Embodying Control in Soft Multistable Robots from Morphofunctional Co-design

TL;DR

This work tackles the challenging control problem of soft robots with infinite degrees of freedom by discretizing their configuration space into a finite set of programmable multistable states encoded directly in morphology. It introduces an energy-based, lumped-parameter model for a Dome Phalanx Finger (DPF) whose nonlinear springs, learned via Recursive Feature Elimination and FE simulations, enable fast inverse co-design of shape, stiffness, and time-response. Through Bayesian optimization and extensive experiments, the authors demonstrate that the DPF can be co-designed to perform tasks such as object classification, grasping with programmable stiffness, and open-loop locomotion, all with electronics-free actuation. The framework reduces control complexity, provides robustness through mechanical intelligence, and is scalable to diverse geometries and soft-material platforms, offering a practical path toward accessible, adaptable soft robotics.

Abstract

Soft robots are distinguished by their flexibility and adaptability, allowing them to perform nearly impossible tasks for rigid robots. However, controlling their behavior is challenging due to their nonlinear material response and infinite degrees of freedom. A potential solution to these challenges is to discretize the infinite-dimensional configuration space into a finite but sufficiently large number of functional modes with programmed dynamics. We present a strategy for co-designing the desired tasks and morphology of pneumatically actuated soft robots with multiple encoded stable states and dynamic responses. Our approach introduces a general method to capture the soft robots' response using an energy-based analytical model, the parameters of which are obtained using Recursive Feature Elimination. The resulting lumped-parameter model facilitates inverse co-design of the robot's morphology and planned tasks by embodying specific dynamics upon actuation. We illustrate our approach's ability to explore the configuration space by co-designing kinematics with optimized stiffnesses and time responses to obtain robots capable of classifying the size and weight of objects and displaying adaptable locomotion with minimal feedback control. This strategy offers a framework for simplifying the control of soft robots by exploiting the nonlinear mechanics of multistable structures and embodying mechanical intelligence into soft material systems

Figures (28)

• Figure 1: Multistable soft robot with pre-programmed dynamics for positioning and stiffness. Our robot displays four grasping set points ($s_0,s_1,s_3, s_4$) and embodied/morphological control. The robot's morphology and mechanical behavior encode its energy landscape's input and output dynamics (G(s)). Feedback H(s) is derived from the dynamic response of the robot, whereby designed attractors for each stable set point are encoded in the robot geometry. The system's output shows four set points as static minima in the energy landscape and attractors in the phase portrait, where $q$ and $\dot{q}$ are a schematic representation of the robot's generalized coordinates. Set points (energy minima) are accessed by activating/inverting the dome units: State 1 $\rightarrow$ Stress-free state (State 1) and $\rightarrow$ Inverted state (State 2).
• Figure 2: Dome Phalanx Finger (DPF) with different encoded mechanical responses and behaviors. a) 5-segment DPF geometry parameters ($i = 5$). b) Effect of dome height on finger response (Every segment with the same height). $H_i$ = 5 mm and $H_i$ = 4 mm show a bistable behavior, and $H_i$ = 3 mm shows a pseudo-bistable (metastable) response (self-resetting system). c) Metastable finger ($H_i = 3$ mm) Tip displacement and pressure over time. d) Bistable finger ($H_i = 5$ mm) Tip displacement and pressure over time. The same final position is achieved despite different actuation magnitudes (Input pressure). e) Time lapse of two gripper architectures showing both bistable and pseudo-bistable responses.
• Figure 3: An energy-based model for static and dynamic analysis of multistable soft robots based on the DPF topology. a) Spring lattice model with linear, rotational, and nonlinear springs. b) Static stable states predicted by the lattice model for $H_1$ = $H_2$ = 4 mm, $H_3$ = $H_4$ = 4.5 mm, and $H_5$ = 5 mm. c) Dynamic response for the soft robot with four bistable units and two metastable units ($H_1 = H_2 = H_3 = H_4 = 5$ mm, and $H_5=H_6=3$ mm). The model captures each bistable unit's snap-through and metastable units' snap-back (See Movie 2).
• Figure 4: DPF inverse design and experimental validation. (a) Predicted results for Target 1 and 3 from the optimization model (Position Design). (b) Objective function values as a function of the number of segments, with the minimum value identified for each target position. (c) The gripper achieves multiple stable kinematical states predicted by the energy-based model, which are successfully transferred to 3D-printed prototypes. (d) Stiffness determination of the DPF using a follower force approach, with Normalized strain energy vs. displacement curves, is shown for Objectives 1, 3, and 5. (e) Comparison of the proposed model and experimental results for position-only (Pos) optimization and combined position + stiffness optimization (Stf). (f) Dynamic response for a six-section DPF under two different loading profiles.
• Figure 5: Dome Phalanx Robot (DPR) architectures and applications. a) Classification loop for the DPG. The gripper reconfigures each design's stable state to sort the objects by size and weight (see Movie 7). b) The DPW actuator has two different zones and three bending directions. The action unit is utilized to create turning at the given pressure command. d) DPW architecture connected to create the tripod gate ($L_1$-$L_4$-$L_5$ and $L_2$-$L_3$-$L_6$). Forward units are utilized to create turns. e) Oscillating phases of the DPW with the robot at 30 psi of pressure. f) Snapshots of embodied pick-and-place tasks: A single pressure input is given for the robot to pick the object (Commanded response) and then release it depending on the viscoelastic material response (Programmed response)(see Movie 6). g) Snapshots of the walking trajectory of the DPW. A command is given by increasing the pressure in the first cycle to enable turning in both directions (Programmed response) (see Movie 9).