External Force Estimation Research Articles

Dynamic force identification considering modeling errors using modal expansion method and relevant vector regression algorithm

Accurate identification and estimation of external forces on launch vehicles, aircraft, and other in-service engineering structures plays a vital role in structural design and health monitoring. Considering structural modeling errors, this paper develops a novel force identification method based on modal expansion and relevant vector regression (RVR). Initially, the incomplete and noisy experimental modal data are used to modify the stiffness and mass matrices of the finite element (FE) model, reducing the impact of modeling errors on force identification accuracy. Subsequently, to account for noise disturbances and potential information about unknown initial conditions in the measured acceleration responses, the external forces and the unknown initial conditions are respectively expanded using trigonometric functions and the mode shapes based on the function fitting technique. On this basis, the force identification equation is established for the updated model. The RVR algorithm is integrated into modal expansion and force identification. Firstly, the mode shapes of the FE model are utilized to expand the incomplete and noisy experimental mode shapes to their full degree of freedom, significantly enhancing the accuracy of the model updating. Secondly, by combining the measured acceleration responses, the base coefficients can be solved sparsely, effectively identifying the dynamic forces even when unknown initial conditions are present.

System identification and force estimation of robotic manipulator using semirecursive multibody formulation

AbstractForce estimation in multibody dynamics relies heavily on knowing the system model with a high level of accuracy. However, in complex mechatronic systems, such as robots or mobile machinery, the values of model parameters may be only roughly estimated based on design information, such as CAD data. The errors in model parameters consequently have a direct effect on force estimation accuracy because the estimator compensates the erroneous inertia, friction, and applied forces by changing the value of estimated external force. The objective of this study is to present the workflow of system identification and state/force estimation of an open-loop multibody structure. The system identification utilizes a linear regression identification method used in robotics adapted to the multibody framework. The semirecursive multibody formulation, in particular, is studied as a formulation for both system identification and force estimation. The multibody state/force estimator is constructed using extended Kalman filter. The specific aim of this paper is to demonstrate the utilization of these per se known modeling, identification, and estimation tools to address their current lack of integration as a complete toolchain in virtual sensing of multibody systems. The methodology of the study is tested with both artificial and experimental data of Stäubli TX40 robotic manipulator. In the experimental analysis, an openly available benchmark data set was used. Artificial data were created by running an inverse dynamics analysis with inertia and friction parameters taken from literature. The results show that the multibody inertia and friction parameters can be accurately identified and the identified model can be used to produce decent estimates of external forces. The proposed multibody system identification method itself opens new opportunities in tuning the multibody models used in product development. Moreover, effective use of system identification together with state estimation helps to build more accurate estimators. When the system model is accurately identified, the capability of state estimator to observe unknown inputs, such as external forces, is significantly enhanced.

A coordinated framework of aerial manipulator for safe and compliant physical interaction

The challenge of ensuring compliant behavior in aerial manipulators during physical interactions is addressed in this study. This work presents a coordinated interactive framework for aerial manipulators, specifically designed to ensure compliant physical interactions during contact with the surroundings. Without the reliance on force sensors, an external force estimator is employed to recognize interaction intentions. The coordinated framework leverages a Model Predictive Control (MPC) planner equipped with adaptive weights, facilitating the coordination of movements for both the quadrotor and manipulator. The adaptive adjustment of weights in the cost function allows for the attainment of diverse interaction behaviors in response to unexpected external forces. Notably, the methodology stands out from current control strategies by incorporating autonomous stiffness adjustment in response to interaction forces, thereby optimizing the delicate balance between safety and precision. The passivity of the system is guaranteed by using a Lyapunov-like function during the physical interaction. The effectiveness of the proposed framework is validated by experiments for the scenario of human operator and aerial manipulator collaborative work.

A Hybrid Method Combining Data-Driven and Model-Based Algorithms for External Force-Sensing and Haptics Control of Cable-Pulley-Driven Surgical Robotic Manipulator

Abstract The implementation of the high-precision tracking control and external force-sensing ability of a manipulator is important for achieving refined surgical robot operation. In this paper, a hybrid method based on data-driven and model-based algorithms is proposed for the manipulator of a cable-pulley-driven surgical robot. This method integrates an artificial neural network and a dynamic model rotation angle estimation, and a full closed-loop control architecture is further constructed. The algorithm compensates for the hysteresis of the joint angle and effectively improves the tracking control precision. Based on the architecture, the external force estimator (EFE) using a joint torque disturbance observer and the force interaction teleoperation control strategy using a direct force feedback framework (DFF) are implemented. In the force loading experiment, it was shown that the EFE performs well for static and dynamic force estimation, and the teleoperated haptic control experiment showed that the DFF-EFE-based system has a high position-tracking accuracy with real-time external force-sensing ability.

Fundamental Study on Force-Projecting Bilateral Control for Pneumatically Driven Follower Device

This paper proposes the application of force-projecting bilateral control to a master-follower teleoperation system with pneumatic drive on the follower side and evaluates its effectiveness. The proposed method directly projects the operating force on the master side to the driving force on the follower side, eliminating the need for both position control and external force detection on the follower side, thereby solving the problem of low rigidity and response delay of a pneumatic servo system and providing highly stable sensor-less force presentation against variable environments. In this study, dynamic response analyses of a 1-DOF master-follower system were performed by numerical simulation using a linear system model, followed by experimental verification by implementing an actual system with an external force estimator. The results showed that the proposed force-projecting bilateral control has significantly higher positioning rigidity and better force control stability than the conventional force-reflecting bilateral control. A theoretical consideration was also given using the equivalent transformation of force transfer functions to provide evidence of high stability.

Collision detection and external force estimation for robot manipulators using a composite momentum observer

<abstract><p>The collision detection and estimation of external forces for robot manipulators are essential to ensure compliance and safety in the interaction between the robot and the environment or humans. The focus of this paper was to design a hybrid approach for collision detection between robots and their environment, and further to estimate external forces acting on a robot manipulator without the need for additional sensors. The current collision detection methods using observers are still suffering from the problem of an unavoidable trade-off between the estimation sensitivity and the reduction of the peaking value at the initial time. To satisfy both robustness and avoid peaking phenomenon at the initial time, a composite observer was designed, consisting of both a momentum observer and an extended state observer. The first observer provides high-precision tracking, while the second one reduces the peak value at the start. Through their complementary roles, the composite observer achieves improved performance in terms of sensitivity and reducing the peaking value. Simulation results, conducted using a 2-degree-of-freedom (2-DOF) robot manipulator, attest to the efficacy of the proposed approach.</p></abstract>

Modeling of an external force estimator for an end-effector of a robot by neural networks

ABSTRACT This paper proposes a method to estimate external forces at the tip of a robot end-effector by using a neural network model. In order to avoid the use of an expensive force sensor in the training purpose, the proposed method implements the indirect training method by including the inverse dynamic model of the robot manipulator to the training algorithm with available information from a default robot system. In this method, the robot dynamics equations are necessary for the training, therefore a disturbance observer is adopted to deal with the existing uncertainties and errors. The performance of the proposed estimation method is evaluated through experiments of a 5-DOF robotic experimental platform, comparing to another existing estimation method using recurrent neural network with a type-1 disturbance observer for the external force estimation. The estimation results show that the behavior of the estimated external forces strongly correlates with the applied external forces and the proposed method is superior to the other method.

GNSS-INS-dynamic fusion with robustness to outliers based on external force state estimation

Multi-source information fusion state estimation algorithms are an important means for drones to perceive ego-state, and accurate and robust estimation of external forces is crucial for precise control of quadrotors. This paper proposes a method that integrates a dynamic model into a multi-rate extended Kalman filter (EKF) framework on manifold. By estimating the magnitude of the external force acting on vehicle, meanwhile, a dynamic constraint on velocity loop is established to reduce the discrepancy between the model-predicted motion and the actual motion. Moreover, the estimated external force is integrated into the zero velocity update criterion for zero speed judgment, effectively reducing false detections while improving the accuracy of zero speed state recognition. However, multi-source measurements significantly increase the probability of data signal errors. To address this issue, we use a robust estimation algorithm to improve EKF’s sensitivity to abnormal measurements, flexibly adjusting measurement weights while rejecting unreasonable measurements. Validation with open-source indoor and outdoor datasets shows that our algorithm improves pose estimation performance while maintaining accurate positioning accuracy compared to non-dynamic fusion under the same filtering parameters, particularly in global navigation satellite system short time denied. It provides accurate external force estimation, offering multi-source data support in areas such as human–machine interaction and carrying variable mass payloads.

External force estimation for industrial robots using configuration optimization

External force estimation for industrial robots can be applied to the scenes such as human–robot interaction and robot machining. The model-based methods have gained the attention of many researchers because they only need motor signals. However, the performance of the above-mentioned methods depends on the accuracy of robot inverse dynamic model (IDM). Traditional methods focus on improving the accuracy of IDM to obtain a better estimation performance. However, suppressing the negative impact of modelling error can be achieved without reducing the modelling error. Thus, this article proposes an external force estimation method that uses the semi-parametric friction model and applies configuration optimization based on Jacobian condition number (JCN) to reduce the modelling error and its negative impact. First, the IDM is identified. Second, the semi-parametric friction model refines the traditional model in the torque observer to improve the estimation accuracy. Third, the JCN is used as an evaluating indicator to optimize the robot configurations. Finally, several simulations and experiments on a 6-DoF industrial robot demonstrate the validity of the proposed method. This method can enhance the performance of online force estimation by up to 48.28%. In addition, the application of the proposed method is verified on the laboratory-developed machining platform.

Forced Servoing of a Series Elastic Actuator Based on Link-Side Acceleration Measurement

Joint stiffness of an elastic-joint robot can be changed according to joint stiffness requirements. A series elastic actuator (SEA) can reduce the contact stiffness between the body and the environment or human, which can further ensure interactive operation in a human–machine-compatible environment. However, the introduction of the SEA improves the complexity of the robot dynamics model. In this paper, we propose a control schema based on link-side acceleration measurement to eliminate the overshoot and vibration in the transient process of force control. An extended Kalman filter (EKF) algorithm that fuses photoelectric encoders and accelerometers is first presented based on the link-side acceleration measurement. Following this, based on the external torque estimation, the vibration reduction control algorithm is designed. The simulation model is built, and the algorithm design and simulation of position control and force control are carried out and finally tested on the real robot platform. The effectiveness of the control algorithm is proved. The experimental results show that the dynamic response of the external force estimation is about 2 ms faster than that of the force sensor, and the error between the estimated external torque and the real external torque is within ±0.16 N·m.

3D Curvature-Based Tip Load Estimation for Continuum Robots

This letter presents a method intended for the estimation of external force and moment applied at the tip of thin rods using vision-based shape measurements, with a view to be applied on continuum robots. A versatile vision process is developed that does not require any additional markers nor sensors to provide an accurate tri-dimensional reconstruction of the deformable rod shape. Then, the tip loads (i.e., forces and moments) are directly deduced from the curvature along this curve formed by deformed rod thanks to the resolution of a linear system without requiring any iterative optimization. The curvature is determined with a robust method that allows filtering out measurement noise and artifacts. Simulations show that this approach gives fast and precise results in both 2D (planar forces estimation without torsion) and 3D (spatial forces estimation). Experimental results on cantilever rods demonstrate an accuracy of 2.2% and 2.7% of the applied forces and moments, respectively.

Publisher Erratum to “Estimation of the External Forces on a Robot Hand with Fingertip Tactile Sensors”

In human-robot collaboration, physical hand-over-hand communication of the human operator’s intention is essential for realizing direct and intuitive cooperation. When an external force acts on a robot hand holding an object, the torque exerted on the finger motor becomes a combination of the grasping torque required to maintain the grasping pose and reaction torque to the external force. To analyze intended interaction, we need to recognize multiple contacts inside and outside the fingertips. In this study, an external force estimation method was developed that uses tactile sensors to measure both grasping and external forces acting on the fingertips of a robot hand. Because a tactile sensor cannot measure all the external force components, it is impossible to directly compute the magnitude and contact angle of an external force. The shear and frictional forces lost during tactile sensing are backwardly estimated according to the difference between the estimated and measured torques. The magnitude and contact angle are computed to estimate external force, which can be used to determine the intention of the user. Simulations based on real sensor responses and experiments were performed to validate the proposed estimation method.

Design and Evaluation of a Robotic Forceps With Flexible Wrist Joint Made of PEEK Plastic

This letter presents the design and evaluation of a robotic forceps in which the wrist joint is made of polyetheretherketone (PEEK) plastic. Due to the structural improvement of enclosing a flexible backbone of PTFE tube inside the wrist joint, the developed forceps simultaneously fulfills the requirements of small diameter, bending dexterity, sufficient axial stiffness, and even the control rigidity. The proposed robotic forceps employs pneumatic drive with wire actuation mechanism. For accurate motion control and external force estimation, we developed a novel inverse dynamics model considering the coupled dynamic effect between the wrist joint and the gripper motions. The position control accuracy of the wrist joint bending angle is at the level of 1 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> and is not affected by the simultaneous open–close motion of the gripper. The translation and grasping forces are beyond 4.5 N, enabling powerful tasks in laparoscopic surgery. Furthermore, the robotic forceps is capable of multi-DOF external force estimation. The estimation accuracy of the translation force is about 0.2 N, and the estimation accuracy of grasping force remains within 0.2 N regardless of the bending angle of the wrist joint. The performance evaluation results demonstrate that the developed forceps is eligible to be used in robotic-assisted laparoscopic surgery.

Disturbance estimation for robotic systems using continuous integral sliding mode observer

AbstractThis article presents a novel force‐sensor‐less method for the estimation of external forces for a general class of second‐order robotic systems. The method is based on the integral sliding mode observer (ISMO) which serves as a second‐order differentiator for the position measurement of the system. As a result, the system states and disturbance are estimated without explicitly using force and velocity measurements. To apply the ISMO to the general second‐order systems, a proper assumption is proposed to address their nonlinearity and discontinuity. The boundary‐layer method is applied to ensure that the virtual inputs of the observer are continuous such that the chattering phenomenon is attenuated. A Lyapunov‐based method is used to analyze the influence of the boundary layers on the convergence of the state‐ and disturbance‐estimation errors. This influence, mainly determined by the boundary‐layer scalars, is given in analytical forms as a reference for parameter selection. The method is evaluated by numerical simulation on a robot manipulator system and compared with a conventional sliding mode observer (SMO). The validation of the performance of the continuous ISMO indicates its generalizability to general second‐order robotic systems. Also, the advantage of continuous ISMO over the conventional SMO is reflected by its small estimation errors and superior responsiveness. In general, the proposed method in this paper may interest those who are seeking solutions for haptic robotic tasks without using force sensors.

External force estimation for robot manipulator based on a LuGre-linear-hybrid friction model and an improved square root cubature Kalman filter

PurposeThe sensorless external force estimation of robot manipulator can be helpful for reducing the cost and complexity of the robot system. However, the complex friction phenomenon of the robot joint and uncertainty of robot model and signal noise significantly decrease the estimation accuracy. This study aims to investigate the friction modeling and the noise rejection of the external force estimation.Design/methodology/approachA LuGre-linear-hybrid (LuGre-L) friction model that combines the dynamic friction characteristics of the robot joint and static friction of the drive motor is proposed to improve the modeling accuracy of robot friction. The square root cubature Kalman filter (SCKF) is improved by integrating a Sage Window outer layer and a nonlinear disturbance observer (NDOB) inner layer. In the outer layer, Sage Window is integrated in the square root Kalman filter (W-SCKF) to dynamically adjust noise statistics. NDOB is applied as the inner layer of W-SCKF (NDOB-WSCKF) to obtain the uncertain state variables of the state model.FindingsA peg-in-hole contact experiment conducted on a real robot demonstrates that the average accuracy of the estimated joint torque based on LuGre-L is improved by 4.9% in contrast to the LuGre model. Based on the proposed NDOB-WSCKF, the average estimation accuracy of the external joint torque can reach up to 92.1%, which is improved by 4%–15.3% in contrast to other estimation methods (SCKF and NDOB).Originality/valueA LuGre-L friction model is proposed to handle the coupling of static and dynamic friction characteristics for the robot manipulator. An improved SCKF is applied to estimate the external force of the robot manipulator. To improve the noise rejection ability of the estimation method and make it more resistant to unmodeled state variable, SCKF is improved by integrating a Sage Window and NDOB, and a NDOB-WSCKF external force estimator is developed. Validation results demonstrate that the accuracy of the robot dynamics model and the estimated external force is improved by the proposed method.

Transfer of learned dynamics between different surgical robots and operative configurations.

Using the da Vinci Research Kit (dVRK), we propose and experimentally demonstrate transfer learning (Xfer) of dynamics between different configurations and robots distributed around the world. This can extend recent research using neural networks to estimate the dynamics of the patient side manipulator (PSM) to provide accurate external end-effector force estimation, by adapting it to different robots and instruments, and in different configurations, with additional forces applied on the instruments as they pass through the trocar. The goal of the learned models is to predict internal joint torques during robot motion. First, exhaustive training is performed during free-space (FS) motion, using several configurations to include gravity effects. Second, to adapt to different setups, a limited amount of training data is collected and then the neural network is updated through Xfer. Xfer can adapt a FS network trained on one robot, in one configuration, with a particular instrument, to provide comparable joint torque estimation for a different robot, in a different configuration, using a different instrument, and inserted through a trocar. The robustness of this approach is demonstrated with multiple PSMs (sampled from the dVRK community), instruments, configurations and trocar ports. Xfer provides significant improvements in prediction errors without the need for complete training from scratch and is robust over a wide range of robots, kinematic configurations, surgical instruments, and patient-specific setups.

Force Control of Grinding Process Based on Frequency Analysis

Hysteresis-induced drift is a major issue in the detection of force induced during grinding and cutting operations. In this letter, we propose an external force estimation method based on the Mel spectrogram of the force obtained from a force sensor. We focus on the frequent strong correlation between the vibration frequency and the external force in operations with periodic vibrations. The frequency information is found to be more effective for an accurate force estimation than the amplitude in cases with large noise caused by vibration. We experimentally demonstrate that the force estimation method that combines the Mel spectrogram with a neural network is robust against drift.

External force estimation and disturbance rejection for Micro Aerial Vehicles

To deploy Micro Aerial Vehicles (MAVs) in real-world applications, there is a need for online methods to cope with uncertainties in localization and external disturbances. In this article, we propose a set of novel real-time embedded Nonlinear Model Predictive Control (NMPC) and Nonlinear Moving Horizon Estimation (NMHE) modules for MAV based external disturbance rejection. The NMPC and NMHE are based on the dynamic model of the MAV, thus, avoiding the need for system identification and creating specific aerodynamic models, a benefit that results in a generic solution capable of being independent of the type of the MAVs. As it will be presented, the NMHE estimates the external forces, while the NMPC generates thrust and attitude commands for the low-level controller to compensate the various disturbances that could occur, such as wind gusts, tethered payload, and varying center of gravity. The proposed method is evaluated extensively in multiple experimental results that include the scenarios of position hold against an actuating wind-wall, adding payload, and changing the MAV’s arm configurations.

Feedforward operational stiffness modulation and external force estimation of planar robots equipped with variable stiffness actuators

Feedforward operational stiffness modulation and external force estimation of planar robots equipped with variable stiffness actuators

External Force Estimation of the Industrial Robot Based on the Error Probability Model and SWVAKF

This study proposes an external force estimation method based on the error probability model and a slide window variational adaptive Kalman filter (SWVAKF) for the problem of industrial robot external force estimation. A probability model with a normal distribution was provided, in which the covariance was linearly related to the joint velocity to address the uncertainty in the estimation error of the friction model. A normal distribution probability model was presented to address the time-varying characteristics of the contact external force when the robot interacts with the environment, in which the covariance of the derivative term of the external force was linearly related to the estimated external force. The robot interaction process was dynamically modeled using generalized momentum and external force as state variables, friction estimation deviation and external force derivative term as random interference, and generalized momentum with normally distributed noise as the measurement output. The parameters of the probability model of random interference items were determined by analyzing the experimental data of system identification, and the covariance related to joint velocity and external force was obtained. A set of adaptive scale factors related to the joint velocity and estimated force change rate when the robot interacts with the environment is proposed, and then the error covariance estimated based on the error probability model and the SWVAKF algorithm is fused by the adaptive scale factor, and a covariance of friction deviation and external force derivative term in the robot interaction process and an external force estimation method were provided. Experimental results reveal that the proposed method reduces the root-mean-square (RMS) error by 17.07% compared to the standard Kalman external force estimation method and has a better external force estimation effect.