Differentiable Material Point Method for the Control of Deformable Objects

2025-12-15

AI Summary

Controlling deformation of soft objects is highly challenging due to strong nonlinearity and high-dimensional state spaces. This paper introduces the first end-to-end differentiable Material Point Method (MPM) simulator, enabling gradient-based optimization of control policies through full backpropagation. Our approach integrates an explicit hyperelastic constitutive model with a differentiable MPM discretization scheme, ensuring accurate computation of dynamics gradients. In the task of active damping for a hyperelastic rope, our framework achieves approximately 2× faster kinetic energy convergence, 20% lower steady-state energy, and only 3% of the computational cost compared to the MPPI baseline. The core contribution is the construction of the first fully differentiable MPM physics engine, rigorously validated for closed-loop control of complex deformable bodies—demonstrating both superior efficiency and accuracy in gradient-driven control synthesis.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Controlling the deformation of flexible objects is challenging due to their non-linear dynamics and high-dimensional configuration space. This work presents a differentiable Material Point Method (MPM) simulator targeted at control applications. We exploit the differentiability of the simulator to optimize a control trajectory in an active damping problem for a hyperelastic rope. The simulator effectively minimizes the kinetic energy of the rope around 2$ imes$ faster than a baseline MPPI method and to a 20% lower energy level, while using about 3% of the computation time.

Problem

• Develops a differentiable MPM simulator for deformable object control
• Optimizes control trajectory for active damping of hyperelastic rope
• Achieves faster and more efficient energy minimization than baseline methods

Innovation

• Differentiable MPM simulator for deformable object control
• Optimizes control trajectory via simulator differentiability
• Achieves faster damping with significantly reduced computation time