Adaptive Control of Mechanical Manipulators

Abstract

When an accurate dynamic model of a mechanical manipu lator is available, it may be used in a nonlinear, model-based scheme to control the manipulator. Such a control formula tion yields a controller that suppresses disturbances and tracks desired trajectories uniformly in all configurations of the manipulator. Use of a poor dynamic model with this kind of model-based decoupling and linearizing scheme, however, may result in performance that is inferior to a much simpler, fixed-gain scheme. In this paper, we develop a parameter-adaptive control scheme in a set of adaptive laws that can be added to the nonlinear, model-based controller. The scheme is unique be cause it is designed specifically for the nonlinear, model- based controller and has been proven stable in a full, nonlin ear setting. After adaptation, the error dynamics of the joints are decoupled with uniform disturbance rejection in all ma nipulator configurations. The issues of sufficient excitation and the effect of disturbances are also discussed. The theory is demonstrated with simulation results and also with data from an implementation for an industrial robot, the Adept One.

Extended Model-Based Feedforward Compensation in ℒ1 Adaptive Control for Mechanical Manipulators: Design and Experiments

“…For model-based adaptive control schemes, a reformulation of the dynamics is required (Craig et al, 1987). The unknown or uncertain parameters to be estimated in real-time have to be separated from the non-linear functions in the dynamic model.…”

“…Besides, the estimated elements within the parameters vector can either appear in a separate form or as a combination of different parameters. Examples of the dynamics reformulation for some manipulators can be found in Craig et al (1987) and Sadegh and Horowitz (1990).…”

Model reference adaptive control for robotic manipulators without velocity measurements

“…The equation of dynamics for an n-link robot manipulator written in the usual form is M(q)q + C(q, 4) + G(q) = T (1) where q E R" denotes the vector of joint positions, M(q) E R"'" denotes the manipulator mass matrix, C(q, q ) E R" denotes the vector of centrifugal and Coriolis terms, G(q) E R" denotes the vector of gravity terms and T E R" denotes the applied torques at the joints. This can also be written in the form where the inertial parameters appear linearly as…”

Speed gradient adaptive control algorithms for mechanical systems

“…We may rewrite (4) in the integral form Then all solutions of system (2), (4) are bounded and Ql -+ 0 as t + 00.…”