In vivo, in silico, in machina: ants and robots balance memory and communication to collectively exploit information Melanie E. Moses, Kenneth Letendre, Joshua P. Hecker, Tatiana P. Flanagan Department of Computer Science, University of New Mexico Albuquerque, NM, USA 87131 {melaniem,kletendre,jhecker,tpaz}@unm.edu Abstract. Ants balance the use of remembered private information and communicated public information to maximally exploit resources. This work determines how the strategy that best balances these two sources of information, and the performance of that best strategy, depend on the information in the distribution that is available to be exploited, and the number of ants in the colony. We answer this question by 1) measuring the rates at which ants foraging for seeds in manipulative field studies, 2) simulating ant foraging strategies and measuring resulting foraging performance, and 3) implementing foraging strategies as algorithms for search behaviors in teams of cooperatively searching robots. Keywords: Ants, swarm robotics, agent based modeling, evolutionary algorithms 1 Introduction The behavior of the largest ant colonies emerges from the individual behaviors of millions of ants, where behaviors can be influenced by distributed communication among nest mates. Ant colonies are canonical distributed systems. Without central control, the interactions among millions of communicating individuals enable ant colonies to search and respond to complex, dynamic landscapes effectively. We hypothesize that ant colonies, immune systems and other complex biological systems use similar strategies to accomplish effective decentralized search. By demonstrating how behavioral rules of individual ants result in colony-level responses to changing food distributions, we elucidate principles that underlie emergent behavior of other complex systems in biology, computation and societies. In this work, we aim to understand how ants balance the use of remembered private information and communicated public information to achieve efficient, robust, and scalable search. We use evolutionary optimization algorithms to find the balance between communication and memory that maximizes seed intake in simulated foraging ants. Those behaviors are then encoded as algorithms in physical robots that search for RFID tags individually or in teams of three.
In vivo. Our field studies are conducted on three species of Pogonomyrmex seed harvesters whose colony size varies from dozens to thousands [6]. Seeds are hard to find, so the duration of a foraging trip, which includes travel time and search time, is dominated by search time. These ants often use site fidelity, a process in which an ant remembers and returns to the last site in which it found a seed [1, 2]. When resources are clumped, site fidelity reduces an individual ant s search times for other nearby seeds [9]. Seed harvesters appear to lay pheromone trails to recruit nest mates to large piles of food, but this may be rare under natural circumstances [11]. We ask how colony size (the number of foragers in the colony) and food distribution affect the rate at which seeds are collected. In silico. We simulate ant foraging using a set of agent-based models (ABMs) of 100 foragers on a grid, with parameters describing individual ant behavior optimized by a genetic algorithm (GA). GAs enable multi-parameter optimization by simulating evolutionary processes. GAs have been successfully used to evolve parameters for use in swarm robotics [5]. Our GA selects parameters that specify how ants travel from the nest, search, and balance use of site fidelity and pheromone communication to maximize seed collection rates in simulations. In machina. Swarm robotics is necessitated by problems that are inherently too complex or difficult for a single robot, and by the need to develop systems that are cheaper, more adaptive, and robust to failures, errors and dynamic environments [4]. Like ant colonies and other complex systems, robotic swarms have potential to utilize efficient, robust, distributed approaches to physical tasks. Effective algorithms for swarm robotics must extend beyond simulation to intelligently deal with the complexities of navigating in real environments. We build low cost robots based on the open source Arduino platform equipped with ultrasound, wifi to allow communication with a central server, a compass, and ability navigate via dead reckoning. We test how quickly individual robots and teams of three robots collect RFID tags distributed in ways that mimic our field studies and simulations. The ant foraging ABM was modified to model our swarm robots and our experimental setup. Thus, simulations provide both a theoretical benchmark and a basic architecture for using GAs to optimize real world parameters. 2 Methods In vivo. We conducted manipulative field experiments on three sympatric species of Pogonomyrmex seed-harvesters in the summers of 2008 and 2009 in Albuquerque, New Mexico [6,7]. We baited each colony with dyed seeds arranged in a ring around the colony entrance (Fig. 1a). Equal numbers of seeds were placed in four distributions varying pile number and size. For the largest colonies we used 1 pile of 256 red seeds; 4 piles of 64 purple seeds; 16 piles of 16 green seeds; and a random scattering of 256 blue seeds. After placing the baits, an observer time stamped the color of each seed brought into the nest. Data are reported for 27 experiments, nine on each of the three species.
For every experiment we calculated a normalized foraging rate: first we calculated the rate at which seeds from each distribution were collected by dividing the number of seeds collected from a distribution by the time between collecting the first and last seed of that color; the normalized foraging rate was calculated by dividing the seed rate for a piled distribution by the seed rate for randomly scattered seeds. These three normalized rates (one each for red, purple, and green seeds) measures how much faster clumped seeds are collected compared to randomly distributed seeds. The normalized measure allows us to meaningfully compare across variable colony sizes and activity levels, and to compare results from the field to those from the model. In silico. Simulations are derived from the model described in [6,12]. We use GAs to optimize the behavior of simulated ants foraging in three different food environments (clumped, power law and random), using site fidelity alone, recruitment alone, neither strategy, or both foraging strategies together. Within each simulated colony, every ant shares the same set of parameters that determines its behavior. 100 ants forage on a grid of 4000 X 4000 cells, with 25,600 seeds placed in one of the three distributions. At model initialization, all ants begin at a nest located at the center of the grid. Upon picking up food, an ant decides whether to leave a pheromone trail on the return trip to the nest, or remember the location and return to it, or abandon that search site. This decision is based on the number of other seeds in neighboring grid cells, as actual ants might use smell or briefly handle seeds nearby to gauge their density. An ant laying a trail deposits pheromone on each cell it walks over during its trip back to the nest. This pheromone evaporates from the grid over time. The ABM requires estimating 12 floating point parameters that are not known from field studies. These parameters determine degree of turning during the correlated random walk of a searching ant; the probability that an ant will remember the site at which the seed was found or lay a trail to that site; the dependence of the probability of remembering or trail laying as a function of local seed density; evaporation rate of the pheromone trails; and probability that ants abandon pheromone trails. We used a GA to find a set of parameters for every ant in a simulated colony that maximized foraging rate by that colony on a particular seed distribution. In machina. We adapted behaviors identified in simulations into algorithms that determine the behavior of robots searching for RFID tags [10]. In each hour-long experiment, robots begin at a nest to which they return once they have located a tag. At the nest, robots communicate with a laptop for localizing and error correction by the robots ultra- sonic sensors, and for managing the communication of pheromone trails (encoded as x,y coordinate pairs where the nest represents 0,0). We programmed each robot to stay within a 3m radius virtual fence to deter drift outside of the experimental area. In every experiment, 32 RFID tags were arranged in one of three different patterns: random, clustered, or power law. Each was distributed in a ring between 50 cm and 200 cm from the nest. The clustered layout has four piles of eight tags. The power law layout mimics the seed distribution in Fig. 1, but with 32 tags
rather than 1024 total seeds. Experiments are replicated 5 times each under identical conditions for individual robots and for groups of three bots. A simulation system was adapted from the ant foraging simulation to precisely replicate the behavior of the robots movements, interactions and their experimental area. In addition to simulating the 3-m radius area to which the physical robots were restricted, we also simulated the behavior of the robots in a much larger unbounded area, with tags distributed in the same density, but in such large numbers that even large swarms of robots collect only a small fraction of the available tags. We simulated 1- and 3-robot swarms, and also scaled up to 30 and 100 robot swarms to observe the scaling properties of the system. 3 Results Fig. 1b shows the normalized foraging rates the rates at which piled seeds are collected divided by rate at which random seeds are collected when seeds are distributed as in Fig. 1a. A value of 0 indicates that seeds from a piled distribution are collected at the same rate as randomly distributed seeds. All piled distributions are collected significantly faster than random seeds. The log 2 -transformed normalized rates are 0.3, 0.5 and 1.2 for seeds distributed in 16, 4 and 1 pile. We note that the foraging rates decrease in proportion to the information required to find additional seeds once a seed of a given color is found (4 bits for the 16 piles, 2 bits for the 4 piles and 0 bits for the single pile). Fig. 1. A) Experimental seed distribution around the nest entrance of a P. rugosus colony. Each colored circle is a pile of millet seeds dyed to that color. The size of each circle represents the relative number of seeds in that pile. All four seed colors are provided simultaneously for each experiment. B) Bars indicate log 2 transformed normalized rates (foraging rate of piled seeds divided by foraging rate of random seeds) for three seed distributions averaged over all 27 experiments. Error bars are standard errors.
Fig. 2. Bars represent number of seeds collected during simulated foraging trials by colonies of 100 foragers. Colonies forage on clustered, random, and power law distributed food, after optimization by GA to maximize food collection rate on those distributions. Results show the effect of using site fidelity, pheromone recruitment, both methods together, or neither (no information use). The foraging success of virtual ants evolved by the GA is shown in Fig. 2. Foragers collect the most food when it is distributed at random (green bars). In this case, the GA evolves parameters that distribute foragers evenly across the grid. Little benefit accrues from memory or communication when seeds are not clumped. In both power law and clustered distributions, seeds are collected faster using site fidelity than communication alone, but both together are most effective. Foraging rate on the clustered distribution (blue bars) is affected by foraging strategy more than the other two distributions. Fig. 3. A robot begins its search at a globally shared central nest site (center circle) and sets a search location. The robot then travels to the search site (yellow line). Upon reaching the search location, the robot searches for tags via a biased random walk(blue line) until tags (red squares) are found or a probabilistic timeout occurs. The robot returns to the nest (purple line), possibly laying a pheromone trail and/or remembering the previous location and returning to it.
Fig. 3 shows how individual physical robots search for RFID tags. Simulations replicate these behaviors. Fig. 4 shows how long it takes a single robot and a team of 3 robots to collect 8 of 32 tags A) in real robots and B) in simulations designed. Results are shown when robots use only site fidelity, and no pheromone communication. 3 robots collect tags twice as fast as a single robot, in real- world and simulated experiments. Fig. 5A shows an example of how quickly tags are collected by a single robot (real and virtual) when robots combine site fidelity and pheromone-like communication. Virtual robots outperform real robots because real robots sometimes get lost and then communicate incorrect locations to team-mates. Fig. 5b and 5c show that large simulated teams of 100 robots collect seeds approximately 70 times faster than individual robots. Each robot in a larger team collects tags slightly slower because robots on larger teams have to travel a further average distances to collect tags (a larger number of tags is necessarily, on average, further from the nest). Fig. 4: Time to collect 25% of the tags from three different distributions for one and three robots A) in simulation and B) in physical robots. Each bar is an average of 5 experiments. Figure 5: Tags collected using pheromones and site fidelity in combination A) example RFID collection curves by teams of 3 real and virtual robots. B) Rate tags are collected and C) minutes to collect a tag per individual robot, in different simulated team sizes.
4 Discussion Collective search depends on the balance of individual memory and communicated information. We are particularly interested in how search strategies change with the size of the collective and the distribution of the resource that is being collected. Fig. 2 shows that the most clumped distributions of seeds are collected substantially faster when individual memory is supplemented with communication. Centralized systems are characterized by diminishing returns each task takes longer to complete in larger systems [13]. However, we see only very modest declines in per-robot foraging rates in large teams when communication is distributed--teams of 100 robots collect tags 70 times faster than single robots. Similarly, we saw no significant difference in seed collection rate across colony sizes in our field study large colonies collect seeds as fast as small colonies, even though the average distance traveled from the nest to a seed is longer for larger colonies [7]. Information theory quantifies information as the amount of randomness in a distribution, but it says nothing about how animals make use of that information in terms relevant to fitness [3]. Our experiments and simulations allow us to quantify how different strategies that exploit information about the distribution of resources improves search. Fig. 2 shows that memory and communication improve foraging success the most on the most clustered distributions. This is because each bit of information about the location of a seed is of greater value when the entire seed distribution can be described with fewer bits. Thus, memory and information exchange helps the colony exploit clumped distributions but not random distributions. We use simple robots to test real-world implementation of swarm foraging algorithms based on site fidelity and pheromone-like communication. Thus far, in our experiments with physical robots, pheromones actually hamper foraging success because lost robots miscommunicate resource locations. However, when we replicate robot behavior in simulation (in which robots are never lost) we find that combining memory and communication is an effective strategy for teams of up to 100 robots, suggesting that by improving robot localization, our architecture and algorithms are scalable to large robotic swarms. Understanding effective decentralized search in ant colonies provides design principles for engineered robotic swarms. Moreover, many other complex systems search effectively without centralized control immune systems find pathogens, market economies find efficient pricing mechanisms, and evolution finds strategies that enable populations to survive. By elucidating how effective search strategies emerge from behaviors of individual components, this work lends insight into complex systems more generally. References 1. Beverly, B. D., McLendon, H., Nacu, S., Holmes, S., & Gordon, D. M. (2009). How site fidelity leads to individual differences in the foraging activity of harvester ants. Behavioral Ecology, 20(3), 633-638.
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