Solving the robot inverse kinematic solution is the key to the subsequent path planning and trajectory tracking control of the robot, which is of great research significance. The inverse kinematic solution of the redundant robotic arm is a great challenge because the parsing solution cannot be obtained by the conventional inverse kinematic solution method. The swarm intelligent optimization algorithm is widely used in the inverse kinematic solution problem of redundant robotic arms by converting the inverse kinematic solution problem of the robotic arm into the minimum value optimization problem of the fitness function, avoiding the tedious process of the traditional inverse kinematic solution. This paper innovatively applies the bald eagle swarm intelligent optimization algorithm (BES algorithm) to the inverse motion solution problem of a 7DOF redundant robotic arm for the first time. The BES algorithm simulates the process of prey hunting by bald eagles in nature and consists of three main phases: selection phase, search phase, and dive phase. In these three phases, the algorithm updates the joint angles to be sought by using different optimization strategies, and obtains high accuracy position values by bringing the obtained joint angles into the positive kinematic expression of the robot arm. The article takes the YuMi 14000 ABB 7DOF industrial robotic arm and the S-R-S humanoid 7DOF robotic arm as the research objects, and the BES algorithm is experimentally compared with the traditional swarm intelligence optimization algorithms DE algorithm, FA algorithm, FOA algorithm, GA algorithm and PSO algorithm in terms of position solving accuracy. The experimental results show that the BES algorithm has higher position solution accuracy and solution stability compared with other algorithms.