dynamics end-to-end from multi-view RGB videos. It encodes images into a 3D Gaussian particle representation, propagates dynamics via a transformer, and renders frames using 3D Gaussian splatting. By jointly training inverse rendering with a dynamics transformer using a temporal encoding and merging layer, 3DGSimembeds physical properties into point-wise latent vectors without enforcing explicit connectivity constraints. This enables the model to capture diverse physical behaviors, from rigid to elastic and cloth-like interactions, along with realistic lighting effects that also generalize to unseen multi-body interactions and novel scene edits.