This paper proposes a new meta-heuristic algorithm, named wild geese migration optimization (GMO) algorithm. It is inspired by the social behavior of wild geese swarming in nature. They maintain a special formation for long-distance migration in small groups for survival and reproduction. The mathematical model is established based on these social behaviors to solve optimization problems. Meanwhile, the performance of the GMO algorithm is tested on the stable benchmark function of CEC2017, and its potential for dealing with practical problems is studied in five engineering design problems and the inverse kinematics solution of robot. The test results show that the GMO algorithm has excellent computational performance compared to other algorithms. The practical application results show that the GMO algorithm has strong applicability, more accurate optimization results, and more competitiveness in challenging problems with unknown search space, compared with well-known algorithms in the literature. The proposal of GMO algorithm enriches the team of swarm intelligence optimization algorithms and also provides a new solution for solving engineering design problems and inverse kinematics of robots.

To advance the calculation performance of the battle royale optimization algorithm (BRO), a hybrid improved BRO algorithm (HBC) is proposed in this paper. The level mechanism of the chicken swarm optimization algorithm (CSO) is integrated into the BRO algorithm to divide all into elite players and ordinary players, and the level relationship of different players is established. Then, an elite player update method of random exploring and directional update in a small range is proposed to improve the development ability. The update method of ordinary players improved, the update mechanism of elite random guidance is introduced to make full use of the excellent location information in the population. The performance verification experiment of the HBC algorithm is carried out on 20 benchmark functions and a practical project. Comparing with several other algorithms, the computational performance of the HBC algorithm is the best. Furthermore, the HBC algorithm is applied to solve the inverse kinematics of the 7R 6DOF robot. The experimental results show that the HBC algorithm effectively improves the average convergence accuracy and reduces the running time, compared with the BRO algorithm. This fully shows that the HBC algorithm is more competitive in stability, calculation accuracy, and speed.

Robot dynamics model uncertainty and unpredictable external perturbations are important factors that influence control accuracy and stability. To accurately compensate for the dynamics model in sliding mode control (SMC), a new parallel network (PCR) is proposed in this paper. The network parallelizes the radial basis function and convolutional neural network, which gives it the advantage of making full use of one-dimensional data fitting results and two-dimensional data feature information, realizing the deep learning of multidimensional data and improving the model’s compensation accuracy and anti-interference ability. Meanwhile, based on the integration of adaptive control techniques and gradient descent, a new weight update algorithm is designed to realize the online learning of PCR networks under loss-free functions. Then, a new sliding mode controller (PCR-SMC) is established. The model-free intelligent control of the robot is accomplished without knowledge of the predetermined upper bounds. Additionally, the stability analysis of the control system is proved by the Lyapunov theorem. Lastly, robot tracking control simulations are performed on two trajectories. The results demonstrate the high-precision tracking performance of this controller in comparison with the RBF-SMC controller.

The non-linearity and uncertainty of air pollutant data add a certain degree of difficulty to the prediction of air quality, and neural networks have a certain ability to solve this problem. But it has the shortcomings of slow convergence and is easy to fall into local minimums. Therefore, this paper optimizes the OIF Elman neural network (IOIF Elman) by the method of adaptive learning rate and direct input to output connections. And an air quality prediction model is established based on the IOIF Elman neural network. The simulation results show that the absolute average error (AAE) and accuracy of the IOIF Elman air quality prediction model are better than those of the OIF Elman and Elman neural network. The establishment of this model can better meet the needs of practical applications and provide a more reliable basis for decision-making for environmental protection departments.