Simulation Studies in Manipulator Impedance Control

Physiotherapy is the treatment to recover a patient’s mobility and limb function after an injury, illness, or disability. Rehabilitation robots can be used to replace human physiotherapists. To ensure safety during robot physical therapy, the patient’s limb needs to be controlled to track a desired joint trajectory, and the torque due to interaction force/torque needs to be measured and regulated. Therefore, hybrid impedance and admittance with position control (HIPC) is required to track the trajectory and simultaneously regulate the contact torque. The literature describes two structures of HIPC: (1) a switched framework between admittance and impedance control operating in parallel (HIPCSW); and (2) a series connection between admittance and impedance control without switching. In this study, a hybrid adaptive impedance and position-based admittance control (HAIPC) in series is developed, which consists of a proportional derivative-based admittance position controller with gravitational torque compensation and an adaptive impedance controller. An extended state observer is used to estimate the interaction joint torque due to human stiff contact with the exoskeleton without the use of force/torque sensor, which is then used in the adaptive algorithm to update the stiffness and damping gains of the adaptive impedance controller. Simulation results obtained using MATLAB show that the proposed HAIPC significantly reduces the mean absolute values of the actuation torques (control inputs) required for the shoulder and elbow joints in comparison with HIPC and HIPCSW.

PurposeComponent positioning is an important part of aircraft assembly, aiming at the problem that it is difficult to accurately fall into the corresponding ball socket for the ball head connected with aircraft component. This study aims to propose a ball head adaptive positioning method based on impedance control.Design/methodology/approachFirst, a target impedance model for ball head positioning is constructed, and a reference positioning trajectory is generated online based on the contact force between the ball head and the ball socket. Second, the target impedance parameters were optimized based on the artificial fish swarm algorithm. Third, to improve the robustness of the impedance controller in unknown environments, a controller is designed based on model reference adaptive control (MRAC) theory and an adaptive impedance control model is built in the Simulink environment. Finally, a series of ball head positioning experiments are carried out.FindingsDuring the positioning of the ball head, the contact force between the ball head and the ball socket is maintained at a low level. After the positioning, the horizontal contact force between the ball head and the socket is less than 2 N. When the position of the contact environment has the same change during ball head positioning, the contact force between the ball head and the ball socket under standard impedance control will increase to 44 N, while the contact force of the ball head and the ball socket under adaptive impedance control will only increase to 19 N.Originality/valueIn this paper, impedance control is used to decouple the force-position relationship of the ball head during positioning, which makes the entire process of ball head positioning complete under low stress conditions. At the same time, by constructing an adaptive impedance controller based on MRAC, the robustness of the positioning system under changes in the contact environment position is greatly improved.

The U.S. Department of Energy has identified robotics as a major technology to be utilized in its program of environmental restoration and waste management, and in particular has targeted robotic handling of hazardous waste to be an essential element in this program. Successful performance of waste‐handling operations will require a robot to perform complex tasks involving both accurate positioning of its end effector and compliant contact between the end effector and the environment, and will demand that these tasks be completed in uncertain surroundings. This article focuses on the development of a robot control system capable of meeting the requirements of hazardous‐waste‐handling applications and presents as a solution an adaptive scheme for controlling the mechanical impedance of kinematically redundant manipulators. The proposed controller is capable of accurate end effector impedance control and effective redundancy utilization, does not require knowledge of the complex robot dynamic model or parameter values for the robot or the environment, and is implemented without calculation of the robot inverse kinematic transformation. Computer simulation results are given for a 4 degree of freedom redundant robot under adaptive impedance control. These results indicate that the proposed controller is capable of successfully performing tasks of importance in robotic waste‐handling applications.

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.

Affected by artificial intelligence and automation technology, robotic arms have become increasingly widespread. However, traditional impedance control algorithms have been unable to adapt robotic arms to increasingly complex environmental changes. Therefore, an adaptive impedance control algorithm based on variable stiffness, neural networks, and motion trajectories is developed. Then, it is used for intelligent control of robotic arms. This method employs an impedance relationship model and dynamically optimizes inertia, damping, and stiffness parameters through PD algorithm. The physical quantities such as joint angular acceleration and end displacement are input into the neural network, which outputs key stiffness and interference to estimate the unknown environment in real-time. An adaptive trajectory generation module is designed and combined with contact force feedback to achieve collaborative optimization. The experimental results showed that in terms of contact force with the environment, the error rate between the contact force controlled by this algorithm and the expected value was about 2%. In terms of joint position, the error between the selected joint position in the experiment and the expected value was kept within 0.5%. When running under the motion trajectory generated by the algorithm, the error of each parameter value was less than 1%. The adaptive impedance control algorithm can significantly improve the stability, accuracy, and safety of robotic arm control. The research results have potential applications in improving the environmental adaptability of robotic arms.

In this paper, adaptive impedance control is developed for an ${n}$ -link robotic manipulator with input saturation by employing neural networks. Both uncertainties and input saturation are considered in the tracking control design. In order to approximate the system uncertainties, we introduce a radial basis function neural network controller, and the input saturation is handled by designing an auxiliary system. By using Lyapunov’s method, we design adaptive neural impedance controllers. Both state and output feedbacks are constructed. To verify the proposed control, extensive simulations are conducted.

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.

Reference trajectory learning based adaptive iterative impedance control for a lower limb rehabilitation exoskeleton with actuator saturation

PurposeThis paper aims to present a smooth transition adaptive hybrid impedance control for compliant connector assembly.Design/methodology/approachThe dynamics of the manipulator is firstly presented with linear property. The controller used in connector assembly is inspired by human operation habits in similar tasks. The hybrid impedance control is adopted to apply force in the assembly direction and provide compliance in rest directions. The reference trajectory is implemented with an adaptive controller. Event-based switching strategy is conducted for a smooth transition from unconstrained to constrained space.FindingsThe method can ensure both ideal compliance behaviour with dynamic uncertainty and a smooth transition from unconstrained to constrained space. Also, the method can ensure compliant connector assembly with a good tolerance to the target estimation error.Practical implicationsThe method can be applied in the connector assembly by “pushing” operation. The controller devotes efforts on force tracking and smooth transition, having potential applications in contact tasks in delicate environment.Originality/valueAs far as the authors know, the paper is original in providing a uniform controller for improving force and position control performance in both unconstrained and constrained space with dynamic uncertainty. The proposed controller can ensure a smooth transition by only adjusting parameters.

In order to improve the adaptability of multi-fingered grasp, a force optimization method was proposed to calculate the contact force of each finger, and an adaptive force tracking impedance control algorithm was designed to improve the compliance during contact. The force optimization was realized through a non-negative linear combination method for initial force calculation, combined with gradient algorithm to optimize the contact force. This method was put forward according to the property that the set of grasp force is a convex cone. First, the external force was decentralized as a linear combination of 12 unit force vectors, and then, the initial basic feasible solution for every unit force vector was calculated offline, at last, the initial value of the contact force was obtained by non-negative linear combination; based on the above calculation, the gradient algorithm was called to optimize the contact force online. The force-tracking impedance control method was applied by considering the contact compliance and the force-tracking precision. The indirect adaptive algorithm was applied to estimate the parameters of the object. Take the three fingered point contact with friction for example, the force can be optimized efficiently and the impedance algorithm can track the desired contact force with a relatively high accuracy.

In order to complete the robot axle hole assembly task in an unstructured environment, an adaptive impedance control algorithm based on joint space force and position double feedback is proposed, and the assembly process adjustment strategy is designed to complete the assembly task. By installing a torque sensor on the joint of the six-axis cooperative robot, the control model of joint force position with double feedback is formed. By combining the model reference adaptive control (MRAC), operational force planning, and operational space motion planning, an assembly system based on joint space flexibility control is finally designed. According to the task of axle hole assembly, the geometric constraint analysis and force analysis are carried out in the axle hole assembly process, and the corresponding adjustment strategy is designed. The assembly experiments were carried out for holes with different gaps, and the pose parameters, contact force, and control adaptability parameters during assembly were analyzed experimentally. The experimental results show that the flexible assembly system can complete the shaft hole assembly well, and the assembly torque is controlled in a small range, which meets the assembly requirements.

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.

This paper addresses the problems to achieve transparency and contact stability for teleoperation that consists of unconstrained and constrained motions, which are commonly seen in a construction site. The proposed teleoperator used for versatile construction operations keeps human workers from hazardous places. The adaptive bilateral control with a local force compensator is developed based on adaptive impedance control and contact force driven compensation with auto-switching functions. With an unknown slave and construction site dynamics and communication delay, the proposed method guarantees good transparency if no human error exists and low contact force to damp oscillation. Based on an actual haptic device and a virtual manipulator, haptic simulations are presented to demonstrate adaptive transparency and contact stability in the presence of communication delays.

Robotic polishing is crucial for achieving superior surface finishes in manufacturing. However, precise force control presents significant challenges, particularly for curved workpieces exhibiting time-varying stiffness. Traditional methods typically struggle to adapt to these dynamic conditions, often leading to inconsistent results and suboptimal surface quality. This study proposes an Adaptive Impedance Control based on Visual Guidance (AICVG) strategy for robotic polishing. This approach integrates real-time visual feedback for geometric perception and adaptive tool path generation with a fuzzy logic system that dynamically adjusts impedance parameters to account for unforeseen surface stiffness variations. Simulations and experimental validations conducted on a robotic platform demonstrate that the AICVG strategy significantly outperforms both traditional impedance control and conventional fuzzy logic-based adaptive impedance control. Specifically, it maintains force control errors within ±1.5 N under dynamic stiffness conditions and achieves a 60% reduction in workpiece surface roughness compared to the aforementioned alternative methods. This study presents a robust and precise control framework that significantly enhances the adaptability and efficacy of robotic polishing for complex geometries, thereby advancing automated solutions in high-precision manufacturing.

SUMMARYTo the best of our knowledge, this is the first paper focus on the adaptive impedance control of robot manipulators with consideration of joint flexibility and actuator dynamics. Controller design for this problem is difficult because each joint of the robot has to be described by a fifth-order cascade differential equation. In this paper, a backstepping-like procedure incorporating the model reference adaptive control strategy is employed to construct the impedance controller. The function approximation technique is applied to estimate time-varying uncertainties in the system dynamics. The proposed control law is free from the calculation of the tedious regressor matrix, which is a significant simplification in implementation. Closed-loop stability and boundedness of internal signals are proved by the Lyapunov-like analysis with consideration of the function approximation error. Computer simulation results are presented to demonstrate the usefulness of the proposed scheme.