In this article, a novel model-free dynamic inversion-based Q-learning (DIQL) algorithm is proposed to solve the optimal tracking control (OTC) problem of unknown nonlinear input-affine discrete-time (DT) systems. Compared with the existing DIQL algorithm and the discount factor-based Q-learning (DFQL) algorithm, the proposed algorithm can eliminate the tracking error while ensuring that it is model-free and off-policy. First, a new deterministic Q-learning iterative scheme is presented, and based on this scheme, a model-based off-policy DIQL algorithm is designed. The advantage of this new scheme is that it can avoid the training of unusual data and improve data utilization, thereby saving computing resources. Simultaneously, the convergence and stability of the designed algorithm are analyzed, and the proof that adding probing noise into the behavior policy does not affect the convergence is presented. Then, by introducing neural networks (NNs), the model-free version of the designed algorithm is further proposed so that the OTC problem can be solved without any knowledge about the system dynamics. Finally, three simulation examples are given to demonstrate the effectiveness of the proposed algorithm.

Compliant force control is a fundamental capability for enabling robots to interact safely and effectively with dynamic and uncertain environments. This paper presents a comprehensive survey of compliant force control strategies, intending to enhance safety, adaptability, and precision in applications such as physical human–robot interaction, robotic manipulation, and collaborative tasks. The review begins with a classification of compliant control methods into passive and active approaches, followed by a detailed examination of direct force control techniques—including hybrid and parallel force/position control—and indirect methods such as impedance and admittance control. Special emphasis is placed on advanced compliant control strategies applied to structurally complex robotic systems, including aerial, mobile, cable-driven, and bionic robots. In addition, intelligent compliant control approaches are systematically analyzed, encompassing neural networks, fuzzy logic, sliding mode control, and reinforcement learning. Sensorless compliance techniques are also discussed, along with emerging trends in hardware design and intelligent control methodologies. This survey provides a holistic view of the current landscape, identifies key technical challenges, and outlines future research directions for achieving more robust, intelligent, and adaptive compliant force control in robotic systems.

This article aims to solve the optimal tracking problem (OTP) for a class of discrete-time (DT) nonlinear systems with completely unknown dynamics. A novel data-driven deterministic approximate dynamic programming (ADP) algorithm is proposed to solve this kind of problem with only input–output (I/O) data. The proposed algorithm has two advantages compared to existing data-driven deterministic ADP algorithms for the OTP. First, our algorithm can guarantee optimality while achieving better performance in the aspects of time-saving and robustness to data. Second, the near-optimal control policy learned by our algorithm can be implemented without considering expected control and enable the system states to track the user-specified reference signals. Therefore, the tracking performance is guaranteed while simplifying the algorithm implementation. Furthermore, the convergence and stability of the proposed algorithm are strictly proved through theoretical analysis, in which the errors caused by neural networks (NNs) are considered. At the end of this article, the developed algorithm is compared with two representative deterministic ADP algorithms through a numerical example and applied to solve the tracking problem for a two-link robotic manipulator. The simulation results demonstrate the effectiveness and advantages of the developed algorithm.

Designing a robot with the best accuracy is always an attractive research direction in the robotics community. In order to create a Gough–Stewart platform with guaranteed accuracy performance for a dedicated controller, this paper describes a novel advanced optimal design methodology: control-based design methodology. This advanced optimal design method considers the controller positioning accuracy in the design process for getting the optimal geometric parameters of the robot. In this paper, three types of visual servoing controllers are applied to control the motions of the Gough–Stewart platform: leg-direction-based visual servoing, line-based visual servoing, and image moment visual servoing. Depending on these controllers, the positioning error models considering the camera observation error together with the controller singularities are analyzed. In the next step, the optimization problems are formulated in order to get the optimal geometric parameters of the robot and the placement of the camera for the Gough–Stewart platform for each type of controller. Then, we perform co-simulations on the three optimized Gough–Stewart platforms in order to test the positioning accuracy and the robustness with respect to the manufacturing errors. It turns out that the optimal control-based design methodology helps get both the optimum design parameters of the robot and the performance of the controller {robot + dedicated controller}.

This brief proposes a novel improved model-free adaptive control (IMFAC) algorithm to address the load frequency control (LFC) problem in multi-area power systems. A new three-term criterion function is introduced and integrated into the traditional MFAC framework for the first time. By incorporating system state increments into the control input computation, the proposed algorithm enhances the suppression of overshoots and oscillations caused by frequency deviations due to sudden load changes. Moreover, the algorithm is entirely data-driven, eliminating the need for mathematical modeling of complex power system dynamics. The effectiveness of the proposed method is validated through theoretical analysis and simulation on a three-area power system.

Aiming at the force-tracking error phenomenon of impedance control in an unknown surface environment, an adaptive variable-damping impedance control algorithm is proposed, and the stability and convergence of the algorithm are deduced. An adaptive-law selection rule is proposed to aim at the phenomenon that the adaptive parameters are too large to cause the system oscillation and overshoot and too small to cause the adaptive line variation in the curved surface environment. Finally, experiments conclude that the impedance control based on the adaptive variable-damping algorithm has a better force-tracking effect than the ordinary impedance control in the curved surface environment where the contact surface between the end-effector of the manipulator and the atmosphere is unknown.