Robust sliding mode based impedance control

This paper proposes an intelligent massage control system by using multi-fingered robot hand with hybrid impedance and force control, which is able to create the movement and force of robot to behave as similar as the human’s massage. Therefore, the various massage points, such as the changing of hardness and softness of human skin muscle condition, can be appropriately controlled by using hybrid impedance and force control method. The impedance control is used to control the lateral position of massage on the human skin muscle. The perpendicular direction one, while force control is carried out for the vertical direction on human skin muscle. This paper also gives a modeling of human skin muscle through robot perception of impedance to decide the parameter of impedance controller. The control strategy using a hybrid impedance and force control to implement an adaptive control system is presented, when human condition is changed with soft and hard skin muscle. For the robot fingertip force, PI servo compensation is used together with impedance control. Based on using both impedance and PI servo compensation, the effectiveness of the massage position and force control is shown through actual massage motion experiments.

Robotic force control is a core research direction in robotics technology. For tasks such as polishing and assembly, it requires not only precise motion control but also compliant force control by adjusting output force and torque. Traditional impedance control can ensure accuracy in a single environment, but it is limited by the difficulty in accurately acquiring parameters in complex environments; although variable impedance control can adapt to the environment, it faces challenges in control law design. This paper integrates the extended Twin Delayed Deep Deterministic Policy Gradient (ex-TD3) algorithm with impedance control, proposing an ex-TD3-based intelligent impedance control optimization algorithm. A Python-MATLAB/SimMechanics co-simulation platform is established to verify its effectiveness. The experiment adopts a scenario where the robot moves linearly along the z-axis, with fixed environmental stiffness and the desired tracking force changing in stages over time. The model training is iterated for 300 episodes, after which the reward tends to stabilize and the control strategy converges. Experimental results show that, compared with the traditional adaptive impedance control algorithm, the proposed algorithm in this paper exhibits faster force response, smaller force fluctuations during force step changes, smoother force output throughout the process: the maximum overshoot of force control decreases from 6.21N to 1.33N (a reduction rate of 77.63%), and the maximum position tracking error is reduced by 69.5%. With the above optimized design, this study significantly improves the energy efficiency and long-term operational sustainability of mechatronic systems; its precise control of force overshoot and position tracking error effectively reduces mechanical losses and unnecessary energy consumption during the system’s dynamic interaction with the environment.

This work addresses the end-effector trajectory-tracking force and motion control of a three-dimensional three-link robot considering measurement noises. The last two links of the manipulator are considered as structurally flexible. An absolute coordinate approach is used while obtaining the dynamic equations to avoid complex dynamic equations. In this approach, each link is modeled as if there is no connection between the links. Then, joint connections are expressed as constraint equations. After that, these constraint equations are used in dynamic equations to decrease the number of equations. Then, the resulting dynamic equations are transformed into a form which is suitable for controller design. Furthermore, the dynamic equations are divided as pseudostatic equilibrium and deviation equations. The control torques resulting from the pseudostatic equilibrium and the elastic deflections are obtained easily as the solution of algebraic equations. On the other hand, the control torques corresponding to the deviations are obtained without any linearization. Encoders, strain gauges, position sensors and force and moment sensors are required for measurements. Low pass filters are considered for the sensors. For the crossover frequencies of the sensors, low and high values are chosen to observe the filtering effect on the robot output.

In this paper, a non-time based tracking controller of a nonholonomic mobile robot is first analyzed. Non-time based motion controllers have been successfully applied to many areas such as robot motion control, multi-robot coordination, force control, robotic teleoperation and manufacturing automation. However, by the traditional non-time based motion controller many suffer from oscillations in both the linear and angular velocities when there is a large initial tracking error. In this paper, a traditional non-time based tracking controller is optimized using a genetic algorithm, which is used to generate the model parameters that could guarantee the system stability and convergence of tracking error. Simulations using a nonholonomic mobile robot model with a four degree of freedom are conducted to investigate the performance of the proposed controller. The results using the proposed model is compared to those of the conventional model. Generally the proposed model performs better than the conventional model because the genetic algorithm can provide better parameters to minimize tracking error and the oscillation.

Introduction With the increasing requirements for performance and safety of lower limb exoskeleton rehabilitation robots, researchers are exploring various active compliance control strategies to improve the compliance of control and enhance safety and effectiveness of rehabilitation training. The focus of this paper is to evaluate existing active compliance control strategies applied to lower limb exoskeleton rehabilitation robots, highlighting their principles, key technologies, and performance. Areas covered Literature searches were conducted in PubMed and Web of Science from 2000 to 2025, starting with the broad keyword ‘active compliance control strategy’ and narrowing down to specific aspects such as ‘impedance control’. Sixty-nine articles were reviewed, and eight active compliance control strategies were divided into three categories according to their core principles: impedance control (n = 18), force, and position hybrid control (n = 27) and machine learning-based hybrid control (n = 24). Their applications in five types of lower limb exoskeleton rehabilitation robots are outlined. Expert opinion Active compliance control strategies for lower limb exoskeleton rehabilitation robots are necessary for safe human-robot interaction and assist-as-needed implementation. This paper envisions the concept of an active compliance controller that covers the entire rehabilitation cycle, ensuring that the robot is continuously aligned with the patient’s rehabilitation needs.

The best exoskeleton control strategy depends on the task, motivating the development and analysis of an exoskeleton capable of position, force, and impedance control. In this paper, we implement and compare the three controller types via sliding mode control on a custom-built pneumatic cylinder ankle exoskeleton. To evaluate each controller's performance, the exoskeleton was tested on the benchtop and with human subject experiments. With the position controller, the exoskeleton achieved an root-mean-square error (RMSE) of under 5 deg for both the benchtop and human tests. It had a bandwidth of approximately 12 rad/s. The force controller tracked sinusoidal trajectories acceptably well at low frequencies (15% of force range at 6 rad/s), with a bandwidth of approximately 24 rad/s. The error was significantly higher (RMSE of 24% of force range) for the more biologically relevant trajectory. The impedance controller demonstrated the desired spring-like behavior, with position RMSE generally under 5 deg compared to expected position. All three controllers worked equally well for benchtop and human tests. Thus, a pneumatically powered ankle exoskeleton with sliding mode control is capable of accurate position and impedance control and is capable of marginally acceptable force control.

An impedance force control framework that enables precise contact force tracking for industrial robots subject to unknown environment dynamics is proposed in this paper. First, a position-based impedance controller is formulated and theoretical analysis reveals that perfect force tracking requires exact knowledge of the environment stiffness and contact position—quantities that are rarely available in practice. To compensate for these uncertainties, a Unified Residual Compensation Iterative Learning Control (URC-ILC) scheme is introduced. Instead of estimating each environment parameter separately, URC-ILC aggregates all modeling errors into a single residual term, which is iteratively updated and fed forward to the impedance loop, guaranteeing stable convergence of the contact force. The controller parameters are tuned off-line by Multi-Directional Particle Swarm Optimization (MDPSO) algorithm, which is developed by (i) injecting four performance-oriented velocity components—response speed, steady-state error, oscillation, and overshoot—into the swarm dynamics, (ii) modulating the inertia weight through a sigmoid schedule, and (iii) applying a mutation operator that prevents premature convergence. Simulations show that MDPSO converges faster and attains higher accuracy than the classical PSO. Experiments further demonstrate that the URC-ILC-based impedance controller, with parameters optimized by MDPSO, reduces steady-state force error by 44.38% relative to the conventional impedance strategy. These results confirm the effectiveness of the proposed approach for high-precision, compliant robotic machining under uncertain contact conditions.

Hybrid impedance/admittance control aims to provide an adaptive behavior to the manipulator in order to interact with the surrounding environment. In fact, impedance control is suitable for stiff environments, while admittance control is suitable for soft environments/free motion. Hybrid impedance/admittance control, indeed, allows modulating the control actions to exploit the combination of such behaviors. While some work has addressed the proposed topic, there are still some open issues to be solved. In particular, the proposed contribution aims: (i) to satisfy the continuity of the interaction force in the switching from impedance to admittance control when a feedforward velocity term is present; and (ii) to adapt the switching parameters to improve the performance of the hybrid control framework to better exploit the properties of both impedance and admittance controllers. The proposed approach was compared in simulation with the standard hybrid impedance/admittance control in order to show the improved performance. A Franka EMIKA panda robot was used as a reference robotic platform to provide a realistic simulation.

This book is the second edition of a textbook published in 1996 by McGraw Hill and originates from a graduate level course given by the authors at the University of Naples. The topics include kinematics, statics and dynamics of robot manipulators together with trajectory planning and active control. There are only minor additions the first edition, which are mainly the use of quaternion to describe the orientation of the end effector and a short description of a closed chain architecture for a manipulator (parallelogram arm). The book is largely devoted to serial manipulators, with special developments about active control including adaptative control, robust controls and stability analysis. Another strength of this book is the great number of problems proposed at the end of each chapter, together with a list of references related to it. The fundamental features covered by the text are illustrated on simple examples of serial manipulators (two-link planar arm, parallelogram arm) including analytical results and numerical tests.The book has nine chapters followed by three appendices. The first appendix is devoted to linear algebra, the second recalls some fundamental aspects of rigid body mechanics and the third gives some basic principles of feedback control of linear systems.Chapter one is an introduction to the study of robot manipulators, giving an interesting classification of their architectures, the corresponding workspace and describes the tasks for which theyare used. After some standard examples of industrial manipulators, bibliographical reference texts are proposed, including textbooks on modelling and control of robots, general books on robotics, specialized texts, scientific robotic reviews and some international conferences on robotics.Chapters two, three and four are devoted to mechanical modelling of robot manipulators. The fundamental basics of kinematics are given in chapter two, including the representation of finite rotations by Euler angles or unit quaternions, homogeneous transformations, Denavit-Hartenberg parameters and workspace. The direct and inverse kinematical problems are solved in analytical form for some typical manipulator structures. The differential kinematics of robots are presented in chapter three, with an introduction to the geometric and analytic Jacobian matrices, kinematic singularities and redundancy. The inverse kinematic problem is presented, with special attention to the case of redundant robots where the solution is obtained by a linear optimization problem leading to the introduction of the pseudo-inverse Jacobian matrix and to the solution of several objectives such as avoidance of collision with an obstacle or moving away from singularities. Several inverse kinematics algorithms are given wih an interesting application to a three-link planar arm. Finally, a property of kineto-statics duality is deduced from the principle of virtual work applied to an equilibrium configuration of the robot. Chapter four is a standard presentation of the derivation of the dynamical model by Lagrange formulation and then by the Newton-Euler method. In the Lagrange formulation method, the linearity with respect to inertial parameters is shown and a detailed formulation of the dynamical model is obtained for a two-link Cartesian arm, a two-link planar arm and a parallelogram arm. The problem of dynamic parameter identification is also briefly presented from a numerical point of view. The recursive algorithm constructed from the Newton-Euler formulation is presented and illustrated by considering a two-link planar arm. Finally, the operational space dynamic model is introduced.In chapter five, paths and trajectory planning in joints and in operational spaces are presented; several classical methods of interpolation are described.Chapter six is an extensive study of active control of manipulators. Several methods are presented, involving classical independent joint control, non-linear centralized control, robust control and adaptative control. Both joint-space control and operational-space control are studied together with stability analysis by using Liapounoff functions. An interesting application to the two-link planar arm already used shows the comparison between various control schemes.Chapter seven deals with interaction control of serial manipulators with the working environment. Several strategies involving compliance control, impedance control, force control and hybrid control are presented.Chapter eight describes the actuators and the sensors used in robotics. Several types of servomotors (electric and hydraulic) are presented, together with the model giving their input/output relationship. Several kinds of sensors are also described including encoders, tachometers, force and vision sensors.The last chapter gives a short presentation of the functional architecture of a robot's control system, including characteristics of the programing environment and the hardware architecture.In conclusion, the book provides a good insight about simulation and control of robot manipulators, with a detailed study of the various control strategies and several interesting and pedagogical applications. This book is an excellent review of the standard knowledge needed not only for graduate students but also for researchers interested in robot manipulators.M Pascal

The interaction force control problem for the object manipulated by the dual-arm manipulator with the unknown environment is addressed in this paper. An adaptive dual-loop impedance control scheme is designed to meet the three control targets, including the trajectory tracking control of the object, the internal force control of the object with the two arms, and the interaction force control of the object with the unknown environment. Firstly, an adaptive variable impedance control method is proposed in the outer loop to copy with the unknown stiffness and position of the environment. Secondly, an impedance control scheme based on the internal force is designed in the inner loop to plan the internal force and the modified position supplied with the outer-loop control. Thirdly, to realize the reference trajectory supplied with the inner-loop control, the virtual decomposition control (VDC) method is incorporated, which is a recursive adaptive control progress, so that the unknown dynamics of the manipulators is acceptable and the computation complexity is also very low to satisfy the real-time control requirement. The stability verifications of the inner-loop impedance control and the VDC method are given based on the Lyapunov method, and the stability analysis of the outer-loop impedance control is obtained using the Routh criterion. Finally, a plane dual-arm robotic manipulator with three degrees of freedom is used to verify the effectiveness of the proposed control scheme.

This paper presents a new actuator system consisting of a micro- actuator and a macro-actuator coupled in parallel via a compliant transmission. The system is called the parallel-coupled micro-macro actuator, or PaCMMA. In this system, the micro-actuator is capable of high-bandwidth force control owing to its low mass and direct-drive connection to the output shaft. The compliant transmission of the macro-actuator reduces the impedance (stiffness) at the output shaft, and increases the dynamic range of force. Performance improvement over single- actuator systems was expected in force control, impedance control, force distortion, and transient impact force reduction. Several theoretical performance limits are derived from the sat uration limits of the system. A control law is presented. A prototype test bed was built and an experimental comparison was performed between this actuator concept and two single-actuator systems. A set of quantitative measures is proposed and the actuator system is evaluated against them with the following results: force bandwidth of 56 Hz, torque dynamic range of 800: 1, peak torque of 1,040 mNm, and minimum torque of 1.3 mNm. Peak impactforce, fonce distortion, and back-driven impedance of the PaCMMA system are shown to be better than either of the single-actuator configurations considered.

In general, the contact force, which is used in controller design for robotic compliant motion, can be either explicitly calculated through complicated computation or measured by expensive force sensors. A force control strategy using the estimated contact force is proposed. The estimation of the contact force and states is primarily based on their previous observer design. It is shown that the controller achieves asymptotic stability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

For a redundantly-actuated wheeled mobile robot, the squeeze force between the robot body and its wheels does not contribute to the motion of the robot, but to squeeze the related rigid bodies each other. It is good to control the squeeze force, regulate it to zero if possible, from the view of energy efficiency or life span of joint components. Thus a scheme controlling robot motion while controlling squeeze force is proposed as the following procedure: After a stable controller is presented for robot motion control, a squeeze force controller is designed to regulate the squeeze force to zero. The proposed scheme is demonstrated in robot regulation and tracking control problem. A PD+ controller is adopted for robot regulation, a modified inverse dynamics control is applied for robot tracking control. In both robot control problems, an integral feedback squeeze force controller is used to minimize the squeeze force. The presented simulation results verify the effect of the proposed scheme.

To solve the problem of insufficient adjustment ability of traditional impedance control due to uncertainty of environmental parameters when the robot grinds castings, an adaptive variable impedance constant force control method for robot grinding with unknown environmental parameters is proposed. In the proposed method, first, self-impedance impedance control is used as inner loop control to realize fast tracking response of actual trajectory to reference trajectory and reduce overshoot of grinding force; secondly, fuzzy adaptive variable impedance control is used as outer loop control to realize real-time prediction of unknown environmental parameters and real-time adjustment of impedance parameters; finally, the constant force control of robot grinding in unknown environment is realized by combining inner and outer loop control. In order to verify the effectiveness of the proposed method, the simulation model of the algorithm is constructed based on the MATLAB-SIMULINK simulation platform for simulation analysis, and experimental verification is carried out on the casting surface defects robot grinding platform. The simulation and experimental results show that the algorithm can control the grinding force well when grinding unknown environmental parameters, the force control accuracy is within ±1N, the average grinding force error of casting fin grinding is about 7.59%, the average grinding force error of casting riser grinding is about 5.31%, and the contour accuracy of casting surface defects is good after grinding by force control, and the surface quality after grinding is improved.

Mitigating collision is a fundamental issue in contact problems, and is required to ensure the safety of a robotic cell. Research into the contact problem between robots and their environment is divided into two parts: one uses the environmental contact model and parameter estimation, the other uses the robot force control method. There are two main problems with this research method. One is that the two research levels are not effectively combined to form a complete solution for force control in practice. The other problem is that research on excessive contact force in the collision phase has not been studied in depth for force control. In this paper, a sensing-executing bionic system is proposed that combines environmental detection and robotic force control based on the way an ant functions. The bionic system clearly explains the process from environment detection to robot control, which can provide guidance when designing a new robot control system. An adaptive switching control algorithm is proposed to mitigate the collision force in the collision phase. From the simulation results, the collision force is significantly reduced due to the implementation of adaptive switching control. Finally, a new self-sensing device is designed which can be integrated into the robot control device. However, as there are no additional sensors or computational complexity in the system, the effectiveness of the circuit and superiority of the adaptive parameter update must be verified by experimentation.