# Biologically-Inspired Learning and Adaptation of Self-Evolving Control for Networked Mobile Robots
## 1 Introduction  
Networked mobile robots that are capable of self-learning have received growing attention in the mobile robotics research community [1; 2; 3]. This emerging technology has surpassed the conventional robotic system by taking advantage of robot collaboration, system robustness, scalability, and greater flexibility. This modern robotic system has been commonly applied in manufacturing, military applications, surveillance, etc. to perform complex tasks [4; 5; 6]. Some self-learning strategies have been proposed to develop motion controllers for networked mobile robots [6; 7]. Among them, an RBFNN incorporating the gradient descent method is regarded as a powerful tool for designing the self-learning controllers of networked mobile robots [7; 8]. The RBFNN introduced by [PERSON] and [PERSON] is a three-layer feedforward artificial neural network in which radial basis functions are used as activation functions [9; 10]. This methodology takes advantage of fast learning capability and universal approximation. To date, it is a useful neural network architecture for addressing many engineering problems [11; 12]. However, traditional RBFNNs adopt a gradient descent approach for training the neural network that is not capable of noise reduction [10; 11; 12]. In other words, these studies did not consider the uncertainty and noise induced in the process and measurement phases. This paper presents a Kalman filter based RBFNN and its application to self-learning control of networked mobile robots. The Kalman filter is a state estimation technique introduced by [PERSON] [13]. It is a classic state estimation technique used widely in engineering applications, including spacecraft navigation, motion planning in robotics, signal processing and wireless sensor networks [14; 15; 16] because of its ability to extract useful information from noisy data. It is an optimal estimator for evaluating the internal state of a dynamic system under certain process patterns and/or measurement disturbances in the physical environment [13; 17; 18]. The objective of the Kalman filter is to minimize the mean squared error between the actual and estimated data. Although the proposed KF-RBFNN is useful for designing learning control schemes with noise reduction, the initial network parameters influences the system performance, namely that the selection of centers, widths and output weights for the Gaussian functions is an important consideration. Parameter-tuning of an RBFNN is challenging when using this neural network to solve multidimensional optimization problems. Over the years, several methods have been developed for addressing this RBFNN optimization problem [19; 20; 21]. However, these traditional RBFNN methods may cause the output to converge to local optimum when the dimensionality of the problem increases [22]. Since RBFNN optimization can be formulated as a search problem, biologically, algorithms are new paths for optimizing RBFNNs. This is a successful hybridization of RBFNNs and evolutionary algorithms. Although there are some metaheuristic algorithms used to develop evolutionary RBFNNs [23; 24; 25; 26], there has been no attempt to present an evolutionary KF-RBFNN using a GA to achieve learning control of networked mobile robotic systems. The GA is one of the most popular evolutionary algorithms for solving optimization problems [27; 28; 29]. Although GAs have been widely applied to various optimization problems, these biologically inspired algorithms suffer from premature convergence. In other words, these traditional computing paradigms may converge to local optimum. This paper contributes to the development of a modified GA to improve the search diversity by including the Levy flight approach. An adaptive determination of crossover and mutation probabilities in the GA is proposed via the Levy flights. This random walk is very efficient in exploring the search space of the optimization problem.