Payload Inertia Research Articles

A Self-Adaptive Inertia Hybrid Control of a Fully Constrained Cable-Driven Parallel Robot

A Cable-Driven Parallel Robot (CDPR) is a special type of parallel robot actuated by elastic cables instead of rigid links, which brings uncertainties of model nonlinearities and structural friction depending on the payload variation. A precise motion with minimum control effort against an unknown payload has been a challenging task. To conquer it, we propose an adaptive hybrid control approach for the fully-constrained CDPR with an unknown payload in this paper. A Cartesian space position control and a joint space cable force control are designed through inertia estimation to encounter the effect of the uncertain payload. And then, an artificial neural network (ANN) is employed to estimate the end-effector force in Cartesian space for precise force control and consecutive uncertainties compensation. The stability of the proposed controller is proven based on the Lyapunov method and the efficacy is verified by the experiments. As for feasibility results, the proposed adaptive hybrid control-based cable force estimation was evaluated on the Mini CDPR. Compared to the traditional control scheme, the tracking error was decreased approximately 56% and the utilized tension was significantly reduced for the given trajectory tracking test. Furthermore, the investigation of free movements of the helix trajectory and pick-and-place tasks showed that the proposed hybrid adaptive control can control the position and cable force altogether while being able to estimate the inertia of the end-effector. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The study was motivated by the control problem of adjusting cable tensions of a cable-driven parallel robot (CDPR) against varying payloads at the end-effector. Several advanced control approaches were proposed for but limited to CDPR model parameter estimation and did not consider varying payload. This paper suggests a practical methodology capable of both self-adaptation to unknown payload inertia and consequently improving tracking control performance for a CDPR. In this paper, we derived an adaptive control model and proved stability to ensure safety. In order to encounter unmodeled uncertainties such as pulley friction and cable characteristics, we utilized an artificial neural network (ANN) trained by experiments. The experimental results could confirm that the proposed scheme can estimate the payload inertia and generate minimized cable tension while maintaining good trajectory tracking performance. In future research, we will show more practical validation for a scale-up CDPR with heavy objects toward logistics or pick-and-place application in practice.

Payload-oriented control scheme for rotating payload satellite considering inertia uncertainties and measurement errors

For the remote sensing satellite with an unbalanced rotating payload suspended by an Active Magnetic Bearing (AMB), this paper proposes a payload-oriented control scheme where the high-precision payload attitude control is dominating. Firstly, to suppress the disturbances induced by payload inertia uncertainties and state measurement errors, an integrated framework of parameter identification and nonlinear predictive filtering is proposed to estimate payload inertia parameters and system states from multi-timescale, noise- and drift-contaminated measurement data, breaking the mutual constraint between identification and filter. Secondly, based on the estimation results, the control law and bearing electromagnetic force allocation strategy of the payload-oriented scheme are provided, so that the payload tracks the desired motion and the satellite platform follows payload to prevent the air gap of AMB from exceeding the safety threshold. Finally, the simulations are carried out to verify the advantages of the proposed control scheme in enhancing the payload control precision and isolating the platform vibration.

Inverse Modeling for Component Selection of Twisted String Actuators

Twisted string actuators (TSAs) have been widely used in numerous mechatronic applications. However, existing literature selects the TSA's components (strings and motors) through ad hoc procedures. The selection of TSA components requires inversion of its mathematical models. This is difficult because many variables are coupled in such a way that prevents direct inversion. This article presents a novel systematic design framework and inversion algorithm for TSAs based on their required performance properties. First, a comprehensive formula to invert the kinetostatic and dynamic models of the TSA is presented. This inversion finds the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TSA-specific properties</i> given the desired performance properties that are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">common to most actuators</i> . The solution is iteratively solved from a synthesis of existing models that account for string compliance, variable TSA radius, friction, the payload's inertia, and its linear velocity. Second, an algorithm recommends the most suitable motor and string pair from a custom-made database. Third, simulations and experiments evaluated the algorithm's performance under different conditions.

Dynamic Modeling and Adaptive Control of a Single Degree-of-Freedom Flexible Cable-Driven Parallel Robot

This paper investigates the dynamic modeling and adaptive control of a single degree-of-freedom flexible cable-driven parallel robot (CDPR). A Rayleigh–Ritz cable model is developed that takes into account the changes in cable mass and stiffness due to its winding and unwinding around the actuating winch, with the changes distributed throughout the cables. The model uses a set of state-dependent basis functions for discretizing cables of varying length. A novel energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the Rayleigh–Ritz model. For control purposes, the massive payload assumption is used to decouple the rigid and elastic dynamics of the system, and a modified input torque and modified output payload rate are used to develop a passive input–output map for the naturally noncollocated system. A passivity-based adaptive control law is derived to dynamically adapt to changes in cable properties and payload inertia, and different forms of the adaptive control law regressor are proposed. It is shown through numerical simulations that the adaptive controller is robust to changes in payload mass and cable properties, and the selection of the regressor form has a significant impact on the performance of the controller.

Experiment research on static and dynamic performance of precision cable-drum drive

The elastic slip and extension of a cable are important problems for a precision cable-drum drive system. Adjusting the design parameters (preload force, payload and so on) is an effective way of improving transmission performance. At present, most researchers focus on sliding mechanisms, Euler’s equation improvement and engineering applications. The effect of design parameters on the transmission performance has not been deeply investigated. In this paper, the static and dynamic performance of a cable-drum drive system was explored for improving precision and response, and the effect of preload force and payload on the static and dynamic performance was analyzed. The static performance was evaluated by the transmission error, which was determined by measuring the rotational angle of input and output drum using SCANCON encodes. The dynamic performance was evaluated by the response bandwidth, which was determined by measuring the amplitude-frequency and phase-frequency curve of cable-drum drive system using TIRA GmbH vibration test system. The results show that the maximum transmission error is 0.75 mrad at a rotational range of 180° when the external torque is 0.19 N×m. The transmission error increases with the increase of the drum rotation angle. The transmission error increases with the increase of the preload force and external torque. The response bandwidth can reach 56 Hz when the payload inertia is 0.0145 kg×m2, which decreases with increase of payload inertia. However, the preload force has little obvious influence on the response bandwidth when the preload force is changed from 99.85 N to 496.99 N. These results are helpful for the design improvement and theory research of precision cable-drum drive system in future.

Integrated vibration isolation and attitude control for spacecraft with uncertain or unknown payload inertia parameters

To meet the spacecraft attitude control requirements with high accuracy and stability, all vibrations in the spacecraft should be reduced in appropriate ways. This paper presents an integrated control method for attitude and the vibrations in both high frequency and low frequency in the spacecraft. The integrated control method includes a vibration isolation platform and a modified adaptive attitude control method. The paper presents a vibration isolation platform with magnetic suspension to reduce high frequency vibrations and a parameter design method for the platform. An adaptive control method is presented to reduce low frequency vibrations while accounting for the bandwidth constraint due to the vibration isolation platform. Firstly, a parameter design method is proposed for the vibration isolation platform, and an entire 6×12 dimensional transformation matrix is derived for the case that the inertia of the payload is of the same order of magnitude as that of spacecraft bus. Then, an adaptive attitude controller is presented that accounts for the coupling characteristics of the spacecraft, the vibration isolation platform and the uncertain or unknown payload inertia parameters. To ensure the robustness of the attitude control system and the performance of the vibration isolation system, a method of estimating the initial value of the payload inertia is presented using classical control theory. Finally, numerical simulations demonstrate that the integrated control method presented in this paper can achieve the attitude control task for spacecraft with high accuracy and stability.

미지의 부하와 흔들림 각속도를 갖는 컨테이너 크레인의 2차 슬라이딩 모드 제어

This paper introduces a sway suppression control for container cranes with unknown payloads and sway rates. With no priori knowledge concerning the magnitude of payload mass and sway rate, the proposed control maintains superior sway suppressing and trolley positioning against external disturbances. The proposed scheme combines a second order sliding mode control and an adaptive control to cope with unknown payloads. A second order sliding mode control without feedback of the sway rate is first designed, which is based on a class of feedback linearization methods for stabilization of the under-actuated sway dynamics of the container. Under applicable restrictions of the magnitude of payload inertia and sway rate, a linear regression model is obtained, and an adaptive control with a payload estimator is then designed, which is based on Lyapunov stability methods for the fast attenuation of trolley oscillations in the vicinity of the target position. The asymptotic stability of the overall closed-loop system is assured irrespective of variations of rope length. Simulation are shown in the existence of initial sway and external wind disturbances.

An existence condition for the inverse dynamics solution of a slewing Euler–Bernoulli beam

Causal inverse dynamics problem of a slewing flexible beam has been identified as being ill-posed because it violates the stability of solution. Such problem has been studied intensively for the past three decades due to its application to the tip tracking control of flexible-link manipulators. A well known remedy has been to modify the location of the boundary point, or the output function in tracking control. This paper re-examines the problem by analyzing a closed form solution. Such a solution is made possible by truncating the assumed modes beam deflection model after the first mode. An existence condition for the solution is established, which links to the deflection mode shape, payload inertia, and the location of boundary point. This condition indicates that for certain system parameters, causal solutions may exist. Existing remedies as suggested by many published results can be explained by the condition. Extension to a multi-mode model is discussed and examined through numerical simulations.

Robust Impedance Control of Manipulators Carrying a Heavy Payload

A heavy payload attached to the wrist force/moment (F/M) sensor of a manipulator can cause the conventional impedance controller to fail in establishing the desired impedance due to the noncontact components of the force measurement, i.e., the inertial and gravitational forces of the payload. This paper proposes an impedance control scheme for such a manipulator to accurately shape its force-response without needing any acceleration measurement. Therefore, no wrist accelerometer or a dynamic estimator for compensating the inertial load forces is required. The impedance controller is further developed using an inner/outer loop feedback approach that not only overcomes the robot dynamics uncertainty, but also allows the specification of the target impedance model in a general form, e.g., a nonlinear model. The stability and convergence of the impedance controller are analytically investigated, and the results show that the control input remains bounded provided that the desired inertia is selected to be different from the payload inertia. Experimental results demonstrate that the proposed impedance controller is able to accurately shape the impedance of a manipulator carrying a relatively heavy load according to the desired impedance model.

Characteristics analysis of joint space inverse mass matrix for the optimal design of a 6-DOF parallel manipulator

Abstract An optimal design method for the Gough–Stewart platform manipulators based on dynamic isotropy is proposed. First, a dynamic isotropy measure is derived from the analysis of the natural frequencies of a Stewart platform at a neutral pose using the inverse of the joint space mass matrix. Next, considering a specific Gough–Stewart platform (SGSP), it is found that, when the payload inertia matrix is diagonal, the neutral pose joint space inverse generalized mass matrix is a symmetric Centro symmetric matrix. Using this property, we derive symbolic expressions for the Eigen values and Eigenvectors and discuss and present various predominant definitions in terms of the Eigen values. We show that one can obtain spatial isotropy based on dynamics whereas it is impossible to get spatial isotropy from kinematics and statics. Finally, we present an optimal design method based on the dynamic isotropy for SGSP. We also give a numerical example to illustrate the design procedure.

Dynamic modeling and mode analysis of flexible-link, flexible-joint robots

This paper presents a systematic approach to dynamic modeling and mode analysis of a single-link flexible robot, which has a flexible joint and a hub at the base end and a payload at the free end. Accurate modes of the system are obtained analytically. The following important conclusions are drawn: (1) even a small joint flexibility can significantly affect the system frequencies; (2) the fundamental frequency is insensitive to the hub inertia or payload inertia; (3) for a given flexible system, the fundamental frequency is mainly affected by the payload mass, while the second frequency is mainly affected by the payload inertia.

Experiments in adaptive model-based force control

Reports experiments with a class of model-based adaptive force control algorithms for robot arms. The problem addressed in this article is the control of robots whose motion is constrained by point contact between the robot tool and a smooth rigid environment or workpiece. Manufacturing applications for force control include a great variety of commonplace tasks, such as grinding, polishing, buffing, deburring, and assembly operations currently performed either manually or by fixed automation equipment. The force control algorithm provides asymptotically exact tracking of both end-effector position and contact-force. This force control algorithm utilizes a sliding-mode control technique of a type first espoused for the case of free (non-contact) robot motion. The stability of the new force control algorithm can be proven with respect to the commonly accepted nonlinear rigid body dynamical equations of motion. Moreover its adaptive extension can be shown to adaptively compensate for unknown plant parameters such as link and payload inertia, joint friction, and friction arising at the contact point between the tool tip and the surface. In Naniwa et al. (1993) and Arimoto and Naniwa (1992) the authors report satisfactory performance of this force control algorithm in numerical simulation studies. This article demonstrates the comparative advantages and disadvantages of this control algorithm under a variety of conditions in actual working implementations.

Effect of Payload on the Dynamics of a Flexible Manipulator—Modeling for Control

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

Use of asymptotic observers in the parameter estimation of robotic manipulators having elastic joints

The parameter estimation is investigated for robots having elastic joints. Dynamic estimates of the payload inertia parameters and of the joint elastic constants are obtained by asymptotic observers. The stability of the algorithm thus obtained is ensured by proper values of the observer gain matrix. Using the model of an actual elastic robot in some simulation tests, various issues are studied in this paper.