When designing a controller for human–robot collaboration, two essential factors need to be considered; adjustable autonomy and mixed-initiative for integrating humans into an autonomous control system. Adjustable autonomy and human initiatives switch the control of tasks between an operator and an automated system in response to changing the demands of the robotic system. In this survey, an application scenario of a collaborative manipulator robot having direct physical collaboration with the human operator in industrial applications for collaborative assembly is considered.

Simple-to-complex control architectures have been presented in the literature. The collaborative control architecture presents a systematic view of the interaction between humans and robots at both low-level (sensors, actuators) and high-level control (perception and cognition), as shown in Figure 2 ^[13][14][25,26].

Another control architecture presented in ^[15][16][27,28] shows a more comprehensive review of interaction control in human–robot collaboration. This framework explains the complex requirements and diverse methods for interaction control, motion planning, and interaction planning. This control architecture is unconventional compared to a classical control architecture due to the planning for safe collaboration ^[17][29]. The control architecture is composed of three abstraction layers (Figure 3).

The highest abstraction layer is the top layer of architecture that plans the global task of the robot based on skill sets in offline mode. Such a task planner creates the different skill states to accomplish the respective global tasks/actions. It generates the task state and sends the initial desired behavior information to lower layers. Each skill state holds the information regarding the current task and action to perform. The job of a robotic system can be, e.g., to grasp the object or hand it over. The examples of non-real time control architectures were presented in ^[18][19][30,31].

The second abstraction layer is responsible for dynamically executing and modifying global plans; it does so by choosing the best action of the current task state, behavior state, human state, and environmental state. This dynamic planning unit is followed by a learning and adaption unit. The unit converts global task planning information into the corresponding dynamic planning language. The planning unit can translate the robot’s desired actions into safe and task-consistent actions, which instantaneously alter the global task plan. Hence, this layer’s primary task is to modify the pre-planned course into safe and consistent actions using the prediction of human intentions. Examples of soft real-time architectures are described in detail in ^{[20][21][22][23][24]}[32,33,34,35,36].

The low-level control layer is the bottom layer with the desired action (ad) and behavior (bd) that is directly forwarded to the robot for task execution. The expected behavior (bd) can alter based on reflex behaviors when accidental situations or collision events occur. The control layer provides feedback on the currently active activity (a) and behavior (b) to the dynamic planning layer, allowing it to perform accordingly.

Human interaction in this control architecture is observed at various levels of abstraction. The human observer states gather all human-related information and knowledge in the second layer (soft real-time) that can be further used for planning in the lower layer. This control architecture ensures human safety in physical interaction for interactive and cooperative tasks with a collaborative robot ^[25][37]. The following subsection highlights the key challenges are highlightthat are considered in the following subsectionour literature review.

The first challenge posed to HR collaboration is the precise estimation of human intention for a controller design. It allows the system to select the correct dynamic planning to anticipate the appropriate safety behavior. The goal here is to equip the robot with the human intention that is easy to interpret and safe for humans and robots to participate in the collaborative task. In the real-time control layer, there is a two-way interaction: the human ability to anticipate the robot movement is as important as the ability of the robot to anticipate human behaviors. The prediction of human actions relies on two factors: (1) predicting the next action; and (2) prediction of action time. Human motion prediction relies on predicting the desired tasks (manipulation, navigation) and the characteristics of human motion. On the other side, with either explicit or implicit cues, the robot can make its intended goals/tasks clearer to the co-located humans, facilitating the humans’ ability to select safe actions and motions.

Industrial collaborative robots can work with humans and perform operations besides them. These robots can move their arms and bodies and operate with dangerous and sharp objects. Such a situation demands specific procedures to ensure human safety while undertaking collaborative tasks. This is an important and emerging issue in the field of human–robot collaboration. Such a problem can be tackled using a collision model for a robot consisting of n joints and a particular link detecting a collision with a human ^[26][38].

The following equation combines linear and angular velocity vectors with joint angular velocities (q) where xc $$ x c  is a state vector, vc is a linear velocity vector and $$ w c wc is an angular velocity vector of the related robot link at the collision contact point, and $$ J c ( q ) Jc(q) is the contact Jacobian. In case of the collision, the robot dynamics can be represented as where $$ M ( q ) M(q) is a joint space inertia matrix, $$ C ( q ) C(q) is a coriolis vector, $$ g ( q ) g(q) is the gravity vector, $$ τ f τf is the dissipative friction torque, $$ τ τ is the motor torque, $$ F e x t Fext is the external force observed by the joint during collision, and then $$ τ e x t τext is external joint torque expressed as

Then, the effective mass of a robot can be estimated as where $$ Λ v ( q ) Λv(q) is the Cartesian kinetic energy matrix. When the collision occurs, an important entity is a force observed at the contact point. This force is characterized in two phases, as shown in Figure 4. In phase I, FI represents a short impulsive force. In phase II, two types of forces come into play in case there is quasi-static contact. If the human is not clamped, then this force is called a pushing force $$ F I I a FIIa. When a human is clamped, the force is called a crushing force $$ F I I b FIIb. The mathematical modeling of robotic systems that includes kinematic modeling and dynamic modeling is a precursor for control design. The comprehensive dynamic modeling of point contact between the human hand and robotic arm is described in ^{[27][28][29][30]}[39,40,41,42].

The unpredictable disturbances of human motion significantly reduce the performance of robotic control. To ensure stable and robust human–robot collaborative assembly manipulation, there is a need to minimize human disturbance.