Wreath Product Cognitive Architecture (WPCA) Anshul Joshi 1 and Thomas C. Henderson 2 Abstract— A Belief-Desire-Intention (BDI) framework closely resembles human practical reasoning approach in day-to-day life, and is a well-studied architecture. The wreath product cognitive model, first described by Leyton is an abstract, although powerful, model which closely couples perception and actuation for representing shape. However, no implementation of the wreath product model exists. Our work is an attempt to combine the wreath product knowledge representation mech- anism with a BDI architecture that works in a real-world setting. A prototype implementation of this combination is demonstrated on an iRobot Create differential-drive robot, with a Kinect One structural sensor, in an indoor environment. The effectiveness of our framework is demonstrated by its accuracy for mapping the environment and localization of the robot for navigation purposes. I. INTRODUCTION We have examined a representation which features com- bined action and perception signals; i.e., instead of having a purely geometric representation of the perceptual data, we include the motor actions, for example, aiming a camera at an object, which produces actions that generate the particular shape. This generative perception-action representation uses Leyton’s cognitive representation based on wreath products [27]. The wreath product is a special kind of group which captures information through symmetries on the sensorimo- tor data. The key insight is the bundling of actuation and perception data together in order to capture the cognitive structure of interactions with the world. This involves de- veloping algorithms and methods: (1) to perform symmetry detection and parsing, (2) to represent and characterize uncertainties in the data and representations, and (3) to provide an overall cognitive architecture for a robot agent. We have previously demonstrated these functions in 2D text classification [21], and in this work we show it on 3D spatial data acquired by a real robot operating in an indoor environment, that uses this cognitive architecture, and maps the environment and localizes itself in that environment. The cognitive architecture called the Wreath Product Cognitive Architecture is developed to support this approach. We have previously proposed innate theories of symmetry as the cognitive basis for embodied robot agents [19], [20] and more recently, a specific cognitive architecture based on Bayesian Symmetry Networks [18], [23]. This representation *This work was supported, in part, by AFOSR grant AFOSR-FA9550- 12-1-0291, and the University of Utah Graduate School Fellowship Program 1 Anshul Joshi is a PhD Candidate at the University of Utah, Salt Lake City. 201 Presidents Cir, Salt Lake City, UT 84112, USA. joshi@cs.utah.edu 2 Thomas C. Henderson is a Professor in School of Computing, Uni- versity of Utah. 201 Presidents Cir, Salt Lake City, UT 84112, USA tch@cs.utah.edu builds on the framework layed out by Leyton [26], [27] wherein he proposes that the wreath product captures the notion of a specific concept which is a representation of what something is or how it works; this may capture either a specific instance of an existing thing or an abstract descrip- tion of a class of related objects. For Leyton, the wreath product provides the basis for concept representation, where a wreath product is a group formed by a splitting extension of the direct product of the fiber group which is acted on by a control group (usually a permutation group) and is derived from related perception and actuation. The distinctive feature of his representation is that it is based on how the set of features comprising the object to be represented is generated – it is a generative theory of shape. Thus, the actuation control sequences are part of the description of an object and determine the control group hierarchy. This is important because objects are expressed in terms of the specific embodiment of the robot agent perceiving them. Our contributions in this regard are as follows: (1) We implement a powerful representation - the wreath product representation - which works practically, and for which no implementation exists yet, (2) we demonstrate the effectiveness of this repre- sentation for an absolutely essential, yet non-trivial, mobile robot functionality – localization in an indoor environment – using wreath products as landmarks. II. RELATED WORK The first problem to be addressed for robot autonomy is that of building a cognitive framework. In recent years robotics researchers have understood the importance of de- veloping cognitive abilities of robots, rather than explicitly programming the robots with the knowledge and algorithms to process that knowledge for achieving results, and a lot of research has been devoted to achieve this. For example, Beeson [2] has explored using cognitive maps as analogous to human spatial mapping process using the Hybrid Semantic Spatial Hierarchy. Desai et al. [7], [8], [9], [10] have used affine feature descriptors for the purpose of autonomous navigation of an Unmanned Ground Vehicle (UGV). Krueger et al. [25] have proposed an Object-Action Complex (OAC) as the basis for closely coupling different objects and the actions associated with them. Interested readers can refer to [1], [16], [17] for more examples. Various paradigms of cognitive frameworks have also been defined, each having its own advantages and disadvantages (see Vernon et al. [31] for an excellent overview of cognitive architectures). The second problem to be addressed for robot autonomy is that of Simultaneous Localization And Mapping (SLAM) deals with the problem of navigating within an environment as