Excitable crawling

TL;DR

The paper addresses soft robotic crawling control by designing a spiking, neuromorphic controller that uses proprioceptive feedback to generate endogenous peristaltic waves. A bistable voltage dynamics with $i_{FHN} = - \alpha V^3 + \beta V$ is coupled to a viscoelastic two-mass crawler via $f = k_v V$, yielding fast electrical and slow mechanical dynamics. Through nondimensionalization and geometric singular perturbation, the authors identify a strain-dependent switching mechanism that produces relaxation oscillations and a stable limit cycle, driving peristaltic locomotion. The approach promises adaptive electrical-to-mechanical scale matching and scalability to multi-segment crawlers, contributing a robust, energy-efficient framework for soft-robotic locomotion control.

Abstract

We propose and analyze the suitability of a spiking controller to engineer the locomotion of a soft robotic crawler. Inspired by the FitzHugh-Nagumo model of neural excitability, we design a bistable controller with an electrical flipflop circuit representation capable of generating spikes on-demand when coupled to the passive crawler mechanics. A proprioceptive sensory signal from the crawler mechanics turns bistability of the controller into a rhythmic spiking. The output voltage, in turn, activates the crawler's actuators to generate movement through peristaltic waves. We show through geometric analysis that this control strategy achieves endogenous crawling. The electro-mechanical sensorimotor interconnection provides embodied negative feedback regulation, facilitating locomotion. Dimensional analysis provides insights on the characteristic scales in the crawler's mechanical and electrical dynamics, and how they determine the crawling gait. Adaptive control of the electrical scales to optimally match the mechanical scales can be envisioned to achieve further efficiency, as in homeostatic regulation of neuronal circuits. Our approach can scale up to multiple sensorimotor loops inspired by biological central pattern generators.

Figures (3)

• Figure 1: (a) Schematic of the soft crawler analyzed in this work. The panel represents the nonlinear anisotropic friction model as given in \ref{['eq:sigma_def']}. (b) Closed-loop system: information flow between the crawler and the neuromorphic excitable controller proposed in Section \ref{['subsec:excitable_controller']}. The neuromorphic controller has the realization of a flip-flop electrical circuit.
• Figure 2: Trajectories of \ref{['eq:dimensionless_electromechanical_dynamics_movingFrame']} obtained in numerical simulation with parameter values: $\zeta = 4.7, \pi_{\mathsf{f}} = 2.5, \pi_{\mathsf{v}} = 0.5 , \pi_{\mathsf{\epsilon}} = 4.7 \cdot 10^3, n_f = 1.5, \pi_{\mathsf{c}} = 10^4, \pi_{\mathsf{l}} = \pi_{\mathsf{s}} = 2 \cdot 10^4$, and initial condition $\mathsf{V}(0) = 2, \mathsf{s}(0) = \mathsf{v_s}(0) = \mathsf{v_{com}}(0) = 0$. (a) and (b) show trajectories and speeds of crawler's head and tail, respectively. (c) Strain levels in the crawler. (d) Relaxation oscillations in the voltage. The fast (slow) dynamics correspond to segments going from purple (red) to red (purple) dots. The values of $\mathsf{V^{+/-}_{switch}}$ are as defined in \ref{['eq:switching condition_voltage-']} and \ref{['eq:switching condition_voltage+']}. All plots display dimensionless variables.
• Figure 3: (a) Limit cycle in the state variables $\mathsf{s}, \mathsf{v_s}, \mathsf{V}$ in red. Single (double) arrows on the limit cycle correspond to trajectories of the slow (fast) dynamics. The slow manifold \ref{['eq:slow_manifold']} is represented in grey. The switching points are indicated in purple; the initial condition is in black. (b) Schematic of the strain-modulated switching. Circled numbers indicate the temporal ordering of the snapshots. The value of the voltage is indicated by the dot in each panel. Purple (red) dots correspond to the value of the voltage right before (after) the switch. Parameter values and initial condition are as in Fig. \ref{['fig:crawling_summary']}.