[Paper Review] Topology optimization of locomoting soft bodies using material point method

Yuki Sato, Hiroki Kobayashi+4 more|arXiv (Cornell University)|Mar 31, 2022

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes a topology optimization framework for locomoting soft bodies by integrating the material point method (MPM) with density-based topology optimization, enabling efficient simulation of large deformations, contact, and motion. The method achieves optimized soft robot designs—such as walkers and crawlers—that successfully locomote forward through time-domain optimization with validated performance gains over reference designs.

ABSTRACT

Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by conventionally used simulation techniques. In the present study, we propose a topology optimization method for moving objects incorporating the material point method, which is often used to simulate the motion of objects in the field of computer graphics. Several numerical experiments demonstrate the effectiveness and the utility of the proposed method.

Motivation & Objective

• To address the challenge of applying topology optimization to soft bodies undergoing large deformations, contact, and motion, which are difficult to simulate with conventional FEM-based methods.
• To integrate the material point method (MPM), known for handling large deformations and contact efficiently, into topology optimization for dynamic soft body design.
• To develop a material representation and density filtering scheme within the MPM framework to enable smooth, manufacturable designs.
• To demonstrate the method's effectiveness through numerical experiments on locomoting soft robots, such as walkers and crawlers.
• To enable computational design of novel soft robotic mechanisms with high design freedom and performance.

Proposed method

• The method uses a hybrid Lagrangian–Eulerian formulation of MPM to simulate large deformations, contact, and collision in soft bodies, overcoming mesh distortion issues common in FEM.
• A density filtering technique is introduced within the MPM framework to regularize the design field and produce smooth, manufacturable topologies.
• The material distribution is represented via particle-based density values ($\rho_p$) in MPM, with a smoothed Heaviside function to interpolate material properties.
• The optimization is formulated in the time domain, with forward and sensitivity analyses performed over a sequence of time steps to evaluate locomotion performance.
• The method of moving asymptotes (MMA) is used to solve the optimization problem, with adaptive refinement of the penalization parameter $\beta$ to promote binary designs.
• The objective function is defined as the negative displacement in the target direction, optimized over time to maximize forward locomotion.

Experimental results

Research questions

• RQ1 Can topology optimization be effectively applied to soft bodies undergoing large deformations and dynamic contact?
• RQ2 How can the material point method (MPM) be integrated into a time-domain topology optimization framework for soft robotics?
• RQ3 Can a density filtering technique be successfully implemented within the MPM framework to produce smooth, manufacturable designs?
• RQ4 What performance gains can be achieved in locomoting soft robots through MPM-based topology optimization compared to reference designs?
• RQ5 Can the proposed method generate novel, high-performance soft robotic mechanisms with minimal prior assumptions?

Key findings

• The optimized walker design achieved a forward displacement objective function value of -0.362, significantly outperforming the reference design (-0.208).
• Post-processed simulations of the optimized walker using particle-based representation yielded an objective value of -0.357, confirming robust performance.
• The optimized crawler design achieved an objective function value of -0.451, surpassing the reference design (-0.379) and post-processed result (-0.401).
• The crawler design successfully demonstrated forward locomotion by alternately pushing against walls using front and rear legs, as intended.
• The method successfully generated leg-like substructures in the walker and symmetric, actuated limbs in the crawler, indicating effective topological innovation.
• The use of MPM enabled stable simulation of large deformations and contact, which would be numerically unstable in standard FEM-based approaches.