Spring Berman

Optimized Stochastic Policies for Task Allocation in Swarms of Robots

We present a scalable approach to dynamically allocating a swarm of homogeneous robots to multiple tasks, which are to be performed in parallel, following a desired distribution. We employ a decentralized strategy that requires no communication among robots. It is based on the development of a continuous abstraction of the swarm obtained by modeling population fractions and defining the task allocation problem as the selection of rates of robot ingress and egress to and from each task. These rates are used to determine probabilities that define stochastic control policies for individual robots, which, in turn, produce the desired collective behavior. We address the problem of computing rates to achieve fast redistribution of the swarm subject to constraint(s) on switching between tasks at equilibrium. We present several formulations of this optimization problem that vary in the precedence constraints between tasks and in their dependence on the initial robot distribution. We use each formulation to optimize the rates for a scenario with four tasks and compare the resulting control policies using a simulation in which 250 robots redistribute themselves among four buildings to survey the perimeters.

Stochastic strategies for a swarm robotic assembly system

We present a decentralized, scalable approach to assembling a group of heterogeneous parts into different products using a swarm of robots. While the assembly plans are predetermined, the exact sequence of assembly of parts and the allocation of subassembly tasks to robots are determined by the interactions between robots in a decentralized fashion in real time. Our approach is based on developing a continuous abstraction of the system derived from models of chemical reactions and formulating the strategy as a problem of selecting rates of assembly and disassembly. These rates are mapped onto probabilities that determine stochastic control policies for individual robots, which then produce the desired aggregate behavior. This top-down approach to determining robot controllers also allows us to optimize the rates at the abstract level to achieve fast convergence to the specified target numbers of products. Because the method incorporates programs for assembly and disassembly, changes in demand can lead to reconfiguration in a seamless fashion. We illustrate the methodology using a physics-based simulator with examples involving 15 robots and two types of final products.

Bio-Inspired Group Behaviors for the Deployment of a Swarm of Robots to Multiple Destinations

We present a methodology for characterizing and synthesizing swarm behaviors using both a macroscopic model that represents a swarm as a continuum and a microscopic model that represents individual robots. We develop a systematic approach for synthesizing behaviors at the macroscopic level that can be realized on individual robots at the microscopic level. Our methodology is inspired by a dynamical model of ant house hunting [1], a decentralized process in which a colony attempts to emigrate to the best site among several alternatives. The model is hybrid because the colony switches between different sets of behaviors, or modes, during this process. At the macroscopic level, we are able to synthesize controllers that result in the deployment of a robotic swarm in a predefined ratio between distinct sites. We then derive hybrid controllers for individual robots using only local interactions and no communication that respect the specifications of the global continuous behavior. Our simulations demonstrate that our synthesis procedure yields a correct microscopic model from the macroscopic description with guarantees on performance at both levels

Design of control policies for spatially inhomogeneous robot swarms with application to commercial pollination

We present an approach to designing scalable, decentralized control policies that produce a desired collective behavior in a spatially inhomogeneous robotic swarm that emulates a system of chemically reacting molecules. Our approach is based on abstracting the swarm to an advection-diffusion-reaction partial differential equation model, which we solve numerically using smoothed particle hydrodynamics (SPH), a meshfree technique that is suitable for advection-dominated systems. The parameters of the macroscopic model are mapped onto the deterministic and random components of individual robot motion and the probabilities that determine stochastic robot task transitions. For very large swarms that are prohibitively expensive to simulate, the macroscopic model, which is independent of the population size, is a useful tool for synthesizing robot control policies with guarantees on performance in a top-down fashion. We illustrate our methodology by formulating a model of rabbiteye blueberry pollination by a swarm of robotic bees and using the macroscopic model to select control policies for efficient pollination.

Dynamic redistribution of a swarm of robots among multiple sites

We present an approach for the dynamic assignment and reassignment of a large team of homogeneous robotic agents to multiple locations with applications to search and rescue, reconnaissance and exploration missions. Our work is inspired by experimental studies of ant house hunting and empirical models that predict the behavior of the colony that is faced with a choice between multiple candidate nests. We design stochastic control policies that enable the team of agents to distribute themselves between multiple candidate sites in a specified ratio. Additionally, we present an extension to our model to enable fast convergence via switching behaviors based on quorum sensing. The stability and convergence properties of these control policies are analyzed and simulation results are presented.

Design of ant-inspired stochastic control policies for collective transport by robotic swarms

In this paper, we present an approach to designing decentralized robot control policies that mimic certain microscopic and macroscopic behaviors of ants performing collective transport tasks. In prior work, we used a stochastic hybrid system model to characterize the observed team dynamics of ant group retrieval of a rigid load. We have also used macroscopic population dynamic models to design enzyme-inspired stochastic control policies that allocate a robotic swarm around multiple boundaries in a way that is robust to environmental variations. Here, we build on this prior work to synthesize stochastic robot attachment–detachment policies for tasks in which a robotic swarm must achieve non-uniform spatial distributions around multiple loads and transport them at a constant velocity. Three methods are presented for designing robot control policies that replicate the steady-state distributions, transient dynamics, and fluxes between states that we have observed in ant populations during group retrieval. The equilibrium population matching method can be used to achieve a desired transport team composition as quickly as possible; the transient matching method can control the transient population dynamics of the team while driving it to the desired composition; and the rate matching method regulates the rates at which robots join and leave a load during transport. We validate our model predictions in an agent-based simulation, verify that each controller design method produces successful transport of a load at a regulated velocity, and compare the advantages and disadvantages of each method.

Study of group food retrieval by ants as a model for multi-robot collective transport strategies

Group food retrieval in some ant species serves as a useful paradigm for multi-robot collective transport strategies that are decentralized, scalable, and do not require a priori information about the payload. We investigate this phenomenon in Aphaenogaster cockerelli in order to extract the ants’ roles during transport, the rules that govern their actions, and the individual forces that they apply to guide a food item to their nest. To measure these forces, we designed and fabricated elastic structures with calibrated stiffness properties, induced ants to retrieve the structures, and tracked the resulting deformations with a camera. We then developed a hybrid system model of the ant behaviors that were observed in the experiments. We conducted simulations of the behavioral model that incorporate a quasistatic model of planar manipulation with compliant attachment points. Our simulations qualitatively replicate individual ant activity as well as certain macroscopic features of the transport.

Pheeno, A Versatile Swarm Robotic Research and Education Platform

Swarms of low-cost autonomous robots can potentially be used to collectively perform tasks over very large domains and time scales. Novel robots for swarm applications are currently being developed as a result of recent advances in sensing, actuation, processing, power, and manufacturing. These platforms can be used by researchers to conduct experiments with robot collectives and by educators to include robotic hardware in their curricula. However, existing low-cost robots are specialized and can lack desired sensing, navigation, control, and manipulation capabilities. This letter presents a new mobile robot platform, Pheeno, that is affordable, versatile, and suitable for multirobot research, education, and outreach activities. Users can modify Pheeno for their applications by designing custom modules that attach to its core module. We describe the design of the Pheeno core and a three degree-of-freedom gripper module, which enables unprecedented manipulation capabilities for a robot of Pheenos size and cost. We experimentally demonstrate Pheenos ability to fuse measurements from its onboard odometry for global position estimation and use its camera for object identification in real time. We also show that groups of two and three Pheenos can act on commands from a central controller and consistently transport a payload in a desired direction.

MARCO: a reachability algorithm for multi-affine systems with applications to biological systems

We present a new algorithm for the reachability analysis of multi-affine hybrid systems. In our previous work on reachability analysis and that of our collaborators [1,2,3], we exploited the convexity of multiaffine functions and the fact that the vector field in modes with rectangular invariants is uniquely determined by its values at the rectangle vertices. In this paper, we explicitly calculate conical overapproximations of the reachable set in the invariant of each mode. We describe our Multi-Affine Reachability analysis using Conical Overapproximations, MARCO, and show that it yields results that are superior to those obtained by existing methods for multi-affine hybrid systems. Finally, we demonstrate the application of MARCO to the analysis of an ant house hunting model that incorporates quorum sensing [4] and the analysis of bi-stability of the lactose induction system regulated by glucose and lactose [5].

An Enzyme-Inspired Approach to Stochastic Allocation of Robotic Swarms Around Boundaries

This work presents a novel control approach for allocating a robotic swarm among boundaries. It represents the first step toward developing a methodology for encounter-based swarm allocation that incorporates rigorously characterized spatial effects in the system without requiring analytical expressions for encounter rates. Our approach utilizes a macroscopic model of the swarm population dynamics to design stochastic robot control policies that result in target allocations of robots to the boundaries of regions of different types. The control policies use only local information and have provable guarantees on the collective swarm behavior. We analytically derive the relationship between the stochastic control policies and target allocations for a scenario in which circular robots avoid collisions with each other, bind to boundaries of disk-shaped regions, and command bound robots to unbind. We validate this relationship in simulation and show that it is robust to environmental changes, such as a change in the number or size of robots and disks.