Darren M. Dawson

Robust control for the tracking of robot motion

In this paper we examine the stability of a proportional derivative (PD) controller for the trajectory-following problem of a robot manipulator. We use Lyapunovs second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.

On the learning control of a robot manipulator

This paper derives a learning control law to achieve trajectory following for a robot manipulator. The controller consists of two parts, a computed torque servo for the rigid body terms that can be modelled and a learning law for the unmodelled dynamics. An advantage of this method is that bounds can be assigned to the position and velocity tracking errors.

A robust adaptive controller for rigid robots

Robust adaptive control schemes for robot manipulators are introduced. A new concept for the adaptive controller guarantees improved performance by gain dynamics relating to the small-gain adaptive mechanism. A control component in the driving acceleration input is exploited. It relates to Riccati equations. New gain dynamics and a linear feedback component increase the exponential convergence rate of a Lyapunov function. Unmodeled dynamics and bounded disturbances are considered in order to deal with the robustification issues. It is possible to adjust the region within which the tracking error is bounded by using design-parameters associated with a Riccati equation and the gain dynamics. This region is a ring-shaped area or a disk-shaped area in which the tracking errors and their derivatives remain. The suggested adaptive control is optimal in that it minimizes a performance index. Simulation results demonstrate the robustified property of the adaptive controller for rigid robots.<<ETX>>

A nominal adaptive controller for a robot manipulator

This article derives an adaptive controller to achieve trajectory following for a robot manipulator. Lyapunovs second method is used for the design. The parameter, position, and velocity errors are shown to be uniformly bounded in the presence of an unknown bounded disturbance. To obtain insight for selecting the various control parameters for maintaining small tracking and parameter errors, we derive an error bound in terms of the system disturbances.

A Simplified Lyapunov-Based Controller for a Robot Manipulator

This paper derives a controller with simplified structure to achieve trajectory following for a robot manipulator. Lyapunovs second method is used for the design. Bounds on the position error and the velocity error are given, and a computer simulation is provided to verify that the error bounds are correct.