An integrative review of control strategies in robotics

1.1. Structure of the paper

The paper structure consists of 6 sections. In Section 2, Fundamentals of control strategies include methods presenting mathematical equations with structure scheme, advantages, limitations and the main key features. In Section 3, the classification of Control methods as linear, nonlinear, and learning based control based on control techniques, and approaches: model-based and model-free types as a method and classification of control strategies as centralized, decentralized and modal control are reviewed. Sections 4 and 5 contain the performance metrics of control strategies, comparative analysis of control methods, and hybridization in the practical implementation of control strategies. At the end, in Section 6, the concluding remarks and recommendations for future research are stated.

1.2. Research and paper selection methodology

The integrative review research papers on robotic control strategies are sourced papers from MDPI, IEEE Xplore, CrossRef and ResearchGate database in English language. The searching methodology for papers is based on the keywords: “Control strategy in Robotics” and “Reviewed paper on control strategies”. The selecting methodology focuses on methods of control strategies, implementation and design of new methods in Robotics, and innovative approach of control system in Robotics.

2.1. Classic control methods

Classic control methods are the basis of modern control and intelligent control theory and studies of linear systems. It is suitable for SISO: single input, single output, solving the analysis of systems and optimization problems [1]. Classical control methods consist of two main methods: proportional integral derivative control (PID) and linear quadratic regulator control (LQR) methods. These kinds of methods offer robust performance and effective control for linear industrial robots and are more effective to ensure the reliability and stability of the system. Implementation of the control in these methods is much easier than others. Table 1 presents the key features of classical methods based on the three main components: robustness, stability and complexity of implementation on 3 different levels of evaluation criteria: high, average and low, advantages, limitations and robotic applications including the examples.

PID control method is used in industrial automation widely, although it requires complex systems, performance improvement and disturbance immunity. PID controllers are the most used in the control system because they are easy to design and implement, clarity of functionality and adaptability [1]. In the other hand, utilization of the error between the desired and actual position or state to adjust the control commands are most used in the control systems [4]. The main advantages of PID control are to improve stability, guarantee product quality and to maximize product efficiency in different sectors using the real-world examples [22]. There are some limitations due to the non-linearity in technological procedures, PID control struggles to achieve ideal results. Moreover, parameter tuning methods are complex, making it difficult to set conventional PID controller parameters without adaptive tuning. These limitations restrict PID control applications in robotics [23]. On the other hand, PID control method is one of the most error deviation and major energy consumption [27].

The PID control consists of three components. The PID components are linear. PID combines proportional, integral, and derivative components [22]. The proportional component reduces the error based on proportional method. If the proportional ($K_p$) gain value is too low, the support signal may be inadequate to compensate for interference effects. The integral component eliminates residual error and relies on the cumulative sum of the uncertainties. If the integral ($K_i$) gain is higher, it can lead to overshoot due to accumulated past errors. The derivative component reduces the rate of change of error. The derivative ($K_d$) gains predict future values based on control error, enhancing system stability and tuning time.

The PID controller has an algorithm block diagram given in Fig. 3. The output of the PID control algorithm is shown in the Eq. (1). This algorithm adjusts the control input based on the error, set point, and output:

where, $e\left(t\right)$ is system error.

Fig. 3PID control technique

Using AI for PID parameter tuning improves adaptability of the systems. By integration of PID controller with fuzzy logic or neural network controller, the system will be optimized the structure and parameters. In another way, the metaheuristic algorithm can achieve optimal performance and can be assisted in designing the nonlinear PID controller [25].

Linear Quadratic Regulator (LQR) control is based on the feedback strategy for using the optimization of minimizing the cost function, which reflects system performance, including error and control effort. LQP is a classical control method, and the main purpose is to optimal state-feedback based on state-space theory, optimization principles and MIMO: multiple input and multiple output, capable designs. It can manage complex systems as a MIMO, but LQR control method demands and requires an accurate system model.

In the other hand, LQR control method is based on the optimal control techniques and in some papers, it uses optimal control methods instead of LQR control methods for nonlinear systems. In general, Optimal control application commonly uses the LQR in vibration suppression [26].

The main advantages of the LQR control method are the most efficient regulating multi-variable system with minimal energy use for MIMO systems [27]. However, request for perfect system modeling and linear assumptions, and incompatibility for nonlinear systems are the main limitations of the LQR control methods. In this regard, LQR is ensuring robust control performance based on the model-based controller [28]. LQR control methods are well-known methods for solution of the control forces for linear systems to ensure stability and robustness, providing the controllable system [29].

LQR algorithm optimizes the control input to minimize a quadratic cost function. LQR control utilizes a state-feedback control law and represents the control law is given as $u=-kx\left(t\right)$, where $K=R^{-1}{B}^{T}P$ and ${P=P}^T>0$ satisfies the Riccati equation $PA+A^{T}P+Q-PB{R}^{-1}{B}^{T}P=0$. The Ricotti Equation helps to calculate the optimal state-feedback gain for optimal control techniques. The Linear Quadratic Regulator (LQR) method formulates a linear state feedback control law as described in Eq. (2):

where, $x\left(t\right)$ and $y\left(t\right)$ present a $n$-dimensional state vector, $n$-dimensional output vector, $u\left(t\right)$ is an $m$ -dimensional control vector. The control law aims to minimize the quadratic performance index (cost function) given in Eq. (3):

where, $Q$ and $R$ are the weight matrix. The $Q$ matrix influences state trajectory deviation and the $R$ matrix is related to the control quantity and actuator saturation.

Fig. 4LQR control technique

The LQR control method is suitable for minimizing the quadratic cost function that balances the state error and control effort under the small uncertainty and distribution in the linear MIMO system. Integrating with PID, Fuzzy Logic, Adaptive and Neural Network control methods, it can achieve the performances of nonlinear system on robustness, adaptability and human-like behavior.

2.2. Modern control methods

Modern control theory starts to be used in the 1950s and 1960 to address the limitation of classical control strategies, which is inadequate for MIMO nonlinear systems [1]. The principles of optimal control, dynamic programming, Kalman filter, and state space description have contributed to the widespread adoption of MIMO control. In recent decades, advancements in modern control methods such as Adaptive Control, Sliding Mode Control (SMC), H-infinity (H∞), and Model Predictive Control (MPC) have been successfully implemented across various industrial processes as sophisticated non-linear control systems. In Table 2, the key features of modern control methods based on the three main components: robustness, stability and complexity of implementation on 3 different levels of evaluation criteria: high, average and low, its advantages, limitations and robotic applications including the examples are shown.

Adaptive control methods are a modern control for dynamically adjust controller parameters to handle parameter uncertainty and external perturbations in robotic systems. Under unknown or changing dynamics, allowing the robotic arm to maintain stable trajectory tracking performance despite varying loads, friction forces, and external disturbances the adaptive control methods modify control parameters [1]. Robots operate in various environments to perform tasks and encounter uncertain environmental conditions. Adaptive control methods excel in managing complex systems with uncertainty, nonlinearity, and time-varying traits through continuous learning and self-optimization, ensuring robustness and efficiency in dynamic environments [34]. Adaptive control faces challenges in ensuring system stability, managing complexity, and reducing computational costs. It requires advanced hardware and software for real-time data processing, and tuning adaptation parameters must balance speed, accuracy, robustness, and sensitivity to noise and disturbances.

Adaptive controller’s parameters adjust automatically to accommodate the changing characteristics of the system being controlled or to account for initial uncertainties. Fig. 5 shows an optimal technique of adaptive control methods based on adaptive algorithm generates direct estimates of the controller’s parameters.

The adaptive controller is derived from the system's mathematical model, represented in the Eq. (4) equation:

where, $x\left(t\right)$ is the system state, $u\left(t\right)$ is the control input, $A\left(\theta \right)$ and $B\left(\theta \right)$ are system matrices that depend on unknown parameters. This algorithm adjusts its parameters in real-time to adapt to changing system dynamics.

There are five methods for adjusting parameters: gain scheduling, dual control, auto-tuning, self-tuning control, and model reference [9]. Adaptive control methods are divided into model-based control algorithms and non-model-based algorithms. Model-based adaptive control requires knowledge of model parameters, and the main advantage allows the physical interpretation of the system’s behavior and can identify system’s parameters variations. Model-free based adaptive control eses fuzzy logic or neural networks. Its main advantages are handling nonlinearity, supporting parallel implementation, and tolerating system uncertainties [32].

Adaptive control is applicable across various fields, offering significant advantages such as high flexibility, strong robustness, and the ability to adjust automatically under varying operating conditions. This results in enhanced system performance, especially when developed using advanced methods like artificial intelligence, neural network control, and fuzzy logic control.

Fig. 5Adaptive control technique

Sliding Mode Control (SMC) is a well-known suitable powerful nonlinear control method for robotics, particularly when dealing with unknown disturbances and system uncertainties. Sliding Mode Control is commonly used in robotic manipulators, humanoid robots, and force-controlled systems for high-performance tracking and robustness. SMC involves designing a switching hyperplane to achieve the desired system dynamic. SMC is resilient to parameter changes and disruptions. Standard SMC design involves knowledge of uncertainty bound, which may be difficult to apply, and it generally employs conservative estimate and excessive gain [21]. It offers robustness and stability at the same time good transient performance [24]. SMC has several disadvantages: chattering which causes high-frequency oscillations in the input, sensitivity to noise when input signals are near zero and the complexity of calculating nonlinear equivalent dynamic formulations crucial for good performance.

The system state model is shown in the Eq. (5) equation:

where, $x\left(t\right)$is the system state vector, $u\left(t\right)$ is a control input, $f(x\left(t\right),u\left(t\right))$ is a known nonlinear function, and $d\left(t\right)$ is an external perturbation. SLC algorithm uses a discontinuous control signal to drive the system state to a desired sliding surface.

Fig. 6Sliding mode control technique

Designing the SMC involves creating a switching function that meets design criteria and selecting a control law to manage system states on the sliding manifold despite disturbances and uncertainties [38].

In general, sliding mode control is one of the best control of robots in nonlinear systems and this theory was initially proposed in the early 1950s by Emelyanov [38]. The traditional SMC evolved significantly in the mid-1980s with the introduction of the “second order sliding” concept. In the subsequent development phase during the 2000s, higher-order concepts gained considerable attention.

Recently, artificial intelligence methods have been applied to SMC systems. Neural networks control, fuzzy logic, and combination of neuro-fuzzy approaches have been integrated with sliding mode controllers and utilized in nonlinear, time-variant, and uncertain systems. Several researchers have developed an advanced and intelligent technique-based Sliding Mode Control (SMC) algorithm that effectively addresses systems with both structured and unstructured uncertainties. The integration of an observer with the SMC approach represents the latest advancement in sliding mode-based control systems.

H-Infinity control (H∞) is a well-known robust control method to optimize worst-case performance by minimizing the H∞ norm and to ensure strong robustness against system uncertainties and external disturbances. H∞ control is highly effective in managing uncertainty and nonlinear systems, as it can significantly suppress perturbations and ensure stable system performance. While applicable for vibration suppression in flexible connecting roads, the design and implementation process are complex and computationally intensive [1]. H-infinity control for robotic manipulators has been widely utilized in industrial applications, providing a solid theoretical foundation that can be applied to cooperative robotics [39]. The H-infinity is utilized to ensure performance and stability in the presence of internal uncertainties and external disturbances in mixed-sensitivity method, including sensor noise, unmodeled dynamics, and actuator control weight limitations [41]. It seeks to reduce the closed-loop effects of disturbances by optimizing the H∞ norm of a particular transfer function.

Advantages of the H∞ control are to provide a systematic approach to designing controllers that meet specific performance requirements, to ensure that the closed-loop system remains stable and performs well even in the presence of uncertainties and disturbances, and to allow for the design of controllers that can handle both structured and unstructured uncertainties. There are some disadvantages: complexity on computationally intensive, especially for high-order systems, conservatism on design process and on high-order controllers which may lead to large control effort requirements.

The H∞-based formulation of the robust control problem is shown in Fig. 7. Where $w$ is the vector of all perturbation signals, $z$ is the cost signal containing all errors, $v$ is the vector containing the measurement variables, and $u$ is the vector of all control variables [1].

Fig. 7H-infinity (H∞) control technique

The generalized system as a $P$ has inputs, first one is an exogenous input $w$ includes reference signal and disturbances, second one is a manipulated variable $u$. The first output is an error signals $z$ which require to minimize. Second output is a measured variables $v$, which use to control the system. $v$ can be used in robust controllers as a $K$ to calculate the variables $u$. Note that all these are generally vectors, while $P$ and $K$ are matrices. In formulae, the system is:

There are fundamentally two methodologies for H∞ system control design: mixed sensitivity and loop shaping design [41]. H∞ algorithm optimizes the control input to achieve robust performance in the presence of uncertainties. Integrating H-infinity control with AI in robotics focuses on developing control systems that can handle uncertainties and disturbances in real-world robotic applications. This method merges the robustness of H-infinity control with the learning capabilities of AI, allowing robots to perform tasks consistently and effectively.

Model Predictive Control (MPC) is based on a mathematical model for predicting the future system behavior and optimizing control commands. Model Predictive Control handles complex systems with constraints and disturbances effectively, but MPC requires an accurate system model and can be computationally demanding [4]. Model Predictive Control remains a critical control strategy in modern robotics, often hybridized with learning-based techniques for enhanced real-time decision-making. MPC is the nonlinear control system for supporting the predicts future states and errors of the system [9, 34]. Unlike classical control methods (e.g., PID, LQR), MPC explicitly incorporates system constraints and handles multi-input, multi-output (MIMO) systems natively, making it advantageous for complex robotic applications. Despite MPC’s broad use, implementing it on high degree of freedom systems demands significant computational power, limiting its application on embedded platforms [44]. It encounters challenges when handling complex, nonlinear processes. These challenges include the requirement for precise models, difficulty in adapting to process changes, and optimizing control actions.

MPC algorithm using a linear model has similar behavior. MPC algorithms can be used as models for predicting future behavior and optimize control inputs of the system:

where $A$ is step response, $Y$ is the predicted output, $Y_0$ is past output, and $u$ is the control law.

To compensate for the uncertainties of the model problem, an error term $E_f$ is added to the system output:

The correction term represents the differences between the actual output and the model’s output.

Fig. 8Model predictive control technique

In conclusion, model predictive control is an effective approach for robot motion planning in intricate environments and used to generate online motion. By integrating dynamic models, optimization algorithms, and rolling optimization techniques, MPC can create secure and efficient trajectories while responding to environmental changes in real time [34, 44, 46].

Machine Learning Based MPC combines traditional MPC with machine learning. It uses ML algorithms for accurate system modeling, behavior prediction, and control action optimization. Key components are data collection, model training, and control optimization. Combining machine learning with MPC can greatly enhance control performance and efficiency.

2.3. Intelligent control methods

Classical and modern control theories face challenges with complex systems that don't fit accurate mathematical models. In the 1970s, Professor Fu Jingsun from Purdue university’s Electrical Engineering Department introduced intelligent control, combining artificial intelligence and automatic control into a new field [1]. Nowadays we can separate the robot system into 2 parts, the first is controlling robot system, and the second is intelligent system for robotics. Robot intelligence is based on intelligent control and involves understanding and identifying the external environment, which includes areas such as computer vision, voice processing, and natural language processing [5]. The intelligent control system's primary limitation was input point errors [17].

Intelligent control in robotics uses AI techniques such as machine learning, neural networks, and fuzzy logic to help robots make decisions and adapt to complex environments, improving their autonomy and performance, while the system learns from past experience for improving the system performance [48]. Intelligent control methods solve the stability of the system, controller tuning, identification and optimization problems, and problems of iterative learning. In Table 3, the key features of intelligent control methods, their advantages, limitations and robotic applications including the examples are shown.

Future research for intelligent control methods aims to address the concept known as “learning-to-learn”, where the agent selects the learning strategy and adjusts its meta-parameters [48]. Additionally, advanced robotics is rapidly increasing based on advanced intelligent control. The trends include the use of intelligent control methods, multi-sensor fusion, and technologies like computer vision, VR & AR, remote control, adaptive sensor networks, human-robot interaction, and machine-to-machine interfaces [50].

Fuzzy logic control is an intelligent control method, that consists of fuzzy set theory, linguistic variables, and logic reasoning, applying fuzzy mathematics and theoretical control to actual controllers [1]. Fuzzy set theory, developed by Lotfi Zadeh in the 1960s, has been increasingly used for control applications in recent years. The fundamental principle of fuzzy logic, as opposed to Boolean logic, is its capability to handle computation with varying degrees of truth. From a theoretical perspective, it is possible to identify a nonlinear controller and model using a fuzzy rule base of logic, which serves as a “universal approximation”. Numerical samples, human expert data, and specific inputs/outputs data are sources that provide relevant system information for each device [49, 51].

Fuzzy control algorithms are capable of handling non-linear systems and do not require precise mathematical modelling. This algorithm uses fuzzy logic to handle uncertainties and nonlinearities in the system. Widely used in flexible robots, which often must deal with complex working environments and uncertainty, fuzzy control handles these variables and enhances the flexibility and adaptability of robot operation. Fuzzy control is used for robot path planning and obstacle avoidance in uncertain environments. By means of fuzzy rules, the robot can autonomously judge variables such as distance and speed, make appropriate decisions, and improve the intelligence and robustness of navigation [1], [16].

The FLC can be used in the non-linear system to support the robust controller for the uncertain, MIMO, and time-variant system model. The control system features fast response, short transient process, high precision, and good robustness [5]. A notable aspect of the fuzzy controller is its ability to implement expert knowledge linguistically and imitate human reasoning to manage complex systems [9].

Fig. 9Fuzzy logic control technique

The fuzzy logic controller consists of four components: rule base, inference mechanism, fuzzification: determine inputs and outputs, converts the crisp inputs to fuzzy inputs; and defuzzification: transform fuzzy set to crisp set (Fig. 9). The center of gravity of the fuzzy set and output can be represented as:

where ${\mu }_B\left(y\right)$ is the output membership function.

Fuzzy control rules are defined as follows:

1. If $\tilde{U}=U^1$ then $t=T^1$,

$⋮$

$k$. If $\tilde{U}=U^k$ then $t=T^k$,

where $U^1={(U_{11}\dots U_{1i})}^R$, $T^1={(T_{11}\dots T_{1i})}^R$, $q=(1,\dots ,p)$ is the linguistic value (fuzzy subset) vector corresponding to the language variable. The controller $n$-dimensional input vector is $u={(u_1,u_2,\dots u_k)}^R$. The control vector is t$={(t_1,t_2,\dots t_k)}^R$. $\tilde{u}$ is the fuzzy variable corresponding to $u$.

FLC is used in industry, medicine and others relevant areas. The main limitation of this method is not ensuring the stability and acceptable performance of the system, but through integration with sliding mode controllers improves to reduce issues like chattering and to enhance system stability, which is a main challenge of FLCs.

Neural Network Control (NNC) is the intelligent control method inspired by the mammalian brain, which handles complex tasks like face recognition, body motion planning, and muscle activity control through billions of interconnected neurons. Throughout the 1940s, researchers focused on replicating the processes of the human brain and developed basic neuron software and device neurons. In the 1950s to 1960s, scientists created the first artificial neural network, which incorporated biological and surgical representations generated by McCulloch Pitts and other scientists [49, 54]. Key components of an NNC include the learning rule, activation function, neuron model, network architecture and training algorithm [11].

Neural network control utilizes artificial neural networks to model, approximate, or optimize control laws for robotic systems [1]. This approach has been extensively applied in the identification of nonlinear systems [5]. A neural network has a parallel structure that enables high-speed computation, fault tolerance, and real-time applications in robot manipulator control [7].

In robotics system, NNC is used mainly in controlling the robot system and identification. In this area, NNC is very effective on robot manipulators have uncertainty in dynamic part [1].

The design of NNC control is classified two stages: identification and design of controlling. Initially, the objective of system identification is to create a neural network model of the process that is regulated. Subsequently, this NNC model is employed to train the networks that are responsible for the system's control [16].

The output of the neural network can be represented as:

where $y$ is the output, $f$ is the activation function, $w_i$ is the weight matrix, $x_i$ is the input vector, and $b$ is the bias term. This algorithm uses neural networks to learn and optimize control inputs.

Fig. 10Neural network control technique

NNC model has three layers: input, hidden, and output (Fig. 10). Combining neural networks with other control methods, like fuzzy logic or traditional controllers like PID, enhances system performance and adapts to dynamic conditions. This hybrid approach leverages the strengths of each method, for example, combining the approximation capabilities of neural networks with the rule-based representation of fuzzy logic. Neural networks can also be used in conjunction with methods like MPC or SMC to improve robustness and accuracy, especially in complex systems with uncertainties [75].

Machine learning (ML) control is a creative adaptive system that learns from previous data and adjust to dynamic changes [11]. Machine learning control provides adaptability, self-learning abilities, and model-free execution, but it is constrained by high computational costs, lack of stability guarantees, and data inefficiencies. It is most effective in autonomous, nonlinear, and high-dimensional robotic tasks where conventional control struggles. Hybrid frameworks combining ML with traditional controllers help bridge reliability gaps, making ML-enhanced control a growing area of research.

Intelligent control offers robot manipulator controller designers an option. Due to uncertainty, real application sectors demand intelligent control strategies above traditional techniques [16]. ML control is a main part of intelligent control and aims to solve optimal control problems using machine learning methods. In machine learning control, a model is trained on a dataset to learn patterns. It is then tested on a separate test set to evaluate its performance and avoid overfitting. Feature engineering involves refining raw data into useful features to enhance model performance. In robotics, features include sensor readings and environmental parameters for accurate predictions. Model quality is assessed using performance metrics; classification tasks use accuracy, precision, recall, and score.

Combining machine learning with control systems advances autonomous robotics by enabling adaptation to dynamic and uncertain environments. Traditional control methods, relying on predefined models, work well in predictable settings but struggle in complex scenarios. Machine learning can learn from experience and data, enhancing robot decision-making and adaptability. This integration improves performance over time, handles uncertainties in sensor data, control parameters, and environment dynamics better than traditional methods.

Fig. 11Machine learning control technique

Machine learning improves robotic technologies and creates new opportunities across industries. Its adaptability, efficiency, and decision-making enhance robotic systems. Future research should refine these models for real-time use and address ethical issues to align advanced robotics with societal and industry needs [58]. In Fig. 12, the main algorithms of machine learning methods are shown and explained based on references: [56], [59], [60], and [65].

In general, Artificial Intelligent is the main elements of advanced robotics and to serve the development of following technologies for robotics: Object Recognition, Motion Planning, Control, Localization and Object Detection [61]. There is several programming languages utilized in robotics, including Python, C++, MATLAB, and ROS (Robot Operating System). These languages offer various libraries and tools that facilitate the integration of control strategies into robotic systems.

Fig. 12Types of machine learning control algorithms in robotics

3.1. Linear, nonlinear and learning based controllers

In control strategies of robotics, the controllers are the main elements that is a device or algorithm for maintaining a process variable at a desired setpoint, even in the presence of disturbances or changes in the system. Controllers are classified into linear, nonlinear, and learning-based (Table 4).

The LQR, PID and H∞ control methods are linear control techniques. Linear controllers are popular for experimental work due to their ease of implementation. Linear control methods are well-suited for systems that can be accurately represented by linear equations, making them easier to analyze and design. In robotics, linear control is often used for tasks such as trajectory tracking, position control, and stabilizing robot movements. Advantages of the linear control are simple to design and implement, making them suitable for various robotic applications, provide stable and predictable performance under certain conditions, and to be robust to certain types of disturbances and uncertainties. Limitations of linear control are linearity assumption, nonlinearities and disturbances.

Nonlinear control techniques often used are model predictive control, sliding mode, and adaptive controllers. Sliding mode control (SMC) is commonly used to manage various nonlinear systems. This method employs the switching and discontinuous nature of the control signal to modify the dynamics of the nonlinear system being managed [62]. Adaptive controllers are the most advanced nonlinear control schemes, aimed at estimating uncertain parameters and tuning the controller in real-time to adjust to dynamic variations in system parameters or environment [63].

Nonlinear control techniques offer advantages like handling complex system dynamics and achieving high performance without linearization, but also present limitations such as increased complexity and potential for instability.

Learning based control is developed in the mid-20th century in optimization theory, optimal control, and dynamic programming [64]. Learning-based controllers do not need precise dynamic models but rely on trials and flight data, including fuzzy logic, neural networks, and machine learning control [9]. The complexities, robustness and stability of robot control are important considerations. Both linear and nonlinear controllers can maintain system stability at the nominal state and ensure system performance. On the other hand, learning based controllers: fuzzy logic and neural networks cannot always guarantee stability, but can achieve high maneuvering performance. Linear controllers generally do not ensure system robustness except for H∞. MPC and adaptive controllers can ensure robustness and acceptable maneuvering performance among nonlinear controllers. Others provide robustness only in performance. Fuzzy and neural networks are inefficient in ensuring robustness for system maneuvering performance. In contrast, nonlinear and learning based controllers are more complex but often perform better [9], [11]. Nonlinear and learning based controllers are complex to design and implement, but they outperform linear controllers.

Learning based control techniques offer advantages such as adaptability to complex, dynamic environments and reduced reliance on precise system models, but also face limitations including high computational cost, potential instability, and the need for extensive training data.

3.2. Model-based and model-free approaches

In robotics, “model-based” and “model-free” describe two approaches to control strategies. Model-based methods use a learned or known model of the robot and environment to guide actions. Model-free methods learn directly from interactions without an explicit model.

Model-free control assumes that all joints are independent, resulting in individual controllers for each joint. Model-free methods do not require precise system models. These techniques use empirical data and learning algorithms to adjust to the robot's behavior in real-time. Examples of model-free control strategies include reinforcement learning, fuzzy logic control, and neural fuzzy control. These methods can address uncertainties but are computationally demanding and may need extensive training and tuning [66].

The model-based segment primarily compensates for the nonlinear systems and dynamics of the robotic system [14]. Model-based control approaches demand exact robot dynamics; hence controller effectiveness depends on robot mathematical model accuracy [18]. Model-based control involves designing controllers based on mathematical models that represent the robot’s dynamics and interactions with the environment. These models help predict the future state of the robot and allow for the computation of control actions that drive the robot its desired trajectory. Techniques such as LQR or MPC are often employed in this domain. While highly effective in structured and known environments, model-based control can struggle in dynamic and unpredictable settings, where real-time adjustments are critical.

Model-based methods are predictable and stable, whereas model-free methods are adaptable in uncertain environments. In general, admittance and impedance approaches of control system are totally suitable for model-based control methods [67].

In Table 5, the comparison of those approaches based on the model, adaptability, and complexity are indicated.

Model-free control differs from model-based control by not relying heavily on an accurate system model. This approach is useful when obtaining a precise model is difficult. In practical applications, model-based methods often suit simulation environments only. To overcome this limitation, model-free control was introduced, eliminating the need for model development and avoiding model uncertainties [67].

3.3. Centralized, decentralized and modal control

Typically, control strategies consist of centralized, decentralized and modal control types [26]. The centralized control is suitable for the dynamic model, and the multiple-input and multiple-output system, and all decisions and managements of system are controlled by one controller.

The transformation of MIMO into SISO based on inverse kinematics and dynamics model are the main elements of the decentralized control. In this type, each sub-system is controlled independently [26]. In a decentralized control system, multiple controllers make decisions independently, based on local information and interactions.

The modal control strategy, pioneered by Balas in the 1970s, offers robust stability for addressing unmodeled vibration modes. Modal control focuses on manipulating the system’s modes (eigenvalues) to achieve desired control objectives. The decoupling method is appropriate for the modal control strategy, which uses modal coordinates to reduce the vibrations of various primary modals [26].

Fig. 13Types of control strategies depending on the controller’s decision-making level