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Achieving fast and accurate collective decisions with a large number of simple agents without relying on a central planning unit or on global communication is essential for developing complex collective behaviors. In this paper, we investigate the speed versus accuracy trade-off in collective decision-making in the context of a binary discrimination problem-i.e., how a swarm can collectively determine the best of two options. We describe a novel, fully distributed collective decision-making strategy that only requires agents with minimal capabilities and is faster than previous approaches. We evaluate our strategy experimentally, using a swarm of 100 Kilobots, and we study it theoretically, using both continuum and finite-size models. We find that the main factor affecting the speed versus accuracy trade-off of our strategy is the agents neighborhood size-i.e., the number of agents with whom the current opinion of each agent is shared. The proposed strategy and the associated theoretical framework can be used to design swarms that take collective decisions at a given level of speed and/or accuracy. Keywords collective decision-making • swarm robotics • majority rule • voter model • self-organization • ordinary differential equations • chemical reaction network • Gillespie algorithm • Kilobot

Designing and analyzing self-organizing systems such as robotic swarms is a challenging task even though we have complete knowledge about the robot's interior. It is difficult to determine the individual robot's behavior based on the swarm behavior and vice versa due to the high number of agent-agent interactions. A step towards a solution of this problem is the development of appropriate models, which accurately predict the swarm behavior based on a specified control algorithm. Such models would reduce the necessary number of time-consuming simulations and experiments during the design process of an algorithm. In this paper we propose a model with focus on an explicit representation of space because the effectiveness of many swarm robotic scenarios depends on spatial inhomogeneity. We use methods of statistical physics to address spatiality. Starting from a description of a single robot we derive an abstract model of swarm motion. The model is then extended to a generic model framework of communicating robots. In two examples we validate models against simulation results. Our experience shows that qualitative correctness is easily achieved while quantitative correctness is disproportionately more difficult but still possible.

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The search for generally applicable methods in swarm intelligence aims to gain new insights about natural swarms and to develop design methodologies for artificial swarms. The ideal would be a 'swarm calculus' that allows to calculate key features such as expected swarm performance and robustness on the basis of a few parameters. A path towards this ideal is to find methods and models that have maximal generality. We report two models that might be examples of exceptional generality. First, we present an abstract model that describes the performance of a swarm depending on the swarm density based on the dichotomy between cooperation and interference. Second, we give an abstract model for decision making that is inspired by urn models. A parameter, that controls the feedback based on the current consensus, allows to understand the effects of an increasing probability for positive feedback over time in a decision making system.

Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a 'swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported.

Besides the life-as-it-could-be driver of artificial life research there is also the concept of extending natural life by creating hybrids or mixed societies that are built from both natural and artificial components. In this paper, we motivate and present the research program of the project flora robotica. We present our concepts of control, hardware design, modeling, and human interaction along with preliminary experiments. Our objective is to develop and to investigate closely linked symbiotic relationships between robots and natural plants and to explore the potentials of a plant-robot society able to produce architectural artifacts and living spaces. These robot-plant bio-hybrids create synergies that allow for new functions of plants and robots. They also create novel design opportunities for an architecture that fuses the design and construction phase. The bio-hybrid is an example of mixed societies between 'hard artificial and 'wet natural life, which enables an interaction between natural and artificial ecologies. They form an embodied, selforganizing, and distributed cognitive system which is supposed to grow and develop over long periods of time resulting in the creation of meaningful architectural structures. A key idea is to assign equal roles to robots and plants in order to create a highly integrated, symbiotic system. Besides the gain of knowledge, this project has the objective to create a bio-hybrid system with a defined function and application -growing architectural artifacts.

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