<p>Kinematic singularity seriously affects the motion performance of robots. To address this issue, researchers have proposed various methods based on damped least squares. However, selecting the maximum damping value and singular region through trial and error may lead to the joint velocities exceeding the corresponding limits, and some methods introduce damping factors in the singular region, resulting in motion errors of the end-effector. To tackle these challenges, a novel damped least-squares algorithm based on the repulsive potential energy function is proposed in this study. The innovations and scientific contributions of this algorithm are as follows: first, a novel variable damping function is presented, and a microbuffer region is introduced to avoid exceeding the maximum joint velocity due to an overly small singular region, while ensuring the continuity of damping in both the micro-buffer region and the singular region to achieve smooth transitions of joint velocities. Second, the tracking accuracy of the end-effector is set as the objective function, and the maximum joint velocities are set as the constraint function. Moreover, the optimal maximum damping value and singular region are determined using the particle swarm optimization algorithm. Third, a singular repulsive potential energy function is introduced to generate smooth virtual forces that push the system away from unsafe regions. Finally, the effectiveness of the algorithm is verified through simulations on non-redundant and redundant robotic manipulators and compared with other methods. The results show that the algorithm can effectively solve the singularity problem and generate smooth virtual forces to move the robotic manipulators away from unsafe regions.</p>