To improve the performance of the arithmetic optimization algorithm (AOA) and solve problems in the AOA, a novel improved AOA using a multi-strategy approach is proposed. Firstly, circle chaotic mapping is used to increase the diversity of the population. Secondly, a math optimizer accelerated (MOA) function optimized by means of a composite cycloid is proposed to improve the convergence speed of the algorithm. Meanwhile, the symmetry of the composite cycloid is used to balance the global search ability in the early and late iterations. Thirdly, an optimal mutation strategy combining the sparrow elite mutation approach and Cauchy disturbances is used to increase the ability of individuals to jump out of the local optimal. The Rastrigin function is selected as the reference test function to analyze the effectiveness of the improved strategy. Twenty benchmark test functions, algorithm time complexity, the Wilcoxon rank-sum test, and the CEC2019 test set are selected to test the overall performance of the improved algorithm, and the results are then compared with those of other algorithms. The test results show that the improved algorithm has obvious advantages in terms of both its global search ability and convergence speed. Finally, the improved algorithm is applied to an engineering example to further verify its practicability.

In order to make a robot track a desired trajectory with high precision and steady gait, a novel intelligent controller was designed based on a new mechanical structure and optimized foot trajectory. Kinematics models in terms of the D-H method were established to analyze the relationship between the angle of the driving joint and the foot position. Inspired by a dog’s diagonal trot on a flat terrain, foot trajectory planning in the swing and support phases without impact were fulfilled based on the compound cycloid improved by the Bézier curve. Both the optimized cascade proportional–integral–derivative (PID) control system and improved fuzzy adaptive PID control system were applied to realize the stable operation of a quadruped robot, and their parameters were optimized by the sparrow search algorithm. The convergence speed and accuracy of the sparrow search algorithm were verified by comparing with the moth flame optimization algorithm and particle swarm optimization algorithm. Finally, a co-simulation with MATLAB and ADAMS was utilized to compare the effects of the two control systems. The results of both displacement and velocity exhibit that the movement of a quadruped bionic robot with fuzzy adaptive PID control systems optimized by the sparrow search algorithm possessed better accuracy and stability than cascade PID control systems. The motion process of the quadruped robot in the co-simulation process also demonstrates the effectiveness of the designed mechanical structure and control system.