# Control System Design and Methods for Collaborative Robots: Review
## 5 Control Methodologies
### Impedance Control Strategy  
The most popular control technique is the impedance control which handles the hybrid force/position control and disturbances in the unknown environments of human-robot physical interaction [43; 44]. This method was developed for robust collaborative object manipulation, in which the impact of involuntary human motions can be compensated by adjusting impedance parameters. Impedance control techniques can handle motion and force in a unified manner for the robotic system. They benefit from hybrid force-motion controllers to produce a motion not constrained by a kinematic workspace [45; 46]. This method expresses the system as a second-order closed loop system of a mass-spring damper. The control objective is defined in operational space coordinates \(x\) as  
\[M_{x}\ddot{x}+D_{x}\dot{x}+K_{x}\dot{x}=F_{ext} \tag{5}\]  
where \(M_{x}\) denotes the desired inertia, \(\dot{x}=x-x_{d}\) is the position error vector, \(x_{d}\) represents the equilibrium position vector, \(D_{x}\) is the damping matrix, and \(K_{x}\) is the stiffness matrix in the operational space. In [47], the authors developed a modified impedance controller that requires angles for the operational space and energy functions for physical interpretation. To eliminate singularities, the end-effector orientation and displacement were used. The extension of adaptive impedance controllers can utilize impedance and feed-forward torques. However, the controller's learning of the desired motion trajectories is a significant problem [48; 49]. To address this issue, the authors proposed an adaptive impedance control method for series elastic actuator (SEA) collaborative robots [50]. This method introduced a controller with two operating modes: the first mode is \"robot-in-charge\", implying that a robot takes the primary role in job execution; and in the second mode, \"human-in-charge\", the human takes charge of executing the operation (Figure 6). The performance of the proposed controller was found to be satisfactory as validated using an experimental setup. Figure 5: Force profiles of collision occurrence. Another control method is that of Cartesian impedance control, which is generally used for grasping objects in co-manipulation tasks, where humans and robots share their roles as leader and follower. However, the authors [51] proposed modifications in this method that shift the human-robot role by sharing control through the operation. The torques applied to the admittance controller developed a wrist deflection, which help transform a virtual vertical force to carry the load. Using a second admittance controller, this force was used to extend or lower the robot's end-effector. The authors that employed this controller approached the mobile robot helper's base to perform the cooperative carrying of a load [52; 53]. The authors of [54; 55] also used a lifting controller with cascaded second-order virtual admittance controllers applied to the same applications. The authors of [56; 57] designed and evaluated an interactive controller for cooperatively carrying a load with the help of the robot and human simultaneously. Figure 7 depicts a simplified diagram for admittance-based collaborative task control. The fundamental problem of collision detection and avoidance was addressed in collaborative robotics. [PERSON] et al. [58] introduced a collision detection approach for industrial robots that uses a closed loop feedback control strategy. They used the measurement for joint positions and velocities as a reference signal for the controller. This technique did not demand the robot's dynamics model. The experimental scenarios of human-robot collaborations with various forces on the KUKA KR5 manipulator and DLR LWR-III were tested [59]. In addition, an impedance controller was designed that adapted itself according to external force collision, obeying safety standards (ISO10218) for force, velocity, and power limitations. The Kuka LWR4 robot was used for experimental verifications for such a collision avoidance strategy [60].