A Fast and Model Based Approach for Evaluating Task-Competence of Antagonistic Continuum Arms

TL;DR

The paper tackles the challenge of designing soft, pneumatically actuated continuum arms by introducing a model-based, fast task-attainability analysis. It builds a planar Cosserat-rod continuum model and formulates a wrench-hull approach that estimates whether a proposed design can sustain a target shape under given loads, achieving orders-of-magnitude speedups over brute-force optimization. The authors demonstrate that antagonistic actuation expands task capability relative to non-antagonistic designs and provide intuitive, graphically interpretable insights into the mechanics. This framework enables rapid, task-specific comparisons to guide design choices in soft robotics, with potential extensions to more complex shapes and dynamics.

Abstract

Soft robot arms have made significant progress towards completing human-scale tasks, but designing arms for tasks with specific load and workspace requirements remains difficult. A key challenge is the lack of model-based design tools, forcing advancement to occur through empirical iteration and observation. Existing models are focused on control and rely on parameter fits, which means they cannot provide general conclusions about the mapping between design and performance or the influence of factors outside the fitting data.As a first step toward model-based design tools, we introduce a novel method of analyzing whether a proposed arm design can complete desired tasks. Our method is informative, interpretable, and fast; it provides novel metrics for quantifying a proposed arm design's ability to perform a task, it yields a graphical interpretation of performance through segment forces, and computing it is over 80x faster than optimization based methods.Our formulation focuses on antagonistic, pneumatically-driven soft arms. We demonstrate our approach through example analysis, and also through consideration of antagonistic vs non-antagonistic designs. Our method enables fast, direct and task-specific comparison of these two architectures, and provides a new visualization of the comparative mechanics. While only a first step, the proposed approach will support advancement of model-based design tools, leading to highly capable soft arms.

Figures (7)

• Figure 1: (A): We propose a method to evaluate fluid-driven soft arm designs on their ability to sustain a task shape at the task load. (B): We mainly demonstrate our method with planar antagonistic arm designs. Each arm segment has two extending and two contracting actuators, and arms move via selective actuator pressurization.
• Figure 2: Overview of our mechanics model. (A): A soft robot arm composed of two bellows and two muscles can be fully parameterized by its centerline twists $\accentset{{\circleright}}{g}_{oi}$ and transformations between actuators ${}_og_{o\alpha}$. (B): When a tip load $\mathbf{q}_{\textrm{tip}}$ is applied, wrenches $\mathbf{q}_i$ are induced along the arm's backbone. To achieve static equilibrium, each actuator contributes a reaction force and moment to balance the load. (C): We consider two types of actuators: contracting McKibben artificial muscles and extensile bellows actuators. The characterized force functions $f(\epsilon, p)$ of each actuator are also shown, with actuation regimes labeled according to olson_eulerbernoulli_2020.
• Figure 3: Visual explanation of attainable wrench spaces. (A-left): an example task shape and load, and consequent requirement wrenches. (A-right): equilibrium shapes that minimize tip position error or tip pose error compared to the specified task shape. (B): Points are uniformly sampled from the pressure space's edges uniformly, and from the interior using a beta distribution with $\alpha = \beta = 0.3$. Stars are the pressures $\tilde{\mathbf{p}}$ and $\bar{\mathbf{p}}$ which yield equilibrium shapes in (A-right). (C): The 2nd attainable wrench hull $\mathcal{H}_2$, with reaction and requirement wrenches superimposed. (D): Attainable wrench sequences corresponding to sampled pressures in (B) and solution pressures from (A). (E): Relative wrench sequences - the lines of the relative attainable wrench sequences are omitted for clarity.
• Figure 4: Visualization of wrench-spaces for different arm shapes. Using the arm design from Fig. \ref{['fig:wrench_hull_explanation']}A, we compute the correspondent attainable wrench-sequences for the sampled interior and edge pressures shown in Fig. \ref{['fig:wrench_hull_explanation']}B. These examples illustrate that the wrench-hull properties utilized in our simplified problem formulation hold across a wide variety of shapes. Note that both the direction and magnitude of the shift in each wrench-space along $i$ corresponds to sign and severity of the change in curvature along the arm centerline shape.
• Figure 5: Attainability methods accurately predict the ability of arm designs to accomplish a range of shared tasks. Reaction wrench requirements are imposed by 67 sampled tip-loads applied to two arm designs held at a task shape. The attainable wrench hull of an antagonistic arm encloses significantly more wrench requirements than that of an arm with only bellows, and this is quantified in (B) and (C) - vertical lines are medians. Attainability thus predicts that the antagonistic arm can complete more of the tasks, and this is confirmed by exhaustively searching in (D) and (E) for each arm's best attempt to match the specified shape while subject to each of the sampled tip loads . Tip loads are plotted without moments, and were uniformly sampled from the range of $\pm 10\textrm{N}\pm 10\textrm{N}\pm 1\textrm{Nm}$.