Materials Matter: Investigating Functional Advantages of Bio-Inspired Materials via Simulated Robotic Hopping

TL;DR

This work investigates how bio-inspired material properties, specifically porosity and elastic modulus, influence the functional performance of a hopping robot. It introduces a MuJoCo-based framework that models porosity via inertia and modulus via series springs, using Ashby-plot bounds to explore a material-design space. Across mono-materials and multi-material gradient links, the study shows that material properties can significantly reduce tracking error, with density and porosity shifts enabling functional tunability, while gradient designs can improve performance with manageable power costs. The findings suggest leveraging material anisotropies and gradients in future robotic fabrication to enhance locomotion, supported by a tractable simulation methodology and quantitative analyses of tracking, power, and jerk.

Abstract

In contrast with the diversity of materials found in nature, most robots are designed with some combination of aluminum, stainless steel, and 3D-printed filament. Additionally, robotic systems are typically assumed to follow basic rigid-body dynamics. However, several examples in nature illustrate how changes in physical material properties yield functional advantages. In this paper, we explore how physical materials (non-rigid bodies) affect the functional performance of a hopping robot. In doing so, we address the practical question of how to model and simulate material properties. Through these simulations we demonstrate that material gradients in the leg of a single-limb hopper provide functional advantages compared to homogeneous designs. For example, when considering incline ramp hopping, a material gradient with increasing density provides a 35% reduction in tracking error and a 23% reduction in power consumption compared to homogeneous stainless steel. By providing bio-inspiration to the rigid limbs in a robotic system, we seek to show that future fabrication of robots should look to leverage the material anisotropies of moduli and density found in nature. This would allow for reduced vibrations in the system and would provide offsets of joint torques and vibrations while protecting their structural integrity against reduced fatigue and wear. This simulation system could inspire future intelligent material gradients of custom-fabricated robotic locomotive devices.

Figures (7)

• Figure 1: Our work explores how material properties (specifically porosities and moduli) influence the functional performance of a robotic system. The bio-inspiration behind this approach is the natural gradient of porosity and modulus across bone and bone-muscle-tendon connections.
• Figure 2: Framework for the experiments conducted with the robotic hopper shown in A) with the materials with mass $m$ and spring constant $k$ taken from modified Ashby plots shown in B) plotted of their density-modulus relationship. The robotic hopper moves via the controller shown in C) to perform the four simulated behaviors shown in D).
• Figure 3: The configuration of the hopper is expressed as $\mathbf{q} = (\mathbf{p}, \boldsymbol{\phi}, \theta_x, \theta_y, l_s)$, in which $\mathbf{p}= (p_x, p_y, p_z) \in \mathbb{R}^3$ represents the position of the base frame relative to the world frame, $\boldsymbol{\phi} = (\phi_x, \phi_y, \phi_z) \in SO(3)$ denotes the orientation of the base frame relative to the world, $\{\theta_x, \theta_y\} \in \mathbb{R}$ represent the joint angles describing the angle of the leg about the axes $\hat{x}_b$ and $\hat{y}_b$, respectively, and $l_s \in \mathbb{R}$ denotes the extended length of the linear actuator controlling hop height.
• Figure 4: The heat map illustrates the effect of material modulus and density on the time step required to maintain stable forward integration of the dynamics. The results show that dense/soft materials allow for faster simulation speeds, while porous/stiff materials require more frequent computation of the dynamics, resulting in slower simulation speeds.
• Figure 5: Gait tiles illustrating the hopping motion for A) forward hopping and B) up-ramp hopping on 3.5% grade.