Cellular Plasticity Model for Bottom-Up Robotic Design

TL;DR

This work addresses the need for adaptable, bottom-up robotic design by embedding cellular plasticity within a morphogenesis-inspired activator–inhibitor framework augmented with environmental stimuli. The authors formulate a simplified factory–product model, derive analytical steady-state and stability conditions, and explore multi-factory extensions with competition, revealing that the system converges to a single stable equilibrium tuned to environmental demand. Key findings show that growth is driven by product scarcity, sustained stimuli modulate functional capacity, and specialization can increase total system capacity, all within a self-contained regulatory structure. The approach offers a principled pathway to emergent robot morphologies that adapt to real-world conditions without relying on comprehensive environmental models, with potential applications in bottom-up design platforms like Loopy and beyond.

Abstract

Traditional top-down robotic design often lacks the adaptability needed to handle real-world complexities, prompting the need for more flexible approaches. Therefore, this study introduces a novel cellular plasticity model tailored for bottom-up robotic design. The proposed model utilizes an activator-inhibitor reaction, a common foundation of Turing patterns, which are fundamental in morphogenesis -- the emergence of form from simple interactions. Turing patterns describe how diffusion and interactions between two chemical substances-an activator and an inhibitor-can lead to complex patterns and structures, such as the formation of limbs and feathers. Our study extends this concept by modeling cellular plasticity as an activator-inhibitor reaction augmented with environmental stimuli, encapsulating the core phenomena observed across various cell types: stem cells, neurons, and muscle cells. In addition to demonstrating self-regulation and self-containment, this approach ensures that a robot's form and function are direct emergent responses to its environment without a comprehensive environmental model. In the proposed model, a factory acts as the activator, producing a product that serves as the inhibitor, which is then influenced by environmental stimuli through consumption. These components are regulated by cellular plasticity phenomena as feedback loops. We calculate the equilibrium points of the model and the stability criterion. Simulations examine how varying parameters affect the system's transient behavior and the impact of competing functions on its functional capacity. Results show the model converges to a single stable equilibrium tuned to the environmental stimulation. Such dynamic behavior underscores the model's utility for generating predictable responses within robotics and biological systems, showcasing its potential for navigating the complexities of adaptive systems.

Figures (7)

• Figure 1: Cellular plasticity model for bottom-up robotic design. This model utilizes a self-replicating factory that produces a product consumed by the environment. This product also inhibits the production and growth rate of the factory, allowing for stable self-regulated adaption to the environmental changes in product consumption.
• Figure 2: Expansion of the cellular plasticity model to multiple unique functions within a single cell, via multiple competing factories that oppose each other at a rate of $O_{ij}$
• Figure 3: A Representative phase portrait of the single factory's response with the product (orange) and factory (blue) nullclines, and a single non-zero equilibrium (red star) with parameters of $G=K=I=1.0$, $C=0.5$, and $R=1.5$. $P_{lim}$ describes the limit product level as the product nullcline approaches infinity. The inward spiral of the phase portrait signifies a stable equilibrium that attracts from any positive state.
• Figure 4: Parametric effects on the relative time constants of the product ($\tau_p$) and factory ($\tau_f$), particularly as system parameters near zero or instability $\tau_f$ becomes much larger than $\tau_p$. The orange region displays where the product time constant exceeds the factory time constant. Damped oscillatory modes emerge when $P_{lim}$ significantly exceeds $P_\infty$, marked by the white region.
• Figure 5: Product ($P$) and Factory ($F$) transient response to short (at $t=50$) and long (at $t=100$) periods of increased in consumption (C). In addition to the net production rate ($PR$) and minimum factory capacity ($F_{min}$). Furthermore, the steady-state factory, product, and production rate are plotted with dotted lines. Parameter values are $G=K=I=1.0$ and $R=1.1$