For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.

Gripping and holding of objects are key tasks for robotic manipulators. The development of universal grippers able to pick up unfamiliar objects of widely varying shape and surface properties remains, however, challenging. Most current designs are based on the multifingered hand, but this approach introduces hardware and software complexities. These include large numbers of controllable joints, the need for force sensing if objects are to be handled securely without crushing them, and the computational overhead to decide how much stress each finger should apply and where. Here we demonstrate a completely different approach to a universal gripper. Individual fingers are replaced by a single mass of granular material that, when pressed onto a target object, flows around it and conforms to its shape. Upon application of a vacuum the granular material contracts and hardens quickly to pinch and hold the object without requiring sensory feedback. We find that volume changes of less than 0.5% suffice to grip objects reliably and hold them with forces exceeding many times their weight. We show that the operating principle is the ability of granular materials to transition between an unjammed, deformable state and a jammed state with solid-like rigidity. We delineate three separate mechanisms, friction, suction, and interlocking, that contribute to the gripping force. Using a simple model we relate each of them to the mechanical strength of the jammed state. This advance opens up new possibilities for the design of simple, yet highly adaptive systems that excel at fast gripping of complex objects.stress-strain | packing density | friction | suction | interlocking

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A central biological question is how natural organisms are so evolvable (capable of quickly adapting to new environments). A key driver of evolvability is the widespread modularity of biological networks—their organization as functional, sparsely connected subunits—but there is no consensus regarding why modularity itself evolved. Although most hypotheses assume indirect selection for evolvability, here we demonstrate that the ubiquitous, direct selection pressure to reduce the cost of connections between network nodes causes the emergence of modular networks. Computational evolution experiments with selection pressures to maximize network performance and minimize connection costs yield networks that are significantly more modular and more evolvable than control experiments that only select for performance. These results will catalyse research in numerous disciplines, such as neuroscience and genetics, and enhance our ability to harness evolution for engineering purposes.

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated ''reverse engineering'' approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.coevolution ͉ modeling ͉ symbolic identification M any branches of science and engineering represent systems that change over time as sets of differential equations, in which each equation describes the rate of change of a single variable as a function of the state of other variables. The structures of these equations are usually determined by hand from first principles, and in some cases regression methods (1-3) are used to identify the parameters of these equations. Nonparametric methods that assume linearity (4) or produce numerical models (5, 6) fail to reveal the full internal structure of complex systems. A key challenge, however, is to uncover the governing equations automatically merely by perturbing and then observing the system in intelligent ways, just as a scientist would do in the presence of an experimental system. Obstacles to achieving this lay in the lack of efficient methods to search the space of symbolic equations and in assuming that precollected data are supplied to the modeling process.Determining the symbolic structure of the governing dynamics of an unknown system is especially challenging when rare yet informative behavior can go unnoticed unless the system is perturbed in very specific ways. Coarse parameter sweeps or random samplings are unlikely to catch these subtleties, and so passive machine learning methods that rely on offline analysis of precollected data may be ineffective. Instead, active learning (7) processes that are able to generate new perturbations or seek out informative part...

Inspired by natural muscle, a key challenge in soft robotics is to develop self-contained electrically driven soft actuators with high strain density. Various characteristics of existing technologies, such as the high voltages required to trigger electroactive polymers ( > 1KV), low strain ( < 10%) of shape memory alloys and the need for external compressors and pressure-regulating components for hydraulic or pneumatic fluidicelastomer actuators, limit their practicality for untethered applications. Here we show a single self-contained soft robust composite material that combines the elastic properties of a polymeric matrix and the extreme volume change accompanying liquid–vapor transition. The material combines a high strain (up to 900%) and correspondingly high stress (up to 1.3 MPa) with low density (0.84 g cm−3). Along with its extremely low cost (about 3 cent per gram), simplicity of fabrication and environment-friendliness, these properties could enable new kinds of electrically driven entirely soft robots.

Animals sustain the ability to operate after injury by creating qualitatively different compensatory behaviors. Although such robustness would be desirable in engineered systems, most machines fail in the face of unexpected damage. We describe a robot that can recover from such change autonomously, through continuous self-modeling. A four-legged machine uses actuation-sensation relationships to indirectly infer its own structure, and it then uses this self-model to generate forward locomotion. When a leg part is removed, it adapts the self-models, leading to the generation of alternative gaits. This concept may help develop more robust machines and shed light on self-modeling in animals.

Biological life is in control of its own means of reproduction, which generally involves complex, autocatalysing chemical reactions. But this autonomy of design and manufacture has not yet been realized artificially. Robots are still laboriously designed and constructed by teams of human engineers, usually at considerable expense. Few robots are available because these costs must be absorbed through mass production, which is justified only for toys, weapons and industrial systems such as automatic teller machines. Here we report the results of a combined computational and experimental approach in which simple electromechanical systems are evolved through simulations from basic building blocks (bars, actuators and artificial neurons); the 'fittest' machines (defined by their locomotive ability) are then fabricated robotically using rapid manufacturing technology. We thus achieve autonomy of design and construction using evolution in a 'limited universe' physical simulation coupled to automatic fabrication.