A novel meta-heuristic algorithm named Egret Swarm Optimization Algorithm (ESOA) is proposed in this paper, which is inspired by two egret species’ hunting behavior (Great Egret and Snowy Egret). ESOA consists of three primary components: a sit-and-wait strategy, aggressive strategy as well as discriminant conditions. The learnable sit-and-wait strategy guides the egret to the most probable solution by applying a pseudo gradient estimator. The aggressive strategy uses random wandering and encirclement mechanisms to allow for optimal solution exploration. The discriminant model is utilized to balance the two strategies. The proposed approach provides a parallel framework and a strategy for parameter learning through historical information that can be adapted to most scenarios and has well stability. The performance of ESOA on 36 benchmark functions as well as 3 engineering problems are compared with Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Harris Hawks Optimization (HHO). The result proves the superior effectiveness and robustness of ESOA. ESOA acquires the winner in all unimodal functions and reaches statistic scores all above 9.9, while the scores are better in complex functions as 10.96 and 11.92.

Service robots, e.g. massage robots, have attracted more and more attention in recent years and the most popular study within this field is trajectory tracking. Due to the actual demand for service robots, the solution of trajectory tracking requires fast convergence and high accuracy. In order to solve the above issues, this paper proposed an enhanced Gated recurrent unit (GRU) to deal with trajectory tracking tasks of robot manipulators. The main feature of enhanced GRU is utilizing cell states as well as various gate units to build a novel neural cell. Besides, the presented enhanced GRU resolves the problem of the general neural network model and large memory occupancy. Then the derivations about the computational process of cell state and mixed hidden state of the proposed model have been illustrated. Finally, three trajectory tracking applications, comparison, and visual simulation have verified feasibility as well as the superiority of the enhanced GRU model.

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