Chaotic Planning Paths Generators by Using Performance Surfaces

Chaotic systems have been widely used as path planning generators in autonomous mobile robots due to the unpredictability of the generated trajectories and the coverage rate of the robots workplace. In order to obtain a chaotic mobile robot, the chaotic signals are used to generate True RNGs (TRNGs), which, as is known, exploit the nondeterministic nature of chaotic controllers. Then, the bits obtained from TRNGs can be continuously mapped to coordinates (\(x_n, y_n\)) for positioning the robot on the terrain. A frequent technique to obtain a chaotic bitstream is to sample analog chaotic signals by using thresholds. However, the performance of chaotic path planning is a function of optimal values for those levels. In this framework, several chaotic systems which are used to obtain TRNGs but by computing a quasi-optimal performance surface for the thresholds is presented. The proposed study is based on sweeping the Poincare sections to find quasi-optimal values for thresholds where the coverage rate is higher than those obtained by using the equilibrium points as reference values. Various scenarios are evaluated. First, two scroll chaotic systems such as Chua’s circuit, saturated function, and Lorenz are used as entropy sources to obtain TRNGS by using its computed performance surface. Afterwards, n-scrolls chaotic systems are evaluated to get chaotic bitstreams with the analyzed performance surface. Another scenario is dedicated to find the performance surface of hybrid chaotic systems, which are composed by three chaotic systems where one chaotic system determines which one of the remaining chaotic signals will be used to obtain the chaotic bitstream. Additionally, TRNGs from two chaotic systems with optimized Lyapunov exponents are studied. Several numerical simulations to compute diverse metrics such as coverage rate against planned points, robot’s trajectory evolution, covered terrain, and color map are carried out to analyze the resulting TRNGs. This investigation will enable to increase several applications of TRNGs by considering the proposed performance surfaces.

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