The control method of inverse kinematics is adopted for free-floating type of obstacles to realize the desired trajectory tracking at the end of the robotic arm, and the collision function and Gronwell's Lemma are introduced to the collision inequality into the acceleration level, which ensures the continuity of the joint angular velocities of the robotic arm. The results of non-obstacle avoidance and obstacle avoidance, stationary and moving obstacles are compared using numerical simulation. The simulation results denote that the proposed obstacle avoidance path planning algorithm can effectively improve the avoidance ability of the underwater multi-jointed robotic arm for stationary and moving obstacles.