Force tracking impedance control with unknown environment via an iterative learning algorithm

In this paper, an image-based impedance control strategy for force tracking of an unmanned aerial manipulator (UAM) is presented. Firstly, image features with nice decoupling characteristics are designed and the relationship between the camera motion and the image features is derived. Then, a two-stage strategy is proposed to achieve force tracking of the UAM on a planar object in an arbitrary pose. The first stage drives the end-effector perpendicular to the object’s planer surface by pure visual servoing. To achieve force tracking under the visual guidance, an adaptive visual impedance control method which adjusts the target stiffness according to the force tracking error and the visual feature error is proposed in the second stage. The closed-loop system is proved asymptotically stable by means of Lyapunov analysis. Further, the stability in free flight phase of the stage two is also analyzed and ensured. Finally, experiments were carried out including a whiteboard cleaning task in different poses. The experimental results illustrate the validity and effectiveness of the proposed approach. Note to Practitioners—This work is motivated by the contact force tracking problem of an unmanned aerial manipulator (UAM) without the position measurement. In recent years, impedance control is widely used in force tracking problems. However, position measurement is needed both for the robot and the object in most studies. To generate desired force under visual guidance, image-based visual servoing is combined with a novel impedance controller with variable stiffness. The idea is intuitive. For a human in contact with a wall, the contact force is controlled by adjusting his arm stiffness, which means the stiffness is adapted to the difference between the desired and actual contact force. Furthermore, the stiffness is also adapted to the visual tracking error, removing the assumption that no tracking error is in the inner loop of the impedance controller in the previous works. The proposed strategy is a promising solution for real applications and is validated by a board cleaning experiment in this paper.

In this research, a virtual simulator (slave system) of an eight-degrees-of-freedom robot (two-DOF crane, one-DOF prismatic (telescopic mast), and five-DOF robot manipulator) is developed and teleoperated by an external hardware haptic device (master system) for nuclear power plant's (NPP) reactor vessel internals (RVI) dismantling operations. For operations such as cutting, the robot end-effector with a laser cutter should maintain a constant distance from the physical wall of RVI. So, a virtual wall near the physical wall is assumed. The end-effector should remain on the virtual wall for optimal cutting which is achieved through force tracking impedance control. In this paper, initially sliding mode control (SMC) was implemented but resulted in chattering in force tracking response. Therefore, super twisting sliding mode control (STSMC)-based force tracking impedance control is designed and implemented for enhanced end-effector force tracking. The control input of the STSMC is composed of a continuous and discrete component. Continuous control input regulates control performance against uncertainties, whereas discrete provides a switching algorithm. STSMC then eliminates the chattering effect and reduces the force tracking error. The performance of SMC-based and STSMC-based impedance control is compared, and the comparison shows that the STSMC-based impedance control provides enhanced performance.

This paper presents design and force-tracking impedance control of 2-degree-of-freedom (DOF) wall-cleaning manipulator equipped with disturbance observer (DOB) and sliding mode control (SMC). In order to keep in contact with various shapes of walls, the proposed manipulator is designed to ensure 2-DOF motions of translation and tilting by using ball screws. The position-based force tracking impedance control (FTIC) is first adopted for the proposed manipulator not only to interact with walls in a desired dynamic behavior but also to maintain a constant contact force. Also, to improve the force tracking capability of proposed manipulator against different walls and brushes for manipulator, the FTIC is combined with the disturbance observer (DOB) and the sliding mode control (SMC). Extensive experiments prove that although different brushes used for manipulator rotate against varying shapes of walls, the proposed manipulator can keep a constant contact force within a bound of ± 4.5 N by virtue of the proposed FTIC equipped with the DOB and the SMC.

In this paper, a new iterative learning algorithm is proposed for repetitive nonlinear systems. The control system employs a combination of state feedback and iterative learning control (ILC) in which the coefficients of states are learned similar to ILC methods. The control system is in a closed loop format both in iteration domain (because of ILC) and in time domain (because of feedback control) which improves the robustness of the conventional ILC. The convergence of the control algorithm is also proved. Finally, simulation results for a 5-DOF manipulator have been presented to illustrate that the proposed algorithm is more robust than a first order P type ILC method at the presence of white Gaussian noise as a nonrepeating disturbance.

This paper presents the novel contact force control approach to a quad-rotor system for interacting with the environment. Utilizing the powerful hovering capability of the quad-rotor system, the force in the altitude direction is regulated by realizing the impedance function. Force tracking impedance control is applied to regulate the contact force to the environment. Simulation studies of force tracking control performances are performed to evaluate the feasibility of the proposed force control task for a quad-rotor system.

This article presents the design and force-tracking impedance control (FTIC) of a two degree-of-freedom (DOF) wall-cleaning manipulator. A novel 2-DOF wall-cleaning manipulator is designed not only to keep in good contact with different shapes of walls but also to avoid various obstacles on walls efficiently. By adopting two ball screws, 2-DOF motions of the manipulator, such as translation of 150 mm and tilting within $ \pm $ 13°, are achieved successfully. Also, the position-based FTIC is derived to enable the proposed manipulator to not only interact with walls in a desired impedance behavior but also maintain a desired contact force. The FTIC consists of a position-based impedance control (PIC) and a disturbance observer (DOB). While the PIC ensures the excellent force-tracking capability of the proposed manipulator in the steady state, the DOB is adopted to enhance its transient response, i.e., to effectively reject the disturbances caused by the various shapes of walls. The extensive experiments using the test bench equipped with the FTIC demonstrate that the proposed manipulator can maintain the desired contact force within $ \pm $ 4.5 N against the varying shapes of walls and the different types of roller brushes.

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.

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 article presents the contact force control approach for a quad-rotor system to perform tasks of interacting with the environment. The hovering capability of the quad-rotor system allows the force in the altitude direction to be regulated by realizing the impedance function. To obtain the better force control performance, inherent and external disturbances to the quad-rotor system are suppressed by designing the acceleration-based disturbance observer (AbDOB). Force tracking impedance control is applied to regulate the contact force to the environment. Simulation studies of force tracking control for changing a light bulb on the ceiling are performed to evaluate the feasibility of the proposed force control task for a quad-rotor system.

Humanoid robots can imitate human behaviour and provide interactive services to humans due to their humanoid form, especially humanoid wheeled robots that can perform more complex tasks with the additional mobility. With the development of robotics technology, humanoid robots have been used increasingly in the domestic environment where the robot needs to interact with unknown environments. This requires the robot to have both the ability to track with high accuracy and the ability to comply with complex environments. It is known that the robots with impedance control can have a superior performance in terms of compliance with unknown contact environments. However, the mobility of humanoid robots with wheels complicates the dynamic model of robots, which makes the development of impedance control challenging. In this letter, a whole-body impedance control approach for humanoid wheeled robots is proposed, with fuzzy adaptive systems to compensate for the uncertain dynamics of the controlled system. This approach realizes safe interaction and compliant operation with unknown environments including humans. Additionally, the experimental results conducted on a humanoid wheeled robot illustrate the effectiveness of the proposed controller.

An iterative learning control algorithm within prescribed input-output subspace

In this paper, iterative learning identification algorithms are proposed to estimate the time-varying parameters in multi-input-single-output (MISO) Wiener nonlinear time-varying systems. The regression model of the Wiener system is built by using the polynomial expansion of the nonlinear inverse function. Then, two iterative learning algorithms, including iterative learning gradient identification and iterative learning least squares identification, are presented to estimate the time-varying parameters of the regression model. The convergence performance of the iterative learning identification algorithms is analyzed, and numerical simulations are provided to verify the effectiveness of the proposed algorithms.

Robotic microinjection has been widely applied in biomedical engineering, but faces a great challenge on the precise force interaction with cells due to their inherently deformable, fragile, and nonlinear viscoelastic properties. This brief proposes a new neural-learning based adaptive sliding mode impedance force control scheme for the robotic microinjection system to improve the interaction performance. The key features of the developed method are as follows: i) Target impedance is derived by utilizing the nonlinear Hunt-Crossley model to match the microscale interaction with environmental cells; ii) An integral terminal sliding mode manifold based on the impedance error is designed to achieve finite-time convergence and accurate force tracking; iii) The proposed scheme relieves the burden of environmental model dependence by estimating the uncertain bound of external disturbances through an adaptive neural network compensator. The control system stability is analyzed by the Lyapunov theory, and the force tracking performance is also verified via a series of experiments.

With the developments of intelligent and autonomous robotic technology, robots are usually designed to confront sophisticated tasks such as automated assembly, which requires both high-speed positioning capabilities and compliance with unknown contact environments. As we know, a high-performance motion tracking control in free space can achieve efficient and accurate positioning, while impedance or force control shows superior performance in terms of sensitive force and compliance with unknown contact environments. However, it is still challenging to achieve both high-performance motion tracking and compliance within one single control framework, especially in unknown contact environments. To this end, in this article, a unified motion/force/impedance approach for unknown contact environments is proposed by robust model-reaching control with dynamic trajectory adaptation. Specifically, the overall control scheme includes two loops: the outer loop replans the trajectories of motion and force in real time to meet the environmental constraints, which are estimated by the recursive least squares estimation law; in the inner loop, the robust model-reaching control law is proposed to realize a target model, which is designed to establish a dynamic relationship between the motion and force tracking errors of the replanned trajectories. Then, by changing the matrices of the target model, the compromise between motion tracking and force tracking can be achieved, as well as different control objectives. Experiments are conducted on a seven-degree-of-freedom manipulator to validate the advantages of the proposed scheme.

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.