Modelling of Bound Estimation Laws and Robust Controllers for Robot Manipulators Using Functions and Integration Techniques

Adaptive robust motion control of linear motors for precision manufacturing

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. However, in practice, feedback gains could be severely limited by hardware factors. Robust control schemes using low feedback gains are desirable. In this paper, we derive 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. Globally asymptotic stability of an n-link robot system with parametric model uncertainties is achieved. As an illustration, the proposed control scheme is applied to a two degrees-of-freedom direct drive robot arm. Simulations were conducted, and the results are in accordance with the theoretical analysis. >

Robust Sliding Mode Trajectory Tracking Controller for a Nonholonomic Spherical Mobile Robot

In this paper, a
 nonlinear robust quaternion-based controller is developed to address the
 three-axis attitude tracking control problem of rigid spacecraft in presence of
 parametric uncertainties, unknown external disturbances and sensor noise. As a
 first step, a robust controller is designed that compensates parametric
 uncertainty and disturbance effects. The robust controller then reformulated to
 deal also with sensor noise. Singularity free unit quaternions are used to
 represent the attitude of the satellite in three-dimensional space. The
 Lyapunov-based stability analysis is applied to prove that a uniformly
 ultimately bounded tracking result is achieved. Simulation results are
 presented to illustrate the feasibility of the proposed control strategy. 

Discussion on: “Application of Logarithmic-based Parameter and Upper Bounding Estimation Rules to Adaptive-Robust Control of Robot Manipulators”

SummaryA new robust adaptive iterative learning control approach is proposed for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well‐designed dead‐zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function‐based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration‐varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single‐link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd.

We present a new optimal control approach to robust control of robot manipulators in the framework of state dependent Riccati equation (SDRE) technique. To treat this highly nonlinear control system, we formulate it as a nonlinear optimal regulator problem. SDRE technique was used to synthesize an optimal controller to this class of robot control problem. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the parameter uncertainties. A typical two-link robot position control problem was studied to show the effectiveness of SDRE approach and robust extra control design to robotic application.

In this article, a novel robust observer-based nonlinear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based nonlinear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness.

In this paper, a nonlinear robust output feedback control is proposed for a class of autonomous underwater vehicles. In specific, we consider the nonlinear mathematical model of a heavy-weight torpedo and design a sliding mode controller to achieve robust stabilization of the closed-loop system in the presence of environmental disturbances and parametric uncertainties. Lyapunovs method is used to present the closed-loop stability analysis of the system. Then, the state feedback sliding mode control law is extended to an output feedback control design using a fourth order observer. It is highlighted that the performance of the state feedback control is recovered arbitrarily fast by the proposed output feedback controller in the presence of parametric uncertainties and environmental disturbances. Finally, the performance of the proposed control design is shown using simulation.

A robust controller is proposed for the accurate trajectory control of a general n degree of freedom robotic manipulator, using feedback of task space coordinates, in the presence of large perturbations of the manipulator dynamic parameters. The controller is shown to consist of two separate devices: 1) a robust compensator which makes the system insensitive to parameter perturbation and causes asymptotic regulation to occur for a certain class of reference input/disturbance signals, and 2) a stabilizing compensator which stabilizes the closed-loop system. Asymptotic stability of the closed-loop system is demonstrated, using a Lyapunov approach, for large perturbations of the plant parameters. A numerical simulation of a two degree of freedom manipulator, with a large unknown payload mass is used to demonstrate the effectiveness of the controller.

This paper proposes \(H_{2}\)/\(H_{\infty }\) full state-feedback synthesis for robot manipulators, using uncertain polytopic linear parameter-varying (LPV) system modeling, with pole placement constraints to assign the poles of closed-loop system in a desired linear matrix inequality (LMI) region. The desired state trajectory of the system is used for generating an uncertain polytopic model of the system applying usual Lagrangian equations. The control gain matrix is derived by solving a set of LMIs to design a robust pole placement controller such that a prescribed mixed \(H_{2}\)/\(H_{\infty }\) performance is fulfilled and the response of the manipulator has a proper damping ratio. A sufficient condition is proposed to guarantee the asymptotic stability of the closed-loop uncertain polytopic LPV system against the uncertainties on the vertices. The proposed scheme is applied to controller synthesis of a two-degree-of-freedom manipulator trajectory-tracking problem. The simulation results show the effectiveness of the proposed controller.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

A new robust control method for robot manipulators is proposed in this paper. The new method possesses two characteristics different from those of known robust control laws: 1) it distinguishes between uncertainty in the inertia matrix, Coriolis and centripetal parameters, and the gravity; and 2) the uncertainty bounds needed to design the control law and to prove uniform ultimate boundedness of the tracking error depend only on the physical parameters and known functions of the generalized co-ordinates, hence they are simple to compute. The proposed method is based on designing a robust controller for each source of uncertainty such that the control parameters can be directly related to properties of the robot dynamics and can be adjusted according to the response to external stimuli. As an illustration, the proposed control method is applied to a robot arm, and the effectiveness of the scheme is confined by simulation. >

This paper addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The T-S fuzzy model is adopted for fuzzy modelling of the nonlinear systems. The continuous-time of the T-S fuzzy system with parametric uncertainties is considered. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The effectiveness of the proposed controller design method is finally demonstrated through numerical simulations on the chaotic Lorenz system.

SummaryThis work proposes a control structure to be applied to robotic manipulators, which are articulated mechanical systems composed of links connected by joints. The proposed controller can be divided into two parts. The first one is a left inverse system, which is used to decouple the dynamic behavior of the joints. The second is a sliding mode controller, which is applied for each decoupled joint. It is important to note that the proposed structure, using only input/output measurements, reduces the control signal ‘chattering’, and it is robust to parametric uncertainties. Besides all the characteristics presented, the proposed structure simplifies the design of sliding mode controller to be applied in robotic manipulators. All these features are verified by simulations. Copyright © 2016 John Wiley & Sons, Ltd.