An Adaptive Controller for Two Cooperating Flexible Manipulators

Abstract

The control problem for two serial flexible multilink robots which carry a common rigid payload is considered. An adaptive controller with feedback and feedforward elements is presented which can track a prescribed trajectory for the payload with simultaneous vibration suppression when the manipulated payload is sufficiently large. A free loadsharing parameter appears in the passivity-based control law which allows the torque requirement to be shared between the two arms in a largely arbitrary fashion. Simulation results using a complex model are given which demonstrate excellent tracking performance in the face of complete payload uncertainty.

Modeling and Control of Flexible Telescoping Manipulators

“…The elastic equations were derived by assuming the payload is approximately nodal, and thus,K ee (ρ) = 0, which through (35) impliesρ T G ρ = 0. In [32], by neglecting the q e -dependence of the mass matrices, the elastic equation of motion can also be simplified leaving f non,e = −˙ M eeqe in (33). The elastic energy for the unforced motion is H e = T e + V e , whose time derivative isḢ…”

“…By ignoring the dependence on the elastic coordinate, the mass matrices can be written as a function of ρ using θ = F −1 r (ρ), where F −1 r is the rigid inverse kinematic map. If the terms O( q e 2 ) are ignored in (32), the equations of motion of the telescoping manipulator become (34) whereṀ ρρ − 2C ρρ is skew-symmetric, and the kth entry of G ρ is…”

Robust computationally efficient control of cooperative closed-chain manipulators with uncertain dynamics

“…Hence, using equations (4), (6), (7), (12), and the kinematics equations (1), (2), and (3), the dynamics equation of the ith manipulator can be rewritten as…”

“…However, it does compensate for the viscous friction in the manipulators' joints as it can be implicitly incorporated within matrix Q i (q i ,q i ) in (4). Although this may also apply to other adaptive algorithms [10][11][12][13][14][15][16][17], the main advantage of the proposed technique lies in its independence of a precise explicit mathematical model of the system's dynamics without the need of a computationally demanding soft computing engine.…”

“…To deal with such uncertainties, several adaptive control schemes were proposed [10][11][12][13][14][15][16][17]. These control algorithms approximate the system's dynamics using a continuous online estimation of a set of the plant's physical parameters through well-defined adaptation laws.…”