[Paper Review] Scalable Differentiable Physics for Learning and Control

Yi-Ling Qiao, Junbang Liang+2 more|arXiv (Cornell University)|Jul 4, 2020

Robot Manipulation and Learning30 citations

TL;DR

The paper presents a mesh-based differentiable physics engine with localized collision handling and fast implicit differentiation, achieving scalable gradient-based learning and control for large scenes with rigid and deformable objects.

ABSTRACT

Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions. To accommodate objects with arbitrary geometry and topology, we adopt meshes as our representation and leverage the sparsity of contacts for scalable differentiable collision handling. Collisions are resolved in localized regions to minimize the number of optimization variables even when the number of simulated objects is high. We further accelerate implicit differentiation of optimization with nonlinear constraints. Experiments demonstrate that the presented framework requires up to two orders of magnitude less memory and computation in comparison to recent particle-based methods. We further validate the approach on inverse problems and control scenarios, where it outperforms derivative-free and model-free baselines by at least an order of magnitude.

Motivation & Objective

• Motivate differentiable physics for learning and control in physical environments.
• Develop a scalable framework that supports many objects with arbitrary geometry.
• Use meshes to represent objects for generality and sparsity in collisions.
• Enable two-way coupling of rigid bodies and cloth.
• Provide gradient-based learning and control capabilities through differentiable simulation.

Proposed method

• Represent objects as meshes to capture arbitrary geometry and topology.
• Group collisions into localized impact zones to reduce variables and enable scalable collision handling.
• Apply implicit differentiation to compute gradients through embedded optimization with nonlinear constraints.
• Accelerate backpropagation by a QR-based scheme for the sparse KKT system in collision resolution.
• Demonstrate differentiable two-way coupling of rigid bodies and cloth within the same framework.
• Embed the differentiable physics engine as a differentiable layer in neural pipelines for end-to-end optimization.

Experimental results

Research questions

• RQ1 How does mesh-based differentiable physics scale with increasing scene size and complexity?
• RQ2 Can gradient-based optimization through the differentiable simulator outperform derivative-free or model-free baselines in learning and control tasks?
• RQ3 What is the impact of localized collision handling and fast differentiation on memory, computation, and accuracy compared to prior approaches?
• RQ4 Can the framework support two-way coupling between rigid bodies and deformable objects like cloth in differentiable simulations?

Key findings

• The framework requires up to two orders of magnitude less memory and computation than recent particle-based methods.
• Collision handling scales linearly with the number of constraints due to localized impact zones.
• Demonstrates two-way coupling of rigid bodies and cloth within a differentiable framework.
• Outperforms derivative-free and model-free baselines by at least an order of magnitude in inverse problems and control tasks.
• Empirically shows scalability and generality across scenes with many objects and varying relative sizes.