Computational co-design of structure and feedback controller for locomoting soft robots

TL;DR

This work tackles robust locomotion for soft robots by jointly optimizing their structure, actuator layout, and a terrain-aware neural controller. It combines density-based topology optimization with relaxed actuator layouts and a neural-network controller, all trained in the presence of terrain uncertainty using an augmented-Lagrangian, AD-enabled, gradient-based framework. The approach yields animal-like, legged morphologies that utilize adaptable actuation under diverse terrains, with numerical results in 2D and 3D showing improved travel performance and posture stability compared to feedforward designs. The framework advances the practical design of soft robots by enabling co-design that accounts for environmental variability and demonstrates promising directions for real-world deployment and more advanced learning architectures.

Abstract

Soft robots have gained significant attention due to their flexibility and safety, particularly in human-centric applications. The co-design of structure and controller in soft robotics has presented a longstanding challenge owing to the complexity of the dynamics involved. Despite some pioneering work dealing with the co-design of soft robot structures and actuation, design freedom has been limited by stochastic design search approaches. This study proposes the simultaneous optimization of structure and controller for soft robots in locomotion tasks, integrating topology optimization-based structural design with neural network-based feedback controller design. Here, the feedback controller receives information about the surrounding terrain and outputs actuation signals that induce the expansion and contraction of the material. We formulate the simultaneous optimization problem under uncertainty in terrains and construct an optimization algorithm that utilizes automatic differentiation within topology optimization and neural networks. We present numerical experiments to demonstrate the validity and effectiveness of our proposed method.

Figures (22)

• Figure 1: Conceptual diagram of our proposed method.
• Figure 2: Neural network for the feedback controller. The input signals consist of feedforward and feedback signals where feedforward signals are given as sinusoidal and cosinusoidal functions, and the feedback signals are the terrain height surrounding the soft robots.
• Figure 3: Conceptual diagram of convolution of terrain features. The star sign represents the center of mass of the soft robot and the black circle represents the grid node corresponding to the center of mass. A large circle defines the surrounding area and the terrain heights of the nodes in the circle (i.e., gray nodes whose indices form $\mathcal{B}^\mathrm{sur}(t)$) are used as feedback signals. Dashed boxes represent $3 \times 3$ neighboring nodes whose terrain heights are convoluted into the center node of each box, whose index forms $\tilde{\mathcal{B}}^\mathrm{sur}(t)$.
• Figure 4: Problem setting for the 2D walker. The gray square represents the design domain of a soft robot and dashed line illustrates the schematic diagram of randomly generated terrains. The soft robot is optimized so that the gray square can travel toward the right direction.
• Figure 5: Optimized structures and actuator layouts for various settings of $W$. (a) $W=0$, (b) $W=0.3$ and (c) $W=0.4$.