Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design sound-focusing/scrambling devices, acoustic filters, and analog computational units. At high amplitude vibrations or low confinement pressures, the effect of nonlinear particle contacts becomes increasingly noticeable, and the interplay of nonlinearity, disorder, and discreteness in the system gives rise to remarkable properties, particularly useful in designing structures with exotic properties. In this paper, we build upon the data-driven methods in dynamical system analysis and show that the Koopman spectral theory can be applied to granular crystals, enabling their phase space analysis beyond the linearizable regime and without recourse to any approximations considered in the previous works. We show that a deep neural network can map the dynamics to a latent space where the essential nonlinearity of the granular system unfolds into a high-dimensional linear space. As a proof of concept, we use data from numerical simulations of a two-particle system and evaluate the accuracy of the trajectory predictions under various initial conditions. By incorporating data from experimental measurements, our proposed framework can directly capture the underlying dynamics without imposing any assumptions about the physics model. Spectral analysis of the trained surrogate system can help bridge the gap between the simulation results and the physical realization of granular crystals and facilitate the inverse design of materials with desired behaviors.

There is growing interest in engineering unconventional computing devices that leverage the intrinsic dynamics of physical substrates to perform fast and energy-efficient computations. Granular metamaterials are one such substrate that has emerged as a promising platform for building wave-based information processing devices with the potential to integrate sensing, actuation, and computation. Their high-dimensional and nonlinear dynamics result in nontrivial and sometimes counter-intuitive wave responses that can be shaped by the material properties, geometry, and configuration of individual grains. Such highly tunable rich dynamics can be utilized for mechanical computing in special-purpose applications. However, there are currently no general frameworks for the inverse design of large-scale granular materials. Here, we build upon the similarity between the spatiotemporal dynamics of wave propagation in material and the computational dynamics of Recurrent Neural Networks to develop a gradient-based optimization framework for harmonically driven granular crystals. We showcase how our framework can be utilized to design basic logic gates where mechanical vibrations carry the information at predetermined frequencies. We compare our design methodology with classic gradient-free methods and find that our approach discovers higher-performing configurations with less computational effort. Our findings show that a gradient-based optimization method can greatly expand the design space of metamaterials and provide the opportunity to systematically traverse the parameter space to find materials with the desired functionalities.

Robots are notoriously difficult to design because of complex interdependencies between their physical structure, sensory and motor layouts, and behavior. Despite this, almost every detail of every robot built to date has been manually determined by a human designer after several months or years of iterative ideation, prototyping, and testing. Inspired by evolutionary design in nature, the automated design of robots using evolutionary algorithms has been attempted for two decades, but it too remains inefficient: days of supercomputing are required to design robots in simulation that, when manufactured, exhibit desired behavior. Here we show for the first time de-novo optimization of a robot's structure to exhibit a desired behavior, within seconds on a single consumer-grade computer, and the manufactured robot's retention of that behavior. Unlike other gradient-based robot design methods, this algorithm does not presuppose any particular anatomical form; starting instead from a randomly-generated apodous body plan, it consistently discovers legged locomotion, the most efficient known form of terrestrial movement. If combined with automated fabrication and scaled up to more challenging tasks, this advance promises near instantaneous design, manufacture, and deployment of unique and useful machines for medical, environmental, vehicular, and space-based tasks.

Unconventional computing devices are increasingly of interest as they can operate in environments hostile to silicon-based electronics, or compute in ways that traditional electronics cannot. Mechanical computers, wherein information processing is a material property emerging from the interaction of components with the environment, are one such class of devices. This information processing can be manifested in various physical substrates, one of which is granular matter. In a granular assembly, vibration can be treated as the information-bearing mode. This can be exploited to realize "polycomputing": materials can be evolved such that a single grain within them can report the result of multiple logical operations simultaneously at different frequencies, without recourse to quantum effects. Here, we demonstrate the evolution of a material in which one grain acts simultaneously as two different NAND gates at two different frequencies. NAND gates are of interest as any logical operations can be built from them. Moreover, they are nonlinear thus demonstrating a step toward general-purpose, computationally dense mechanical computers. Polycomputation was found to be distributed across each evolved material, suggesting the material's robustness. With recent advances in material sciences, hardware realization of these materials may eventually provide devices that challenge the computational density of traditional computers.

Empowerment -- a domain independent, information-theoretic metric -- has previously been shown to assist in the evolutionary search for neural cellular automata (NCA) capable of homeostasis when employed as a fitness function. In our previous study, we successfully extended empowerment, defined as maximum time-lagged mutual information between agents' actions and future sensations, to a distributed sensorimotor system embodied as an NCA. However, the time-delay between actions and their corresponding sensations was arbitrarily chosen. Here, we expand upon previous work by exploring how the time scale at which empowerment operates impacts its efficacy as an auxiliary objective to accelerate the discovery of homeostatic NCAs. We show that shorter time delays result in marked improvements over empowerment with longer delays, when compared to evolutionary selection only for homeostasis. Moreover, we evaluate stability and adaptability of evolved NCAs, both hallmarks of living systems that are of interest to replicate in artificial ones. We find that short-term empowered NCA are more stable and are capable of generalizing better to unseen homeostatic challenges. Taken together, these findings motivate the use of empowerment during the evolution of other artifacts, and suggest how it should be incorporated to accelerate evolution of desired behaviors for them. Source code for the experiments in this paper can be found at: https://github.com/caitlingrasso/empowered-nca-II.

Nature provides several examples of organisms that utilize shape change as a means of operating in challenging, dynamic environments. For example, the spider Araneus Rechenbergi [1, 2] and the caterpillar of the Mother-of-Pearl Moth (Pleurotya ruralis) [3] transition from walking gaits to rolling in an attempt to escape predation. Across larger time scales, caterpillar-tobutterfly metamorphosis enables land to air transitions, while mobile to sessile metamorphosis, as observed in sea squirts, is accompanied by radical morphological change. Inspired by such change, engineers have created caterpillar-like rolling [4], modular [5, 6, 7], tensegrity [8, 9], plant-like growing [10], and origami [11, 12] robots that are capable of some degree of shape change. However, progress toward robots which dynamically adapt their resting shape to attain different modes of locomotion is still limited. Further, design of such robots and their controllers is still a manually intensive process. Despite the growing recognition of the importance of morphology and embodiment on enabling intelligent behavior in robots [13], most previous studies have approached the challenge of operating in multiple environments primarily through the design of appropriate control strategies.

Robots deployed at orders of magnitude different size scales, and that retain the same desired behavior at any of those scales, would greatly expand the environments in which the robots could operate. However it is currently not known whether such robots exist, and, if they do, how to design them. Since self similar structures in nature often exhibit self similar behavior at different scales, we hypothesize that there may exist robot designs that have the same property. Here we demonstrate that this is indeed the case for some, but not all, modular soft robots: there are robot designs that exhibit a desired behavior at a small size scale, and if copies of that robot are attached together to realize the same design at higher scales, those larger robots exhibit similar behavior. We show how to find such designs in simulation using an evolutionary algorithm. Further, when fractal attachment is not assumed and attachment geometries must thus be evolved along with the design of the base robot unit, scale invariant behavior is not achieved, demonstrating that structural self similarity, when combined with appropriate designs, is a useful path to realizing scale invariant robot behavior. We validate our findings by demonstrating successful transferal of self similar structure and behavior to pneumatically-controlled soft robots. Finally, we show that biobots can spontaneously exhibit self similar attachment geometries, thereby suggesting that self similar behavior via self similar structure may be realizable across a wide range of robot platforms in future.

--Catastrophic forgetting continues to severely restrict the learnability of controllers suitable for multiple task environments. Efforts to combat catastrophic forgetting reported in the literature to date have focused on how control systems can be updated more rapidly, hastening their adjustment from good initial settings to new environments, or more circumspectly, suppressing their ability to overfit to any one environment. When using robots, the environment includes the robot's own body, its shape and material properties, and how its actuators and sensors are distributed along its mechanical structure. Here we demonstrate for the first time how one such design decision (sensor placement) can alter the landscape of the loss function itself, either expanding or shrinking the weight manifolds containing suitable controllers for each individual task, thus increasing or decreasing their probability of overlap across tasks, and thus reducing or inducing the potential for catastrophic forgetting. It has been shown in various single-task settings how an appropriate robot design can simplify the control problem [18, 27, 4, 2, 17, 22], but because these robots were restricted to a single training environment, they did not suffer catastrophic forgetting. Catastrophic forgetting is a major and unsolved challenge in the machine learning literature [9, 11, 15, 20].

A robot's mechanical parts routinely wear out from normal functioning and can be lost to injury. For autonomous robots operating in isolated or hostile environments, repair from a human operator is often not possible. Thus, much work has sought to automate damage recovery in robots. However, every case reported in the literature to date has accepted the damaged mechanical structure as fixed, and focused on learning new ways to control it. Here we show for the first time a robot that automatically recovers from unexpected damage by deforming its resting mechanical structure without changing its control policy. We found that, especially in the case of "deep insult", such as removal of all four of the robot's legs, the damaged machine evolves shape changes that not only recover the original level of function (locomotion) as before, but can in fact surpass the original level of performance (speed). This suggests that shape change, instead of control readaptation, may be a better method to recover function after damage in some cases.

Organisms result from adaptive processes interacting across different time scales. One such interaction is that between development and evolution. Models have shown that development sweeps over several traits in a single agent, sometimes exposing promising static traits. Subsequent evolution can then canalize these rare traits. Thus, development can, under the right conditions, increase evolvability. Here, we report on a previously unknown phenomenon when embodied agents are allowed to develop and evolve: Evolution discovers body plans robust to control changes, these body plans become genetically assimilated, yet controllers for these agents are not assimilated. This allows evolution to continue climbing fitness gradients by tinkering with the developmental programs for controllers within these permissive body plans. This exposes a previously unknown detail about the Baldwin effect: instead of all useful traits becoming genetically assimilated, only traits that render the agent robust to changes in other traits become assimilated. We refer to this as differential canalization. This finding also has implications for the evolutionary design of artificial and embodied agents such as robots: robots robust to internal changes in their controllers may also be robust to external changes in their environment, such as transferal from simulation to reality or deployment in novel environments.