Environmental influence on the evolution of morphological complexity in machines

Enhancing robot evolution through Lamarckian principles

Evolutionary robot systems offer two principal advantages: an advanced way of developing robots through evolutionary optimization and a special research platform to conduct what-if experiments regarding questions about evolution. Our study sits at the intersection of these. We investigate the question "What if the 18th-century biologist Lamarck was not completely wrong and individual traits learned during a lifetime could be passed on to offspring through inheritance?" We research this issue through simulations with an evolutionary robot framework where morphologies (bodies) and controllers (brains) of robots are evolvable and robots also can improve their controllers through learning during their lifetime. Within this framework, we compare a Lamarckian system, where learned bits of the brain are inheritable, with a Darwinian system, where they are not. Analyzing simulations based on these systems, we obtain new insights about Lamarckian evolution dynamics and the interaction between evolution and learning. Specifically, we show that Lamarckism amplifies the emergence of 'morphological intelligence', the ability of a given robot body to acquire a good brain by learning, and identify the source of this success: newborn robots have a higher fitness because their inherited brains match their bodies better than those in a Darwinian system.

Phenotypic complexity and evolvability in evolving robots

The propensity of evolutionary algorithms to generate compact solutions have advantages and disadvantages. On one side, compact solutions can be cheaper, lighter, and faster than less compact ones. On the other hand, compact solutions might lack evolvability, i.e. might have a lower probability to improve as a result of genetic variations. In this work we study the relation between phenotypic complexity and evolvability in the case of soft-robots with varying morphology. We demonstrate a correlation between phenotypic complexity and evolvability. We demonstrate that the tendency to select compact solutions originates from the fact that the fittest robots often correspond to phenotypically simple robots which are robust to genetic variations but lack evolvability. Finally, we demonstrate that the efficacy of the evolutionary process can be improved by increasing the probability of genetic variations which produce a complexification of the agents' phenotype or by using absolute mutation rates.

How the History of Changing Environments Affects Traits of Evolvable Robot Populations

The environment is one of the key factors in the emergence of intelligent creatures, but it has received little attention within the Evolutionary Robotics literature. This article investigates the effects of changing environments on morphological and behavioral traits of evolvable robots. In particular, we extend a previous study by evolving robot populations under diverse changing-environment setups, varying the magnitude, frequency, duration, and dynamics of the changes. The results show that long-lasting effects of early generations occur not only when transitioning from easy to hard conditions, but also when going from hard to easy conditions. Furthermore, we demonstrate how the impact of environmental scaffolding is dependent on the nature of the environmental changes involved.

The Effects of Learning in Morphologically Evolving Robot Systems

Simultaneously evolving morphologies (bodies) and controllers (brains) of robots can cause a mismatch between the inherited body and brain in the offspring. To mitigate this problem, the addition of an infant learning period has been proposed relatively long ago by the so-called Triangle of Life approach. However, an empirical assessment is still lacking to-date. In this paper, we investigate the effects of such a learning mechanism from different perspectives. Using extensive simulations we show that learning can greatly increase task performance and reduce the number of generations required to reach a certain fitness level compared to the purely evolutionary approach. Furthermore, we demonstrate that the evolved morphologies will be also different, even though learning only directly affects the controllers. This provides a quantitative demonstration that changes in the brain can induce changes in the body. Finally, we examine the learning delta defined as the performance difference between the inherited and the learned brain, and find that it is growing throughout the evolutionary process. This shows that evolution produces robots with an increasing plasticity, that is, consecutive generations become better learners and, consequently, they perform better at the given task. Moreover, our results demonstrate that the Triangle of Life is not only a concept of theoretical interest, but a system methodology with practical benefits.

Morphological Evolution: Bioinspired Methods for Analyzing Bioinspired Robots

To fully understand the evolution of complex morphologies, analyses cannot stop at selection: It is essential to investigate the roles and interactions of multiple processes that drive evolutionary outcomes. The challenges of undertaking such analyses have affected both evolutionary biologists and evolutionary roboticists, with their common interests in complex morphologies. In this paper, we present analytical techniques from evolutionary biology, selection gradient analysis and morphospace walks, and we demonstrate their applicability to robot morphologies in analyses of three evolutionary mechanisms: randomness (genetic mutation), development (an explicitly implemented genotype-to-phenotype map), and selection. In particular, we applied these analytical techniques to evolved populations of simulated biorobots—embodied robots designed specifically as models of biological systems, for the testing of biological hypotheses—and we present a variety of results, including analyses that do all of the following: illuminate different evolutionary dynamics for different classes of morphological traits; illustrate how the traits targeted by selection can vary based on the likelihood of random genetic mutation; demonstrate that selection on two selected sets of morphological traits only partially explains the variance in fitness in our biorobots; and suggest that biases in developmental processes could partially explain evolutionary dynamics of morphology. When combined, the complementary analytical approaches discussed in this paper can enable insight into evolutionary processes beyond selection and thereby deepen our understanding of the evolution of robotic morphologies.

Environmental Adaptation of Robot Morphology and Control Through Real-World Evolution

Robots operating in the real world will experience a range of different environments and tasks. It is essential for the robot to have the ability to adapt to its surroundings to work efficiently in changing conditions. Evolutionary robotics aims to solve this by optimizing both the control and body (morphology) of a robot, allowing adaptation to internal, as well as external factors. Most work in this field has been done in physics simulators, which are relatively simple and not able to replicate the richness of interactions found in the real world. Solutions that rely on the complex interplay among control, body, and environment are therefore rarely found. In this article, we rely solely on real-world evaluations and apply evolutionary search to yield combinations of morphology and control for our mechanically self-reconfiguring quadruped robot. We evolve solutions on two distinct physical surfaces and analyze the results in terms of both control and morphology. We then transition to two previously unseen surfaces to demonstrate the generality of our method. We find that the evolutionary search finds high-performing and diverse morphology-controller configurations by adapting both control and body to the different properties of the physical environments. We additionally find that morphology and control vary with statistical significance between the environments. Moreover, we observe that our method allows for morphology and control parameters to transfer to previously unseen terrains, demonstrating the generality of our approach.

Embodied intelligence via learning and evolution

The intertwined processes of learning and evolution in complex environmental niches have resulted in a remarkable diversity of morphological forms. Moreover, many aspects of animal intelligence are deeply embodied in these evolved morphologies. However, the principles governing relations between environmental complexity, evolved morphology, and the learnability of intelligent control, remain elusive, because performing large-scale in silico experiments on evolution and learning is challenging. Here, we introduce Deep Evolutionary Reinforcement Learning (DERL): a computational framework which can evolve diverse agent morphologies to learn challenging locomotion and manipulation tasks in complex environments. Leveraging DERL we demonstrate several relations between environmental complexity, morphological intelligence and the learnability of control. First, environmental complexity fosters the evolution of morphological intelligence as quantified by the ability of a morphology to facilitate the learning of novel tasks. Second, we demonstrate a morphological Baldwin effect i.e., in our simulations evolution rapidly selects morphologies that learn faster, thereby enabling behaviors learned late in the lifetime of early ancestors to be expressed early in the descendants lifetime. Third, we suggest a mechanistic basis for the above relationships through the evolution of morphologies that are more physically stable and energy efficient, and can therefore facilitate learning and control.

Real-World Robot Evolution: Why Would it (not) Work?

This paper takes a critical look at the concept of real-world robot evolution discussing specific challenges for making it practicable. After a brief review of the state of the art several enablers are discussed in detail. It is noted that sample efficient evolution is one of the key prerequisites and there are various promising directions towards this in different stages of maturity, including learning as part of the evolutionary system, genotype filtering, and hybridizing real-world evolution with simulations in a new way. Furthermore, it is emphasized that an evolutionary system that works in the real world needs robots that work in the real world. Obvious as it may seem, to achieve this significant complexification of the robots and their tasks is needed compared to the current practice. Finally, the importance of not only building but also understanding evolving robot systems is emphasised, stating that in order to have the technology work we also need the science behind it.

Understanding Organismal Capacity to Respond to Anthropogenic Change: Barriers and Solutions

Global environmental changes induced by human activities are forcing organisms to respond at an unprecedented pace. At present we have only a limited understanding of why some species possess the capacity to respond to these changes while others do not. We introduce the concept of multidimensional phenospace as an organizing construct to understanding organismal evolutionary responses to environmental change. We then describe five barriers that currently challenge our ability to understand these responses: 1) Understanding the parameters of environmental change and their fitness effects, 2) Mapping and integrating phenotypic and genotypic variation, 3) Understanding whether changes in phenospace are heritable, 4) Predicting consistency of genotype to phenotype patterns across space and time, and 5) Determining which traits should be prioritized to understand organismal response to environmental change. For each we suggest one or more solutions that would help us surmount the barrier and improve our ability to predict, and eventually manipulate, organismal capacity to respond to anthropogenic change. Additionally, we provide examples of target species that could be useful to examine interactions between phenotypic plasticity and adaptive evolution in changing phenospace.

Multi-Level Evolution for Robotic Design

Multi-level evolution (MLE) is a novel robotic design paradigm which decomposes the design problem into layered sub-tasks that involve concurrent search for appropriate materials, component geometry and overall morphology. This has a number of advantages, mainly in terms of quality and scalability. In this paper, we present a hierarchical approach to robotic design based on the MLE architecture. The design problem involves finding a robotic design which can be used to perform a specific locomotion task. At the materials layer, we put together a simple collection of materials which are represented by combinations of mechanical properties such as friction and restitution. At the components layer we combine these materials with geometric design to form robot limbs. Finally, at the robot layer we introduce these evolved limbs into robotic body-plans and learn control policies to form complete robots. Quality-diversity algorithms at each level allow for the discovery of a wide variety of reusable elements. The results strongly support the initial claims for the benefits of MLE, allowing for the discovery of designs that would otherwise be difficult to achieve with conventional design paradigms.

Criticality-Driven Evolution of Adaptable Morphologies of Voxel-Based Soft-Robots

The paradigm of voxel-based soft robots has allowed to shift the complexity from the control algorithm to the robot morphology itself. The bodies of voxel-based soft robots are extremely versatile and more adaptable than the one of traditional robots, since they consist of many simple components that can be freely assembled. Nonetheless, it is still not clear which are the factors responsible for the adaptability of the morphology, which we define as the ability to cope with tasks requiring different skills. In this work, we propose a task-agnostic approach for automatically designing adaptable soft robotic morphologies in simulation, based on the concept of criticality. Criticality is a property belonging to dynamical systems close to a phase transition between the ordered and the chaotic regime. Our hypotheses are that 1) morphologies can be optimized for exhibiting critical dynamics and 2) robots with those morphologies are not worse, on a set of different tasks, than robots with handcrafted morphologies. We introduce a measure of criticality in the context of voxel-based soft robots which is based on the concept of avalanche analysis, often used to assess criticality in biological and artificial neural networks. We let the robot morphologies evolve toward criticality by measuring how close is their avalanche distribution to a power law distribution. We then validate the impact of this approach on the actual adaptability by measuring the resulting robots performance on three different tasks designed to require different skills. The validation results confirm that criticality is indeed a good indicator for the adaptability of a soft robotic morphology, and therefore a promising approach for guiding the design of more adaptive voxel-based soft robots.

Constrained by Design: Influence of Genetic Encodings on Evolved Traits of Robots

Genetic encodings and their particular properties are known to have a strong influence on the success of evolutionary systems. However, the literature has widely focused on studying the effects that encodings have on performance, i.e., fitness-oriented studies. Notably, this anchoring of the literature to performance is limiting, considering that performance provides bounded information about the behavior of a robot system. In this paper, we investigate how genetic encodings constrain the space of robot phenotypes and robot behavior. In summary, we demonstrate how two generative encodings of different nature lead to very different robots and discuss these differences. Our principal contributions are creating awareness about robot encoding biases, demonstrating how such biases affect evolved morphological, control, and behavioral traits, and finally scrutinizing the trade-offs among different biases.

Environmental Regulation Using Plasticoding for the Evolution of Robots

Evolutionary robot systems are usually affected by the properties of the environment indirectly through selection. In this paper, we present and investigate a system where the environment also has a direct effect-through regulation. We propose a novel robot encoding method where a genotype encodes multiple possible phenotypes, and the incarnation of a robot depends on the environmental conditions taking place in a determined moment of its life. This means that the morphology, controller, and behavior of a robot can change according to the environment. Importantly, this process of development can happen at any moment of a robot's lifetime, according to its experienced environmental stimuli. We provide an empirical proof-of-concept, and the analysis of the experimental results shows that environmental regulation improves adaptation (task performance) while leading to different evolved morphologies, controllers, and behavior.

Science-Driven Societal Transformation, Part I: Worldview

Humanity faces serious social and environmental problems, including climate change and biodiversity loss. Increasingly, scientists, global policy experts, and the general public conclude that incremental approaches to reduce risk are insufficient and transformative change is needed across all sectors of society. However, the meaning of transformation is still unsettled in the literature, as is the proper role of science in fostering it. This paper is the first in a three-part series that adds to the discussion by proposing a novel science-driven research-and-development program aimed at societal transformation. More than a proposal, it offers a perspective and conceptual framework from which societal transformation might be approached. As part of this, it advances a formal mechanics with which to model and understand self-organizing societies of individuals. While acknowledging the necessity of reform to existing societal systems (e.g., governance, economic, and financial systems), the focus of the series is on transformation understood as systems change or systems migration—the de novo development of and migration to new societal systems. The series provides definitions, aims, reasoning, worldview, and a theory of change, and discusses fitness metrics and design principles for new systems. This first paper proposes a worldview, built using ideas from evolutionary biology, complex systems science, cognitive sciences, and information theory, which is intended to serve as the foundation for the R&D program. Subsequent papers in the series build on the worldview to address fitness metrics, system design, and other topics.

Environmental influences on evolvable robots

The field of Evolutionary Robotics addresses the challenge of automatically designing robotic systems. Furthermore, the field can also support biological investigations related to evolution. In this paper, we evolve (simulated) modular robots under diverse environmental conditions and analyze the influences that these conditions have on the evolved morphologies, controllers, and behavior. To this end, we introduce a set of morphological, controller, and behavioral descriptors that together span a multi-dimensional trait space. Using these descriptors, we demonstrate how changes in environmental conditions induce different levels of differentiation in this trait space. Our main goal is to gain deeper insights into the effect of the environment on a robotic evolutionary process.

Reinforcement Learning for Improving Agent Design

In many reinforcement learning tasks, the goal is to learn a policy to manipulate an agent, whose design is fixed, to maximize some notion of cumulative reward. The design of the agent's physical structure is rarely optimized for the task at hand. In this work, we explore the possibility of learning a version of the agent's design that is better suited for its task, jointly with the policy. We propose an alteration to the popular OpenAI Gym framework, where we parameterize parts of an environment, and allow an agent to jointly learn to modify these environment parameters along with its policy. We demonstrate that an agent can learn a better structure of its body that is not only better suited for the task, but also facilitates policy learning. Joint learning of policy and structure may even uncover design principles that are useful for assisted-design applications.

Scalable co-optimization of morphology and control in embodied machines

Evolution sculpts both the body plans and nervous systems of agents together over time. By contrast, in artificial intelligence and robotics, a robot's body plan is usually designed by hand, and control policies are then optimized for that fixed design. The task of simultaneously co-optimizing the morphology and controller of an embodied robot has remained a challenge. In psychology, the theory of embodied cognition posits that behaviour arises from a close coupling between body plan and sensorimotor control, which suggests why co-optimizing these two subsystems is so difficult: most evolutionary changes to morphology tend to adversely impact sensorimotor control, leading to an overall decrease in behavioural performance. Here, we further examine this hypothesis and demonstrate a technique for 'morphological innovation protection', which temporarily reduces selection pressure on recently morphologically changed individuals, thus enabling evolution some time to 'readapt' to the new morphology with subsequent control policy mutations. We show the potential for this method to avoid local optima and converge to similar highly fit morphologies across widely varying initial conditions, while sustaining fitness improvements further into optimization. While this technique is admittedly only the first of many steps that must be taken to achieve scalable optimization of embodied machines, we hope that theoretical insight into the cause of evolutionary stagnation in current methods will help to enable the automation of robot design and behavioural training-while simultaneously providing a test bed to investigate the theory of embodied cognition.

Morphologically induced stability on an underwater legged robot with a deformable body

For robots to navigate successfully in the real world, unstructured environment adaptability is a prerequisite. Although this is typically implemented within the control layer, there have been recent proposals of adaptation through a morphing of the body. However, the successful demonstration of this approach has mostly been theoretical and in simulations thus far. In this work we present an underwater hopping robot that features a deformable body implemented as a deployable structure that is covered by a soft skin for which it is possible to manually change the body size without altering any other property (e.g. buoyancy or weight). For such a system, we show that it is possible to induce a stable hopping behavior instead of a fall, by just increasing the body size. We provide a mathematical model that describes the hopping behavior of the robot under the influence of shape-dependent underwater contributions (drag, buoyancy, and added mass) in order to analyze and compare the results obtained. Moreover, we show that for certain conditions, a stable hopping behavior can only be obtained through changing the morphology of the robot as the controller (i.e. actuator) would already be working at maximum capacity. The presented work demonstrates that, through the exploitation of shape-dependent forces, the dynamics of a system can be modified through altering the morphology of the body to induce a desirable behavior and, thus, a morphological change can be an effective alternative to the classic control.

Evolving Soft Locomotion in Aquatic and Terrestrial Environments: Effects of Material Properties and Environmental Transitions

Designing soft robots poses considerable challenges; automated design approaches may be particularly appealing in this field, as they promise to optimize complex multimaterial machines with very little or no human intervention. Evolutionary soft robotics is concerned with the application of optimization algorithms inspired by natural evolution to let soft robots (both their morphologies and controllers) spontaneously evolve within physically realistic simulated environments, figuring out how to satisfy a set of objectives defined by human designers. In this article, a powerful evolutionary system is put in place to perform a broad investigation on the free-form evolution of simulated walking and swimming soft robots in different environments. Three sets of experiments are reported, tackling different aspects of the evolution of soft locomotion. The first two explore the effects of different material properties on the evolution of terrestrial and aquatic soft locomotion: particularly, we show how different materials lead to the evolution of different morphologies, behaviors, and energy-performance trade-offs. It is found that within our simplified physics world, stiffer robots evolve more sophisticated and effective gaits and morphologies on land, while softer ones tend to perform better in water. The third set of experiments starts investigating the effect and potential benefits of major environmental transitions (land↔water) during evolution. Results provide interesting morphological exaptation phenomena and point out a potential asymmetry between land→water and water→land transitions: while the first type of transition appears to be detrimental, the second one seems to have some beneficial effects.

Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence

Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical systems. Within this framework, we show that decidability imposes absolute limits on the stable growth of complexity in computable dynamical systems. Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems. Complexity is assessed in terms of three measures: sophistication, coarse sophistication, and busy beaver logical depth. These three complexity measures assign low complexity values to random (incompressible) objects. As time grows, the stated complexity measures allow for the existence of complex states during the evolution of a computable dynamical system. We show, however, that finding these states involves undecidable computations. We conjecture that for similar complexity measures that assign low complexity values, decidability imposes comparable limits on the stable growth of complexity, and that such behavior is necessary for nontrivial evolutionary systems. We show that the undecidability of adapted states imposes novel and unpredictable behavior on the individuals or populations being modeled. Such behavior is irreducible. Finally, we offer an example of a system, first proposed by Chaitin, that exhibits strong OEE.

The trade-off between morphology and control in the co-optimized design of robots

Conventionally, robot morphologies are developed through simulations and calculations, and different control methods are applied afterwards. Assuming that simulations and predictions are simplified representations of our reality, how sure can roboticists be that the chosen morphology is the most adequate for the possible control choices in the real-world? Here we study the influence of the design parameters in the creation of a robot with a Bayesian morphology-control (MC) co-optimization process. A robot autonomously creates child robots from a set of possible design parameters and uses Bayesian Optimization (BO) to infer the best locomotion behavior from real world experiments. Then, we systematically change from an MC co-optimization to a control-only (C) optimization, which better represents the traditional way that robots are developed, to explore the trade-off between these two methods. We show that although C processes can greatly improve the behavior of poor morphologies, such agents are still outperformed by MC co-optimization results with as few as 25 iterations. Our findings, on one hand, suggest that BO should be used in the design process of robots for both morphological and control parameters to reach optimal performance, and on the other hand, point to the downfall of current design methods in face of new search techniques.

Real-World Evolution of Robot Morphologies: A Proof of Concept

Evolutionary robotics using real hardware has been almost exclusively restricted to evolving robot controllers, but the technology for evolvable morphologies is advancing quickly. We discuss a proof-of-concept study to demonstrate real robots that can reproduce. Following a general system plan, we implement a robotic habitat that contains all system components in the simplest possible form. We create an initial population of two robots and run a complete life cycle, resulting in a new robot, parented by the first two. Even though the individual steps are simplified to the maximum, the whole system validates the underlying concepts and provides a generic workflow for the creation of more complex incarnations. This hands-on experience provides insights and helps us elaborate on interesting research directions for future development.

Compartmentalization of an all-E. coli Cell-Free Expression System for the Construction of a Minimal Cell

Cell-free expression is a technology used to synthesize minimal biological cells from natural molecular components. We have developed a versatile and powerful all-E. coli cell-free transcription-translation system energized by a robust metabolism, with the far objective of constructing a synthetic cell capable of self-reproduction. Inorganic phosphate (iP), a byproduct of protein synthesis, is recycled through polysugar catabolism to regenerate ATP (adenosine triphosphate) and thus supports long-lived and highly efficient protein synthesis in vitro. This cell-free TX-TL system is encapsulated into cell-sized unilamellar liposomes to express synthetic DNA programs. In this work, we study the compartmentalization of cell-free TX-TL reactions, one of the aspects of minimal cell module integration. We analyze the signals of various liposome populations by fluorescence microscopy for one and for two reporter genes, and for an inducible genetic circuit. We show that small nutrient molecules and proteins are encapsulated uniformly in the liposomes with small fluctuations. However, cell-free expression displays large fluctuations in signals among the same population, which are due to heterogeneous encapsulation of the DNA template. Consequently, the correlations of gene expression with the compartment dimension are difficult to predict accurately. Larger vesicles can have either low or high protein yields.

Open Issues in Evolutionary Robotics

One of the long-term goals in evolutionary robotics is to be able to automatically synthesize controllers for real autonomous robots based only on a task specification. While a number of studies have shown the applicability of evolutionary robotics techniques for the synthesis of behavioral control, researchers have consistently been faced with a number of issues preventing the widespread adoption of evolutionary robotics for engineering purposes. In this article, we review and discuss the open issues in evolutionary robotics. First, we analyze the benefits and challenges of simulation-based evolution and subsequent deployment of controllers versus evolution on real robotic hardware. Second, we discuss specific evolutionary computation issues that have plagued evolutionary robotics: (1) the bootstrap problem, (2) deception, and (3) the role of genomic encoding and genotype-phenotype mapping in the evolution of controllers for complex tasks. Finally, we address the absence of standard research practices in the field. We also discuss promising avenues of research. Our underlying motivation is the reduction of the current gap between evolutionary robotics and mainstream robotics, and the establishment of evolutionary robotics as a canonical approach for the engineering of autonomous robots.

A Theory of Cheap Control in Embodied Systems

We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent’s embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

Given a body and an environment, what is the brain complexity needed in order to generate a desired set of behaviors? The general understanding is that the physical properties of the body and the environment correlate with the required brain complexity. More precisely, it has been pointed that naturally evolved intelligent systems tend to exploit their embodiment constraints and that this allows them to express complex behaviors with relatively concise brains. Although this principle of parsimonious control has been formulated quite some time ago, only recently one has begun to develop the formalism that is required for making quantitative statements on the sufficient brain complexity given embodiment constraints. In this work we propose a precise mathematical approach that links the physical and behavioral constraints of an agent to the required controller complexity. As controller architecture we choose a well-known artificial neural network, the conditional restricted Boltzmann machine, and define its complexity as the number of hidden units. We conduct experiments with a virtual six-legged walking creature, which provide evidence for the accuracy of the theoretical predictions.

Advantages of Task-Specific Multi-Objective Optimisation in Evolutionary Robotics

The application of multi-objective optimisation to evolutionary robotics is receiving increasing attention. A survey of the literature reveals the different possibilities it offers to improve the automatic design of efficient and adaptive robotic systems, and points to the successful demonstrations available for both task-specific and task-agnostic approaches (i.e., with or without reference to the specific design problem to be tackled). However, the advantages of multi-objective approaches over single-objective ones have not been clearly spelled out and experimentally demonstrated. This paper fills this gap for task-specific approaches: starting from well-known results in multi-objective optimisation, we discuss how to tackle commonly recognised problems in evolutionary robotics. In particular, we show that multi-objective optimisation (i) allows evolving a more varied set of behaviours by exploring multiple trade-offs of the objectives to optimise, (ii) supports the evolution of the desired behaviour through the introduction of objectives as proxies, (iii) avoids the premature convergence to local optima possibly introduced by multi-component fitness functions, and (iv) solves the bootstrap problem exploiting ancillary objectives to guide evolution in the early phases. We present an experimental demonstration of these benefits in three different case studies: maze navigation in a single robot domain, flocking in a swarm robotics context, and a strictly collaborative task in collective robotics.