Dynamic Parameter Uncertainties Research Articles

Adaptive control of a constrained robot - ensuring zero tracking and zero force errors

A constrained robot is a mathematical model that describes the interaction between a robot and the environment as the robot moves along a prescribed trajectory. The main difficulty in the control of constrained robots is to ensure zero error for the constraint force in addition to accurate trajectory tracking. This study extends the result of Slotine and Li (1991) to design a simple adaptive controller for constrained robots. The proposed controller achieves both control objectives in the presence of dynamic parameter uncertainty. The overall system is proven to be globally stable in the Lyapunov sense. Simulation results are provided to demonstrate the performance of the proposed method.

Nonlinear Position-Dependent Circuits: Another Language for Describing Robot Motions and Mechatronic Systems

A class of nonlinear position-dependent circuits is introduced in order to give a physical understanding of nonlinear dynamics of mechanical systems and facilitate the performance analysis of robot controllers such as PD and SP-ID with or without regressors. The robustness of such simple controllers against uncertainty of dynamic parameters is analyzed on the basis of "passivity" of an input-output pair of a circuit, which is considered to be a generalization of impedance concept. It is shown that the passivity implies the H∞-tuning in a sense of disturbance attenuation. In addition, a necessary and sufficient condition for such a nonlinear system to maintain the passivity for all structural disturbances within a given margin is obtained.

Constrained motion task control of robotic manipulators

Control 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 as 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.

A neural net controller for underwater robotic vehicles

Results of a study on the application of neural networks to the control system of underwater robotic vehicles (URVs) are presented. The robustness of the control system with respect to nonlinear dynamic behavior and parameter uncertainties is investigated by computer simulation. The results show the feasibility of using unpredictable changes in the dynamics of the vehicle and its environment.

Modeling and control of underwater robotic vehicles

With the increased utilization of remotely operated vehicles in subsea applications, the development of autonomous vehicles becomes highly desirable to enhance operator efficiency. The dynamic model of an untethered remotely operated underwater vehicle is presented, and an adaptive control strategy for such vehicles is described. The robustness of the control system with respect to nonlinear dynamic behavior and parameter uncertainties is investigated by computer simulation. The results show that the use of the adaptive control system can provide high performance of the vehicle in the presence of unpredictable changes in the dynamics of the vehicle and its environment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability and robustness of a high gain nonlinear robot manipulator controller

A nonlinear controller is proposed for the trajectory control of an n degree of freedom rigid link robotic manipulator, using task space feedback of the end-effector position and orientation. With a Lyapunov approach, a proof of the local asymptotic stability of the proposed nonlinear control law is given. The closed-loop system is shown analytically to be robust to two separate classes of parameter uncertainty. This parameter uncertainty includes dynamic (i) parameter perturations caused by manpulation of unknown payloads and manipulator operation in the presence of unknown viscous joint friction and (ii) controller parameter error arising from uncertainty in the kinematic and dynamic parameters of the manipulator. Through the choice of a particular high gain nonlinear controller term, it is shown that sufficient conditions are satisfied for local asymptotic stability in the presence of large dynamic parameter perturbations caused principally by manipulation of unknown payloads. Hence, for sufficiently high gain the closed-loop system is robust to large parameter perturbations. In addittion to an analytic proof of the asymptotic trajectory capability for constant reference input signals, close trajectory tracking is also demonstrated analytically for a particular class of input trajectories, again a result of the high gain nonlinear controller term. Finally, a numerical simulation of a two degree of freedom robot demonstrates both the asymptotic trajectory tracking capability for constant reference inputs and the close trajectory tracking capability for time varying trajectories with high gain feedback in the presence of kinematic and dynamic controller modelling errors and large dynamic parameter uncertainty.

Robust Control of Robotic Manipulators in the Presence of Dynamic Parameter Uncertainty

Sufficient conditions are proved for a robotic manipulator controller so that asymptotic tracking/regulation occurs, independent of dynamic parameter uncertainty, for a certain class of input signals. The uncertainty can be quite large, and arise chiefly from the manipulation of payloads with unknown mass/inertia properties. The control is obtained using a robust controller which consists of two separate parts: 1) a compensator which makes the closed-loop robotic system insensitive to parameter uncertainty and generates asymptotic regulation of a certain class of input signals and 2) a stabilizing compensator, whose purpose is to stabilize the closed-loop system. Stability of the closed-loop system is guaranteed by choosing large feedback gains. In addition to the above, it is also shown that the proposed feedback controller provides an arbitrarily small tracking error capability for the particular class of input trajectories.

Suboptimal estimation of systems with large parameter uncertainties

The design of a filter that must estimate the state of a system when large parameter uncertainties in the plant dynamics or plant and measurement noise covariance matrices are present is considered. Filter designs are evaluated relative to the trade off between filter sensitivity to the uncertain parameters and minimum mean-square estimation error. This is accomplished by reformulating the estimation problem as an optimization problem with vector-valued performance index. The dominant design has form similar to the Kalman-Bucy filter, and employ open-loop compensation for the uncertain parameters.