Amanda Prorok

Formalizing the impact of diversity on performance in a heterogeneous swarm of robots

We are interested in a principled study of the impact of diversity in heterogeneous large-scale distributed robotic systems. In order to evaluate the implications of heterogeneity on performance, we consider the concrete problem of distributing a large group of robots among a set of tasks that require specialized capabilities in order to be completed. We model the system of heterogeneous robots as a community of species, where each species (robot type) is defined by the traits (capabilities) that it owns. We develop a continuous model of the system at a macroscopic level, and formulate an optimization problem that produces an optimal set of transition rates for each species, so that the desired trait distribution is reached as quickly as possible. In order to evaluate the effects of heterogeneity, we propose a diversity metric that defines the notion of eigenspecies. We show that our metric correlates with performance: the higher the cardinality of the eigenspecies, the harder it becomes to optimize the system. Our approach is validated over multiple levels of abstraction, and real robot results confirm its validity on physical platforms.

Resilient Flocking for Mobile Robot Teams

We present a method that enables resilient formation control for mobile robot teams in the presence of noncooperative (defective or malicious) robots. Recent results in network science define graph topological properties that guarantee resilience against faults and attacks on individual nodes in static networks. We build on these results to propose a control policy that allows a team of mobile robots to achieve resilient consensus on the direction of motion. Our strategy relies on dynamic connectivity management that makes use of a metric that characterizes the robustness of the communication network topology. Our method distinguishes itself from prior work in that our connectivity management strategy ensures that the network lies above a critical resilience threshold, guaranteeing that the consensus algorithm always converges to a value within the range of the cooperative agents’ initial values. We demonstrate the use of our framework for resilient flocking, and show simulation results with groups of holonomic mobile robots.

Formations for Resilient Robot Teams

All cooperative control algorithms for robot teams assume the ability to communicate without considering the possibility of a malicious or malfunctioning robot that may either communicate false information or take wrong actions. This paper addresses the development of formations that enable resilience, the ability to achieve consensus, and to cooperate in the presence of malicious or malfunctioning robots. Specifically, we use the notion of robust graphs to build resilient teams, and focus on the problem of designing robot formations with communication graphs (each edge models a bidirectional communication link) that are robust. We present algorithms to build robust graphs. Given a set of robots and the maximum number of malicious or malfunctioning robots, we are able to 1) state if it is possible to build a resilient team; 2) say what the proximity relationships that enable communication ought to be; 3) construct elemental resilient graphs; and 4) develop a framework for composing resilient teams to build larger resilient teams. We illustrate these algorithms by constructing resilient robot formations in the plane.

Resilient consensus for time-varying networks of dynamic agents

We consider networks of dynamic agents that execute cooperative, distributed control algorithms in order to coordinate themselves and to collectively achieve goals. The agents rely on consensus algorithms that are based on local interactions with their nearest neighbors in the communication graph. However, such systems are not robust to one or more malicious agents and there are no performance guarantees when one or more agents do not cooperate. Recent results in network science deal with this problem by requiring specific graph topological properties. Nevertheless, the required network topologies imply high connectivity levels, which may be difficult to achieve in systems that exhibit time-varying communication graphs. In this paper, we propose an approach that provides resilience for networks of dynamic agents whose communication graphs are time-varying. We show that in the case where the required connectivity constraints cannot be satisfied at all times, we can resort to a consensus protocol that guarantees resilience when the union of communication graphs over a bounded period of time satisfies certain robustness properties. We propose a control policy to attain resilient behavior in the context of perimeter surveillance with a team of robots. We provide simulations that support our theoretical analyses.

Calibration-free network localization using non-line-of-sight ultra-wideband measurements

We present a method for calibration-free, infrastructure-free localization in sensor networks. Our strategy is to estimate node positions and noise distributions of all links in the network simultaneously -- a strategy that has not been attempted thus far. In particular, we account for biased, NLOS range measurements from UWB devices that lead to multi-modal noise distributions, for which few solutions exist to date. Our approach circumvents cumbersome a-priori calibration, allows for rapid deployment in unknown environments, and facilitates adaptation to changing conditions. Our first contribution is a generalization of the classical multidimensional scaling algorithm to account for measurements that have multi-modal error distributions. Our second contribution is an online approach that iterates between node localization and noise parameter estimation. We validate our method in 3-dimensional networks, (i) through simulation to test the sensitivity of the algorithm on its design parameters, and (ii) through physical experimentation in a NLOS environment. Our setup uses UWB devices that provide time-of-flight measurements, which can lead to positively biased distance measurements in NLOS conditions. We show that our algorithm converges to accurate position estimates, even when initial position estimates are very uncertain, initial error models are unknown, and a significant proportion of the network links are in NLOS.

The Impact of Diversity on Optimal Control Policies for Heterogeneous Robot Swarms

We consider the problem of distributing a large group of heterogeneous robots among a set of tasks that require specialized capabilities in order to be completed. We model the system of heterogeneous robots as a community of species, in which each species (robot type) is defined by the traits (capabilities) that it owns. In order to solve the distribution problem, we develop centralized as well as decentralized methods to efficiently control the heterogeneous swarm of robots. Our methods assume knowledge of the underlying task topology and are based on a continuous model of the system that defines transition rates to and from tasks, for each robot species. Our optimization of the transition rates is fully scalable with respect to the number of robots, number of species, and number of traits. Building on this result, we propose a real-time optimization method that enables an online adaptation of transition rates as a function of the state of the current robot distribution. We also show how the robot distribution can be approximated based on local information only, consequently enabling the development of a decentralized controller. We evaluate our methods by means of microscopic simulations and show how the performance of the latter is well predicted by the macroscopic equations. Importantly, our framework also includes a diversity metric that enables an evaluation of the impact of swarm heterogeneity on performance. The metric defines the notion of minspecies, i.e., the minimum set of species that are required to achieve a given goal. We show that two distinct goal functions lead to two specializations of minspecies, which we term as eigenspecies and coverspecies. Quantitative results show the relation between diversity and performance.

A Macroscopic Privacy Model for Heterogeneous Robot Swarms

To date, the issues of privacy and security remain poorly addressed within robotics at large. In this work, we provide a foundation for analyzing the privacy of swarms of heterogeneous robots. Our premise is that information pertaining to individual robot types must be kept private in order to preserve the security and resilience of the swarm system at large. A main contribution is the development of a macroscopic privacy model that can be applied to swarms. Our privacy model draws from the notion of differential privacy that stems from the database literature, and that provides a stringent statistical interpretation of information leakage. We combine the privacy model with a macroscopic abstraction of the swarm system, and show how this enables an analysis of the privacy trends as swarm parameters vary.

Towards Differentially Private Aggregation of Heterogeneous Robots.

We are interested in securing the operation of robot swarms composed of heterogeneous agents that collaborate by exploiting aggregation mechanisms. Since any given robot type plays a role that may be critical in guaranteeing continuous and failure-free operation of the system, it is beneficial to conceal individual robot types and, thus, their roles. In our work, we assume that an adversary gains access to a description of the dynamic state of the swarm in its non-transient, nominal regime. We propose a method that quantifies how easy it is for the adversary to identify the type of any of the robots, based on this observation. We draw from the theory of differential privacy to propose a closed-form expression of the leakage of the system at steady-state. Our results show how this model enables an analysis of the leakage as system parameters vary; they also indicate design rules for increasing privacy in aggregation mechanisms.

ADAPTIVE DISTRIBUTION OF A SWARM OF HETEROGENEOUS ROBOTS

We present a method that distributes a swarm of heterogeneous robots among a set of tasks that require specialized capabilities in order to be completed. We model the system of heterogeneous robots as a community of species, where each species (robot type) is defined by the traits (capabilities) that it owns. Our method is based on a continuous abstraction of the swarm at a macroscopic level as we model robots switching between tasks. We formulate an optimization problem that produces an optimal set of transition rates for each species, so that the desired trait distribution is reached as quickly as possible. Since our method is based on the derivation of an analytical gradient, it is very efficient with respect to state-of-the-art methods. Building on this result, we propose a real-time optimization method that enables an online adaptation of transition rates. Our approach is well-suited for real-time applications that rely on online redistribution of large-scale robotic systems.

Triangular Networks for Resilient Formations.

Consensus algorithms allow multiple robots to achieve agreement on estimates of variables in a distributed manner, hereby coordinating the robots as a team, and enabling applications such as formation control and cooperative area coverage. These algorithms achieve agreement by relying only on local, nearest-neighbor communication. The problem with distributed consensus, however, is that a single malicious or faulty robot can control and manipulate the whole network. The objective of this paper is to propose a formation topology that is resilient to one malicious node, and that satisfies two important properties for distributed systems: (i) it can be constructed incrementally by adding one node at a time in such a way that the conditions for attachment can be computed locally, and (ii) its robustness can be verified through a distributed method by using only neighborhood-based information. Our topology is characterized by triangular robust graphs, consists of a modular structure, is fully scalable, and is well suited for applications of large-scale networks. We describe how our proposed topology can be used to deploy networks of robots. Results show how triangular robust networks guarantee asymptotic consensus in the face of a malicious agent.