Robust control of robotic manipulators with task space feedback (original) (raw)

Asymptotically stable robust control of robot manipulators

Mechanism and Machine Theory, 1996

Most robust control methods of robot manipulators guarantee small tracking errors by applying sufficiently high feedback gains. Infinite gains are required for zero tracking errors under such controllers. However, in practice, feedback gains could be severely limited by hardware factors. Robust control schemes without using high gains are desirable. In this paper, we propose a globally asymptotically stable robust control scheme by combining integral control with a robust saturation control law. The proposed robust control method takes advantage of both saturation control and integral control techniques, while the disadvantages attributed to them are remedied by each other. Global asymptotic stability of an n-link robot system with parametric model uncertainties is achieved. The proposed control scheme has been implemented on a direct drive robot arm. Experiments were conducted to evaluate the proposed control method and to compare it with pure saturation and integral control methods, and experimental results are reported herein.

New Method for Tuning Robust Controllers Applied to Robot Manipulators

International Journal of Advanced Robotic Systems, 2012

This paper presents a methodology to select the parameters of a nonlinear controller using Linear Matrix Inequalities (LMI). The controller is applied to a robotic manipulator to improve its robustness. This type of dynamic system enables the robust control law to be applied because it largely depends on the mathematical model of the system; however, in most cases it is impossible to be completely precise. The discrepancy between the dynamic behaviour of the robot and its mathematical model is taken into account by including a nonlinear term that represents the model's uncertainty. The controller's parameters are selected with two purposes: to guarantee the asymptotic stability of the closed-loop system while taking into account the uncertainty, and to increase its robustness margin. The results are validated with numerical simulations for a particular case study; these are then compared with previously published results to prove a better controller performance.

Robust impedance control of robotic manipulators

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004

A task space robust trajectory tracking control is developed for robotic manipulators. A second order linear model, which defines the desired impedance for the robot, is used to generate the reference position, velocity and acceleration trajectories under the influence of an external force. The control objective is to make the robotic manipulator's end effector to track the reference trajectories in the task space. A sliding mode based robust control is used to deal with system uncertainties and unmodeled dynamics. Thus, a sliding manifold is defined by a linear combination of the tracking errors of the system in the task space built from the difference between the real and the desired position, velocity and acceleration trajectories. Moreover, the ideal relay has been substituted by a relay with a dead-zone in order to fit in with the actual way in which a real computational device implements the sign function being typical in sliding mode control. Furthermore, a higher level supervision algorithm is proposed in order to reduce the amplitude of the high frequency components of the output associated to a overestimation of the system uncertainties bounds. Then, the robust control law is applied to the case of a robot with parametric uncertainties and unmodeled dynamics. The closed-loop system is proved to be stable while the control objective fulfilled is in practice. Finally, a simulation example which shows the usefulness of the proposed scheme is presented.

Constrained motion task control of robotic manipulators

Mechanism and Machine Theory, 1994

Almeract-Controi of robotic manipulator during constrained motion task execution is the subject of this brief paper. Our previous work in this area addressed control of manipulators during constrained motion subject only to kinematic position constraints. This paper addresses the problem of manipulator constrained motion control for the case of arbitrary kinematic constraints acting on the system as well am dynamic parameter uncertainty. Hence, this brief paper represents a generalization of our previous results. A method is presented which permits the asymptotic regulation of both generalized forces and position of the manipulator. Regulation of these outputs is achieved in the presence of constant unmodelled disturbances which may act on the system. The control system synthesis is based on a general theory associated with the control of descriptor variable systems. The linearized manipulator dynamics is decomposed into a "slow" and "fast" subsystem. The slow subsystem, corresponding to the manipulator states that lie within the subspace of constrained states, is stabilized to yield an asymptotically stable system. The dynamics of the fast subsystem may be ignored, as shown in the paper. Synthesized from a linearized model of the manipulator dynamics, the method is valid only in a neighborhood about the point of linearization. It is assumed in this paper that the kinematics of the manipulator and the contact environment are known. A numerical example serves to illustrate the method presented here.

Robust control of robot manipulators based on dynamics decomposition

IEEE Transactions on Robotics and Automation, 1997

This paper presents a new robust saturation-based control method for robot manipulators and related experimental results. The proposed method distinguishes between uncertainty in the inertia, Coriolis and centripetal forces, gravity and friction. A robust compensator is designed for each type of uncertainty, and each control parameter is directly related to a specific behavior of the closed-loop robot system and can be adjusted accordingly. The goal is to achieve better performance by using this fine-tuning capability of the control law. The proposed control method has been implemented on a direct-drive robot arm. Experiments were conducted to investigate the effectiveness of the proposed method, and the results are reported in this paper.

Robust Trajectory Tracking Control of Space Manipulators in Extended Task Space

Pomiary Automatyka Robotyka

This study provides a new class of controllers for freeflying space manipulators subject to unknown undesirable disturbing forces exerted on the end-effector. Based on suitably defined taskspace non-singular terminal sliding manifold and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured disturbing forces. The numerical computations which are carried out for a space manipulator consisting of a spacecraft propelled by eight thrusters and holonomic manipulator of three revolute kinematic pairs, illustrate the performance of the proposed controller.

Robust Impedance Control of Manipulators Carrying a Heavy Payload

Journal of Dynamic Systems Measurement and Control, 2010

A heavy payload attached to the wrist force/moment ͑F / M͒ 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.

Robust model-following control for a robot manipulator

IEE Proceedings - Control Theory and Applications, 1997

A robust model-following control scheme for a rigid-body robot manipulator. is proposed. Given a nominal model of the manipulator, the manipulator dynamics are approximately linearised by nonlinear compensation based on the nominal model. Then the dynamics of tracking error between the state vectors of the linearised manipulator and a reference model are described as a descriptorform equation. A state feedback controller is designed for the descriptor-form equation so as to guarantee robust stability and robust performance of the closed-loop system in the presence of uncertain nonlinear perturbations. The proposed control scheme is applied to a twolink direct-drive manipulator. Results of experiments carried out to evaluate tracking performance of the manipulator show the effectiveness and robustness of the proposed controller.

Some Aspects of Modeling and Robust Control of a Robotic Manipulator

The problem of exact linearization via feedback consists in transforming a nonlinear system into a linear one using a state feedback. In the multivariable case, the nonlinear control law achieves also decoupling. The use of feedback linearization requires the complete knowledge of the nonlinear system. In practice, there are many processes whose dynamics is very complex, highly nonlinear and usually incompletely known. It is possible that the controlled system become unstable in the presence of significant model uncertainties. To improve robustness, it may be necessary to modify the exact linearization controller. In this paper, some robustification techniques for the exact linearization method are presented and applied for some multivariable models of a robotic manipulator. Numerical simulations are included to demonstrate the behavior and the performances of these controllers.

Revising the Robust-Control Design for Rigid Robot Manipulators

IEEE Transactions on Robotics, 2010

Robust controllers for robot manipulators ensure stability of the closed-loop system, even if only partial knowledge of the dynamic model of the manipulator is available. Existing derivations of robust-control laws, while guaranteeing the stability result, present an undesired dependence of the robust-control term on the gains of the controller for the nominal system. This dependence forces larger robust-control terms when the nominal control gains are large. Based on a structured representation of the model uncertainty, this paper proposes a derivation of the robust-control law, where these limitations are removed. Experimental results on the COMAU SMART 3S industrial robot in a 3-degree-of-freedom (DOF) configuration confirm the advantages of the proposed controller.