Mathematical approach to sensory motor control and memory

Abstract

In this chapter we provide mathematical models for a general memory structure and for sensory-motor control via perception, detailing on some of the Recurrent Neural Networks (RNNs) introduced in Chapter 4. In the first section we study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks (RNN). We provide a theoretical basis concerning the learning process convergence and the network response to novel stimuli. We show that a nD network can learn static and dynamic patterns and can also replicate a sequence of up to n different vectors or frames. Such networks can also perform arithmetic calculations by means of pattern completion. In the second section we introduce a robot platform including the simplest probabilistic sensory and motor layers. Then we use the platform as a test-bed for evaluating the capabilities of robot navigation with different neural networks. We show that the basic robot element, the short-time memory, is the key element in obstacle avoidance. However, in the simplest conditions of no obstacles the straightforward memoryless robot is usually superior in performance. Accordingly, we suggest that small organisms (or agents) with short life-time do not require complex brains and even can benefit from simple brain-like (reflex) structures. In section 3 we propose a memotaxis strategy for target searching, which requires minimal computational resources and can be easily implemented in hardware. The strategy makes use of a dynamical system modeling short time memory which "collects" information on successful steps and corrects decisions made by a gradient strategy. Thus a memotactic robot can take steps against the chemotactic-like sensory gradient. We show (theoretically and experimentally) that the memotaxis strategy effectively suppresses stochasticity observed in the behavior of chemotactic robots in the region of low SNR and provides from 50 to 200% performance gain. © Springer-Verlag Berlin Heidelberg 2009.