[Paper Review] ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

Yuanming Hu, Jiancheng Liu+6 more|arXiv (Cornell University)|Oct 2, 2018

Fluid Dynamics Simulations and Interactions23 references16 citations

TL;DR

ChainQueen is a real-time, differentiable physical simulator for soft robotics based on the Moving Least Squares Material Point Method (MLS-MPM), enabling efficient forward simulation and backward gradient computation. It achieves 4–9× speedup over state-of-the-art simulators while maintaining high precision, supporting gradient-based optimization for control, design, and system co-design in complex soft robotic tasks.

ABSTRACT

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects including contact and can be seamlessly incorporated into inference, control and co-design systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of control tasks for soft robots, including problems with nearly 3,000 decision variables.

Motivation & Objective

• To address the challenge of simulating deformable objects in soft robotics due to high degrees of freedom, complex contact dynamics, and computational cost.
• To develop a differentiable simulator that enables gradient-based optimization for inverse problems such as optimal control and motion planning.
• To achieve real-time performance with accurate gradients for both state and model parameters in a physically grounded, GPU-accelerated framework.
• To support novel applications in soft robotics, including controller design, physical property inference, and co-design of geometry, materials, and control.
• To provide a user-friendly, open-source toolchain for researchers and practitioners to develop soft robotic systems without low-level implementation expertise.

Proposed method

• Employs the Moving Least Squares Material Point Method (MLS-MPM) as the core simulation framework, combining Lagrangian particles with Eulerian grids for efficient large-deformation and contact handling.
• Introduces full differentiability of the MLS-MPM simulator with respect to both state variables (e.g., positions, velocities) and model parameters (e.g., Young’s modulus, density, mass).
• Derives analytical gradients through backpropagation using the chain rule, with closed-form expressions for gradients of energy, forces, and constraints, including friction and contact.
• Optimizes computational performance via GPU acceleration and leverages existing high-performance MPM optimization practices from prior work.
• Implements a hybrid Lagrangian-Eulerian formulation that naturally supports self-collisions, large deformations, and material transitions common in soft robotics.
• Supports end-to-end differentiability through all simulation stages, including grid-to-particle (G2P), particle-to-grid (P2G), and friction projection, enabling gradient flow from final states back to initial parameters.

Experimental results

Research questions

• RQ1 Can a differentiable physical simulator for soft robotics achieve real-time performance while maintaining high accuracy in both forward simulation and gradient computation?
• RQ2 How effectively can a differentiable simulator enable gradient-based optimization for complex soft robotic control and design tasks with thousands of decision variables?
• RQ3 To what extent does the differentiability of the MLS-MPM framework support inverse problems such as system identification and co-design of robot geometry, materials, and controllers?
• RQ4 How does the proposed simulator compare in speed and precision to existing state-of-the-art simulators for deformable objects with contact and large deformations?
• RQ5 Can the simulator be effectively integrated into high-level Python workflows to enable user-friendly development of soft robotic systems without low-level implementation knowledge?

Key findings

• ChainQueen achieves 4–9× speedup over the current state-of-the-art differentiable simulator while maintaining high precision in both forward simulation and gradient computation.
• The simulator enables successful optimization of soft robotic controllers with nearly 3,000 decision variables, demonstrating scalability to complex inverse problems.
• Gradient computation is accurate and efficient, with analytical gradients derived for all components including contact, friction, and material forces via backpropagation.
• Numerical and experimental validation confirms that ChainQueen closely matches real-world physical behavior in deformation, contact, and dynamic response.
• The simulator successfully supports system identification tasks, enabling inference of physical properties such as Young’s modulus, density, and mass from observed motion.
• Integration with high-level Python scripts enables user-friendly development, and the code and data will be open-sourced to benefit the broader robotics community.