Autonomous mobile robots have become very popular and essential in our life, especially in industry. One of the crucial activities of the robot is planning the path from a start point to a target point, avoiding obstacles in the environment. Recently, path planning received more attention, and many methodologies have been proposed. Path planning studies have shown the effectiveness of swarm intelligence in complex and known or unknown environments. This paper presents a global path planning method based on grasshopper optimization algorithm (GOA) in a known static environment. This algorithm is improved using the bias factor to increase the efficiency and improve the resulting path. The resulting path from this algorithm is further enhanced using an improved version multinomial logistic regression algorithm (MLR). The algorithms were evaluated using three different large environments of varying complexities. The GOA algorithm has been compared with the ant colony optimization algorithm (ACO) using the same environments. The experiments have shown the superiority of our algorithm in terms of time convergence and cost.
In this paper, we investigate the bifurcation of a third order rational difference equation. Firstly, we show that the equation undergoes a Neimark-Sacker bifurcation when the parameter reaches a critical value. Then, we consider the direction of the Neimark-Sacker bifurcation. Finally, we give some numerical simulations of our results.
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