Exact modeling for control of flexible manipulators

Abstract

This work presents the dynamic modeling and active vibration control of planar multilink manipulators having flexible links. Since the eigenvalue problem of such continuous structures is strongly dependent on the posture configuration, at first an efficient matrix formulation is provided in order to derive exact natural frequencies and mode shapes of a robot in its general posture. The analytical modal data are used to develop the forced vibration model; this is accomplished through the analytical decoupling of the modal coordinates of the manipulator; to this latter end, orthogonality conditions of modal shapes sets of planar multilink manipulators are demonstrated. The suppression of vibrations is challenged through a full-state linear quadratic regulator controller by optimally placing collocated sensor/actuator pairs. An optimal stochastic observer is designed in line with the noise-corrupted truncated model, i.e. the continuous Kalman-Bucy filter. The simulation results demonstrate that the presented matrix formulation for deriving exact modal data is effective, and the designed control method, along with the forcedvibration solving strategy, is feasible and efficient.

Review of modelling and control of flexible-link manipulators

“…The eigenmodes as well as the eigenfrequencies of such robots strongly depend on the linearisation position. 45,46 Therefore, it is not possible to use exact modes for the description of the elastic deflection. By increasing the number of assumed modes, more precise dynamic models may be expected, but the model will be more complex for controller designs.…”

Sensing linear viscoelastic constitutive parameters with a Timoshenko beam on a multi-layer foundation: Modeling and simulation

“…To induce a deformation of the beam coupled with the substrate we consider two different force inputs. In the first case we consider in (18) all the other forcing terms are zero. The forces are applied for 20 nondimensional time units, so that the forcing term becomes…”

“…In the second case we considered a distributed torque p c in (18), while the remaining forcing parameters in (18) are zero. The distributed torque is nonzero in the nondimensional time interval ½0; 20, so that the expression for p c is…”

“…Inverse problems for hyper redundant mechanisms with different geometric and dynamic conditions include: dynamic modeling of multi-link flexible robotic manipulators [14], calibration of model parameters of flexible manipulator [15], model reduction of rigid-flexible manipulators [16], the approximation of state space equations of flexible link manipulators [17], and modeling and trajectory planning of mobile manipulators with flexible links [18,19]. For elongated hyper-redundant systems, models of one dimensional continua with local Euclidean structure (beam models) are often naturally adopted, due to their suitability in describing the features associated with the slenderness.…”

Vibration control of a pneumatic driven piezoelectric flexible manipulator using self-organizing map based multiple models

“…Among the rigid and flexible manipulator types, attention is focused more towards flexible manipulators [1]. Flexible manipulators have many advantages: lower cost, higher operational speed, greater payload-to-manipulator-weight ratio, lower energy consumption, better maneuverability, better transportability and safer operation [2].…”