A six-degree-of-freedom robotic manipulator inverse kinematics (IK) for position control is proposed for the bilateral teleoperation process that is implemented through a joystick for nuclear power plant dismantling operations. The control strategy of the manipulator includes the use of the joystick to generate the Cartesian space trajectory followed by the IK to yield the joint space trajectory for implementing position control. In this paper, a novel technique for the IK is proposed. It involves the use of the particle swarm optimization (PSO) algorithm with the inverse Jacobian (IJ). The special case of the dual PSO is based on dividing the PSO algorithm into two such that the trajectory position and orientation are separately optimized by the algorithms, resulting in a faster convergence. In contrast, the inverse Jacobian aids in generating a smooth joint trajectory. The integral sliding mode control (ISMC) is proposed for position control because it does not require information on system dynamics. The ISMC improves the system trajectory tracking performance by using a switching gain to compensate for system dynamics and perturbations (disturbance and unmatched uncertainties), ultimately reducing the time delay. The effectiveness of the PSO combined with the IJ and the robustness of the ISMC in the teleoperation process are confirmed by the experimental results. INDEX TERMS Teleoperation, inverse kinematics, robotic manipulator, PSO, inverse Jacobian, ISMC