Anonymous Cooperation in Robotic Sensor Networks

Potential performance benefits motivate the application of networks of proactive robotic sensor platforms to information gathering tasks. To achieve scalable implementations of such systems, it is necessary to restrict the knowledge at each element and the interaction among nodes in order to manage the required computation and communication complexity. This paper presents a decentralized architecture that enables networked robotic controllers to pursue global cooperative sensing objectives in anonymity and without global system knowledge. The architecture builds on techniques established for the problem of Decentralized Data Fusion (DDF). It defines interfaces for network nodes that realize decentralized estimation and negotiated cooperative control through the exchange of information measures. Results for a networked team of robotic sensors engaged in cooperative feature localization are presented to illustrate the characteristics of this approach. Introduction Applying networks of proactive robotic sensors to information gathering tasks offers enticing performance benefit s such as increased resolution, reduced execution time, high er flexibility and improved robustness over single robot implementations. Many common, mobile robot tasks may be formulated as problems of information acquisition including target tracking, feature localization and exploration . The advantage of focusing only on information acquisition prob lems is that the control objective is well defined and many tools exist for comparison and fusion of information in distributed and decentralized networks. This paper presents an approach that builds on the techniques established for the related problem of Decentralize d Data Fusion (DDF) (Manyika & Durrant-Whyte 1994). The underlying structure in this information fusion problem is used to develop an architecture that enables an anonymous network of robotic sensors to reach cooperative active sens ing outcomes. Decentralization by no means implies any sacrifice in the quality of the solution obtained in comparison to a centralized approach. Compared to a centralized or Copyright c © 2004, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. distributed system, a decentralized system is characteriz ed by three constraints : 1. There is no single central decision center; no one node should be central to the successful operation of the network. 2. There is no common communication facility; nodes cannot broadcast results and communication must be kept on a strictly node-to-node basis. 3. Nodes do not have any global knowledge of network topology; nodes should only know about connections in their own neighborhood. The constraints imposed provide a number of important characteristics for decentralized systems: • Eliminating the central decision center and any common communication facility ensures that the system is scalable as there are no limits imposed by centralized computational bottlenecks or lack of communication bandwidth. • Ensuring that no node is central and that no global knowledge of the network topology is required for control means that the system can be made survivable to the online loss (or addition) of sensing nodes and to dynamic changes in the network structure. • As all decision processes must take place locally at each site and no global knowledge of the network is required a priori, nodes can be constructed and programmed in a modular fashion. The established DDF approach to decentralized estimation, yields estimates equivalent to that of a global centralized Kalman filter while satisfying the strict constraints defining a decentralized system. A remarkable property of the resulting architecture is that the communication and compu tational requirements for each network node are independen t of the number of network nodes. Key to this result is the abstraction and anonymous aggregation of observations and estimates obtained through the information or inverse covariance formulation of the Kalman filter. This property is exploited in this work to develop a de centralized architecture for determining cooperative sen sing actions. Starting with a brief review of related work, this paper is organized as follows. A decentralized sensor network archi tecture is presented and anonymity is explored with regard to sensing, communication and action utility. Approaches t o proactive control of sensing resources follow. A distincti on is drawn between coordination mechanisms that influence decisions made over time, as opposed to cooperative mechanisms that provide for predictive influence and negotiatio n. The characteristics of both devices are illustrated throug h application to an active feature localization problem. Related Work This work is related to developments in data fusion (distributed estimation and sensor management), multi-agent systems (cooperative control and planning) and sensor networks (routing, aggregation and topology control) disciplines. The aggregation of sensor measurements in estimates through probabilistic data fusion parallels the data aggregation data centric concepts in non-probabilistic sensor networks (Krishnamachari, Estrin, & Wicker 2002). Both promote implementation scalability. We do not consider the impact data flow of optimal routing or dynamic network topologies. Such aspects should be considered in future studies. This work builds on an approach to sensor management presented in (Manyika & Durrant-Whyte 1994). Examples of recent related work that use information based utility measures for sensor selection include (Zhao, Shin, & Reich 2002) and (Wanget al. 2003). This work extends the architecture previously presented (Grocholskyet al. 2003) and is closely related to ongoing developments at the University of Sydney (Makarenko et al. 2004). This architecture establishes the structure and int erfaces for sensing, communication and control processes at each network node. It is admissible for nodes to have null sensing and or null actuation. There is no distinction between robot and network nodes as made in alternative approaches such as (Estrin et al. 2002). The mechanism presented here that leads to cooperative decision making is similar to the coordination variables concept in decentralized cooperative control literature (McL ain et al. 2001). These methods couple decentralized decision making and control processes allowing cooperative global objectives to be reached. An Anonymous Sensor Network Architecture This section details the proposed sensor network architecture. The information filter approach to decentralized data fusion is briefly presented. This leads to an agent node struc ture from which the network is composed. Anonymity in this architecture is explored with respect to sensing, comm unication and the utility of agent actions across the network . Decentralized Data Fusion The Decentralized Data Fusion (DDF) method provides techniques for fusing information in a fully distributed ne twork of sensors. The problems of interest center around generating estimates of some unknown, time varying, state x(t) given a sequence of observations Z(t) from a group of sensors. In a centralized data fusion system, such problems are often addressed using a Kalman filter or Bayes estimator (Maybeck 1979). These algorithms generate an estimate of the statêx(t) together with an uncertainty measure, normally represented as a covariance matrix P(t). In DDF methods, these are replaced by the mathematically equivalent information filters which generate estimates of the inf ormation statêy(t) and the corresponding Information matrix Y(t) which are related to the state and covariance as: Y(t) = P−1(t), ŷ(t) = Y(t)x̂(t) (1) These information measures are formally related to both Fisher information and Shannon information (Cover & Thomas 1991). The information filter equations are now stated briefly. See (Manyika & Durrant-Whyte 1994) for a full derivation. Consider a system described in standard linear form x(k) = F(k)x(k − 1) + w(k), (2) where F(k) is the state transition matrix and the vector w(k) ∼ N(0,Q(k)) is the associated process noise. This state is observed by a sensor according to the non-linear observation model z(k) = h(k,x(k)) + v(k) (3) where z(k) is the vector of observations and the vector v(k) ∼ N(0,R(k)) is the associated observation noise. The information measures associated with an observation are i(k) 4 = H (k)R−1(k)(z(k)−h(x̂(k|k−1)) + H(k)x̂(k|k−1), I(k) 4 = H (k)R−1(k)H(k), (4) whereH(·) is the Jacobian∇xh(·). With these definitions, the information filter can be summarized in two stages as: Prediction: Y(k|k−1) = [ F(k)Y−1(k−1|k−1)FT (k) + Q(k) ]−1 , ŷ(k|k−1) = Y(k|k−1)F(k)Y−1(k−1|k−1)ŷ(k−1|k−1). (5)