Robust Adaptive Control of Cooperating Mobile Manipulators With Relative Motion

In this paper, coupled dynamics are presented for two cooperating mobile robotic manipulators manipulating an object with relative motion in the presence of uncertainties and external disturbances. Centralized robust adaptive controls are introduced to guarantee the motion, and force trajectories of the constrained object converge to the desired manifolds with prescribed performance. The stability of the closed-loop system and the boundedness of tracking errors are proved using Lyapunov stability synthesis. The tracking of the constraint trajectory/force up to an ultimately bounded error is achieved. The proposed adaptive controls are robust against relative motion disturbances and parametric uncertainties and are validated by simulation studies.

Nomenclature

Contact point between the end effector of mobile manipulator I and the object.

Point where the end effector of mobile manipulator II holds the object.

Mass center of the object.

Frame fixed with the tool of mobile manipulator I with its origin at the contact point .

Frame fixed with the end effector of mobile manipulator II with its origin at point .

Frame fixed with the object with its origin at the mass center .

World coordinates.

Vector describing the posture of frame with .

Vector describing the posture of frame with .

Vector describing the posture of frame with .

Vector describing the posture of frame expressed in with .

Vector describing the posture of frame expressed in with .

Vector of joint variables of mobile manipulator I.

Vector of joint variables of mobile manipulator II.

Degrees of freedom of mobile manipulator I.

Degrees of freedom of mobile manipulator II.

Position vector of , the origin of frame .

Position vector of , the origin of frame .

Position vector of , the origin of frame .

Position vector of , the origin of frame expressed in .

Position vector of , the origin of frame expressed in .

Orientation vector of frame .

Orientation vector of frame .

Orientation vector of frame .

Orientation vector of frame expressed in .

Orientation vector of frame expressed in .