Force Tracking Error Research Articles

Modular adaptive robust control of SISO nonlinear systems in a semi‐strict feedback form

AbstractIn this paper, a modular modification of the adaptive robust control (ARC) technique is presented. The modular design has all of the original ARC properties with an estimation‐based update law instead of a Lyapunov‐based update law. In this design, the controller is divided into two modules: a control module and an identification module. A key new idea is to set a priori bounds on the time derivatives of the estimates to be maintained by the update law. As a result, their effects on the system tracking accuracy can be dominated by the control law. A modification is proposed for the standard gradient and least‐square update laws to guarantee the bounds. This modification also makes the controller robust against the generalized (unparameterized) uncertainties considered in the ARC formulation while allowing asymptotic output tracking without the generalized uncertainties. Both the ARC and the modular ARC techniques are applied to a force control problem for an active suspension system. Simulations and experimental results are provided to show that the update law of the modular design is less sensitive to measurement noise which results in smaller force tracking error and smaller control gain. Copyright © 2004 John Wiley & Sons, Ltd.

Adaptive Control For Robotic Manipulators Executing Multilateral Constrained Task

ABSTRACTThis paper presents a model‐based adaptive control in task coordinates for robotic manipulators executing multilateral constrained tasks The controller works based on the concept of orthogonality between force and motion in the subspaces derived from the constraints. The control gains are independently adjustable in each subspace. The friction force, depending on the contact force, is compensated adaptively. Asymptotic convergence for both force and motion tracking errors is guaranteed by the Lyapunov‐Like Lemma. Experimental results obtained using a 3 D.O.F. robot are given.

Nonlinear adaptive control of master–slave system in teleoperation

This paper is devoted to the nonlinear control design problem to achieve stability of master–slave manipulators in teleoperation system and its transparency in the sense of motion/force tracking. Nonlinear adaptive controllers are bilaterally designed for both master and slave sites to guarantee the stability of whole system and motion tracking performance. Global boundedness of the overall adaptive system and asymptotic motion (velocity/position) tracking are established. Especially, the concept of “virtual master manipulator” is introduced to increase degree of freedom of control design for force tracking performance. The resulting force tracking error depends only on the acceleration of the designed virtual master manipulator. Accurate dynamic parameters of manipulators, their acceleration information as well as models of human operator and environment are not required in the control design. Another important feature of our approach is the relaxation for the trade-off between motion and force tracking performances.

Adaptive tracking control for cooperative multiple robot systems

This study presents a novel adaptive controller for cooperative multiple robot systems to obtain both zero motion and force tracking errors. First, by introducing the concepts of force decomposition and virtual control input, we reformulate the control problem of cooperative manipulators as a problem of controlling a single constrained manipulator. Next, a stable subspace is defined by both motion and internal force errors. This subspace includes both zero motion and force errors as its largest invariant set. The controller is then designed to drive the error dynamics into the stable subspace. A non‐adaptive and an adaptive approach both systematically show the asymptotic motion/internal force tracking. Note here that the zero force tracking error is achieved without needing the persistent excitation (PE) condition in the adaptive control scheme. Furthermore, based on a decentralized method, the proposed controllers are implemented in multiprocessor systems to balance the computation load. Finally, two cooperative planar robots are used to demonstrate the developed methodology where the simulation results illustrate the expected performance.

ROBUST HYBRID CONTROL OF UNCERTAIN CONSTRAINED MECHANICAL SYSTEMS

Robust hybrid controller design is presented in this paper for motion/force control of mechanical systems subjected to a set of holonomic or classical nonholonomic constraints and in the presence of uncertainties about plant parameters. A unified and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic constrained mechanical systems, respectively. The proposed controllers can guarantee the system motion asymptotically converges to the desired manifold, and the force tracking errors to be bounded. Numerical simulation has been done to show the effectiveness of the proposed controllers.

Experimental evaluation of a variable structure controller for constrained robots

In this paper, a variable structure control scheme for constrained robots is developed. This control law ensures the asymptotic convergence of the position errors to zero and also the boundedness of the force tracking error. The control scheme requires a few online computations and thus can be easily implemented. The proposed control law does not require measurements of the joint accelerations or the estimation of the derivative of the force. Experimental results are presented to verify the theoretical developments.

Experimental evaluation of a variable structure controller for constrained robots

In this paper, a variable structure control scheme for constrained robots is developed. This control law ensures the asymptotic convergence of the position errors to zero and also the boundedness of the force tracking error. The control scheme requires a few online computations and thus can be easily implemented. The proposed control law does not require measurements of the joint accelerations or the estimation of the derivative of the force. Experimental results are presented to verify the theoretical developments.

Adaptive neural network control of coordinated manipulators

In this article, adaptive neural network control of coordinated manipulators is considered in an effort to eliminate the time-consuming and error prone dynamic modeling process which is necessary for the implementation of conventional adaptive control. After a concise dynamic model in the object coordinate space is developed for the coordinated manipulators, an adaptive neural network controller is presented by combining the techniques of neural network parameterization, adaptive control, and sliding mode control. It can be shown that the motion tracking errors converge to zero asymptotically whereas the internal force tracking error remains bounded and can be made arbitrarily small. Numerical simulations are conducted to show the effectiveness of the proposed method. ©1999 John Wiley & Sons, Inc.

Adaptive Neural Network Feedback Linearization Control of Coordinated Manipulators

In this paper, coordinated control of multiple manipulators is considered. A concise dynamic model in the object coordinate space is developed for the coordinated manipulators. Based on this model, an adaptive neural network controller has been designed. It can be shown that the motion tracking errors converges to zero asymptotically whereas the internal force tracking error remains bounded and can be made arbitrarily small.

Adaptive neural network control of flexible joint manipulators in constrained motion

This paper addresses the control problem of flexible joint manipulators in constrained motion. The singular perturb ation method is applied to reduce the original system into slow and fast subsystems. By adopting the composite control strategy, an adaptive neural network controller is first developed to control the slow subsystem. Then a fast feedback control is designed to stabilise the fast subsystem along its equilibrium trajectory. The system stability is proven using Lyapunov theory. It is shown that the motion tracking error converges to zero asymptotically, whereas the force tracking error remains bounded and can be made arbitrarily small. Numerical simulations are provided to show the effectiveness of the approach.

Adaptive Force-Position Control for Constrained Robotic Manipulators

This paper presents an adaptive force-position control in task coordinates for constrained robot manipulators. In general, the constraints can be represented separately by the subset of generalized coordinates in task space. This controller works on a concept of orthogonalization between force and motion in the subspaces derived from constraints. The friction force is compensated adaptively. The globally asymptotic convergence for both force and motion tracking errors is guaranteed by the Lyapunov-Like Lemma. The implementation method of the controller in joint space is also given. Computer simulation results for a three-link manipulator are shown to demonstrate the effectiveness of the proposed method.

Force Tracking in Impedance Control

This article presents two simple on-line schemes for force tracking within the impedance-control framework. The force- tracking capability of impedance control is particularly important for providing robustness in the presence of large uncertainties or variations in environmental parameters. The two proposed schemes generate the reference position trajec tory required to produce a desired contact force despite lack of knowledge of the environmental stiffness and location. The first scheme uses direct adaptive control to generate the refer ence position on-line as a function of the force-tracking error. Alternatively, the second scheme utilizes an indirect adaptive strategy in which the environmental parameters are estimated on-line, and the required reference position is computed based on these estimates. In both schemes, adaptation allows au tomatic gain adjustment to provide a uniform performance despite variations in the environmental parameters. Simula tion studies are presented for a 7-DOF Robotics Research arm using full arm dynamics, demonstrating that the adaptive schemes are able to compensate for uncertainties in both the environmental stiffness and location. The simulation studies also highlight the limitations of pure impedance control without the force-tracking capability for robust execution of realistic contact tasks. Experimental results are also presented for the Robotics Research arm to demonstrate that the end effector applies the desired contact force while exhibiting the specified impedance dynamics.

Combined direct and indirect adaptive control of constrained robots

The force tracking error is dependent on both the position tracking error and the estimated parameter error so that, in constrained adaptive robot control, the convergence of the estimated parameter error becomes more important than in unconstrained adaptive robot control. However, in the direct adaptive controller, the parameter adaptation is driven only by the tracking error in the joint motion, while in the indirect adaptive controller, the parameter estimation is driven only by the prediction error in the joint torque. Based on this observation a new combined direct and indirect adaptive controller driven by both the tracking error and the prediction error is developed for constrained robots with inertia parameter uncertainty. Stability of the combined adaptive controllers is established in the Lyapunov sense. The combined control improves both position and force tracking performance compared with direct adaptive control. The computer simulations are presented to demonstrate the proposed schemes.

A passivity-based adaptive sliding mode position-force control for robot manipulators

Based on a novel orthogonalized sliding mode error co-ordinate system, a passivity-based adaptive sliding mode control that yields the global exponential convergence of position and force tracking errors is proposed. The holonomic constraint is efficiently manipulated to derive two orthogonal transformations at the velocity level. These transformations are used to propose a convenient representation of error modelling such that simple proofs of passivity and stability are established. Sliding modes arise on the tangential and normal subspaces at the contact point. The parametric uncertainty is compensated via an adaptive control loop and the sliding modes allow one to conclude the exponential convergence. Computer simulation data show a robust performance.

Adaptive Motion and Force Control of Manipulators During Constrained Motion Tasks

This paper addresses the problem of adaptive controller design for constrained robots. Since the force tracking errors in the constrained adaptive robot control are dependent on both the position tracking errors and the estimation parameter errors, the convergence of the estimation parameter errors becomes more important than in the unconstrained adaptive robot control. With this in mind, a new parameter estimation algorithm, which gives a parameter convergence under a weaker excitation condition, is presented using the information from both input and output channels of the constrained robot systems.

Hybrid force/position control for robot manipulators based on a D-type learning law

SummaryA learning control algorithm is proposed for hybrid force/position tracking of a manipulator in contact with a hard surface. The algorithm utilizes acceleration errors and force errors for learning the inputs required to perform repetitive tasks. We prove the convergence of both force and position tracking errors theoretically. The speed of convergence of the tracking errors is shown to be improved by proper choice of learning gains. The method is compared with PI and PID learning, and similarities with the free-space case are outlined. The robustness of the new scheme to uncertainties in surface geometry and link parameters is discussed. Results of simulation studies and experimental implementation on 3-link robot manipulators are presented to illustrate the effectiveness of the proposed learning controller.

Adaptive Control of Robot Manipulators in Constrained Motion—Controller Design

Adaptive motion and force control of manipulators in constrained motion in the presence of parametric uncertainties both in the robot and contact surfaces are considered in this paper. A new constrained dynamic model is obtained to account for the effect of contact surface friction. An adaptive law is suggested with unknown parameters updated by both the motion and force tracking errors to guarantee asymptotic motion and force tracking without any persistent excitation conditions to be satisfied. The suggested controller has the expected PI type force feedback control structure with a low proportional (P) force feedback gain. Detailed simulation results are given to show the effectiveness of the proposed controller.

Position and force tracking control of rigid-link electrically driven robots actuated by switched reluctance motors

Abstract In this paper, we design a tracking controller for rigid-link electrically driven (RLED) robot manipulators actuated by switched reluctance (SR) motors operating under constrained and unconstrained conditions. Using models of the robot dynamics and environmental constraints, a reduced-order dynamic model is obtained for the mechanical subsystem with respect to a set of constraint variables. A tracking control is then formulated for the reduced-order manipulator dynamics and the SR motor dynamics. The control assumes exact model knowledge and requires measurement of the robot link positions, link velocities and motor currents. The proposed controller yields global exponential stability (GES) for the position, velocity and force tracking errors on and off a rigid, frictionless constraint surface.

Experimental results for a robust position and force controller implemented on a direct drive robot

SummaryIn this paper we present the results obtained from the implementation of a robust position/force controller on a two-degree-of-freedom direct drive robot. The controller is based on the theoretical work presented in references 1 & 2, which guarantees Globally Uniformly Ultimately Bounded (GUUB) position tracking error and bounded force tracking error. The controller accomplishes this stability result in spite of robot model uncertainty and only requires; joint position and velocity measurements, end-effector force measurements, and bounds on the model parameters. Experimental results described in this paper serve to verify the theoretical claims.

Hybrid position/force control of constrained manipulators in presence of uncertainties

In this paper the problem ofthe hybrid position/force control of constrained robots is discussed. 1be analysis is based on the decoupling of singular dynamic systems, representing the constrained dynamics. In particular the existence of a class of coordinate transfonnations, allowing the decoupling of the equations describing the motion in a neighbour of a reference trajectory, from those representing the reaction forces, is discussed. Then a position/velocity feedback control law is proposed guaranteeing boundedness of both position and force tracking errors. Finally the robustness of the control scheme, with respect to uncertainties in the constraints geometry, and robot inertial characteristics, is analysed.