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Differentiable Simulation of Soft Robots with Frictional Contacts

Etienne Ménager, Louis Montaut, Quentin Le Lidec, Justin Carpentier

TL;DR

This work tackles differentiable simulation for soft robots in contact-rich environments by integrating FEM with a nonlinear complementarity problem for frictional contact and differentiable collision detection. The authors develop an end-to-end differentiable pipeline using implicit differentiation to compute gradients through continuum mechanics, collision resolution, and contact forces, enabling gradient-based control, design, and model reduction in soft robotics. Key contributions include differentiable collision detection for deformables, NCP derivative computation, and a method to chain these derivatives with FEM to obtain end-to-end gradients, demonstrated on parameter identification and inverse dynamics tasks. The approach advances the ability to optimize soft-robot systems in the presence of contact and friction, with open-source code planned for broader adoption.

Abstract

In recent years, soft robotics simulators have evolved to offer various functionalities, including the simulation of different material types (e.g., elastic, hyper-elastic) and actuation methods (e.g., pneumatic, cable-driven, servomotor). These simulators also provide tools for various tasks, such as calibration, design, and control. However, efficiently and accurately computing derivatives within these simulators remains a challenge, particularly in the presence of physical contact interactions. Incorporating these derivatives can, for instance, significantly improve the convergence speed of control methods like reinforcement learning and trajectory optimization, enable gradient-based techniques for design, or facilitate end-to-end machine-learning approaches for model reduction. This paper addresses these challenges by introducing a unified method for computing the derivatives of mechanical equations within the finite element method framework, including contact interactions modeled as a nonlinear complementarity problem. The proposed approach handles both collision and friction phases, accounts for their nonsmooth dynamics, and leverages the sparsity introduced by mesh-based models. Its effectiveness is demonstrated through several examples of controlling and calibrating soft systems.

Differentiable Simulation of Soft Robots with Frictional Contacts

TL;DR

This work tackles differentiable simulation for soft robots in contact-rich environments by integrating FEM with a nonlinear complementarity problem for frictional contact and differentiable collision detection. The authors develop an end-to-end differentiable pipeline using implicit differentiation to compute gradients through continuum mechanics, collision resolution, and contact forces, enabling gradient-based control, design, and model reduction in soft robotics. Key contributions include differentiable collision detection for deformables, NCP derivative computation, and a method to chain these derivatives with FEM to obtain end-to-end gradients, demonstrated on parameter identification and inverse dynamics tasks. The approach advances the ability to optimize soft-robot systems in the presence of contact and friction, with open-source code planned for broader adoption.

Abstract

In recent years, soft robotics simulators have evolved to offer various functionalities, including the simulation of different material types (e.g., elastic, hyper-elastic) and actuation methods (e.g., pneumatic, cable-driven, servomotor). These simulators also provide tools for various tasks, such as calibration, design, and control. However, efficiently and accurately computing derivatives within these simulators remains a challenge, particularly in the presence of physical contact interactions. Incorporating these derivatives can, for instance, significantly improve the convergence speed of control methods like reinforcement learning and trajectory optimization, enable gradient-based techniques for design, or facilitate end-to-end machine-learning approaches for model reduction. This paper addresses these challenges by introducing a unified method for computing the derivatives of mechanical equations within the finite element method framework, including contact interactions modeled as a nonlinear complementarity problem. The proposed approach handles both collision and friction phases, accounts for their nonsmooth dynamics, and leverages the sparsity introduced by mesh-based models. Its effectiveness is demonstrated through several examples of controlling and calibrating soft systems.

Paper Structure

This paper contains 15 sections, 17 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. FEM modelling in soft robotics
  4. Interactions with the external environment
  5. Soft Robot's internal mechanics
  6. Differentiable Soft-Robotics Simulation with Contact NCP
  7. Collision detection derivatives
  8. NCP derivatives using implicit differentiation
  9. Chaining FEM model derivatives and contact derivatives
  10. Experiments
  11. Verification of analytical derivatives
  12. Soft-systems and associated tasks
  13. Identification of material properties with the deformable beam
  14. Control tasks with soft robots
  15. Discussions and Conclusion

Figures (3)

  • Figure 1: Toy examples developed to test the calculation of derivatives. (1) Multi-contact and multi-material. (2) Actuation, constrained motion, and rigidification. (3) Collision detection and optimization of contact point positions.
  • Figure 2: Simulated deformable systems considered in this work. (1) Deformable beam with contact. (2) Deformable beam without contact. (3) Trunk robot. (4) The robot pianist, composed of three identical Finger robots. (5) Soft Gripper.
  • Figure 3: Optimization of the Young Modulus of the beam to achieve a target position for the mesh nodes. Young's modulus is expressed in MPa, distance in mm. Only the useful parts of the graphs are retained.