This paper considers the problem of dynamic modeling and identification of robot manipulators with respect to their elasticities. The so-called flexible joint model, modeling only the torsional gearbox elasticity, is shown to be insufficient for modeling a modern industrial manipulator accurately. The extended flexible joint model, where non-actuated joints are added to model the elasticity of the links and bearings, is used to improve the model accuracy. The unknown elasticity parameters are estimated using a frequency domain gray-box identification method. The conclusion is that the obtained model describes the movements of the motors and the tool mounted on the robot with significantly higher accuracy. Similar elasticity model parameters are obtained when using two different output variables for the identification, the motor position and the tool acceleration.

In this paper, we study the problem of estimating unknown parameters in nonlinear gray-box models that may be multivariable, nonlinear, unstable, and resonant at the same time. A straightforward use of time-domain predication-error methods for this type of problem easily ends up in a large and numerically stiff optimization problem. We therefore propose an identification procedure that uses intermediate local models that allow for data compression and a less complex optimization problem. The procedure is based on the estimation of the nonparametric frequency response function (FRF) in a number of operating points. The nonlinear gray-box model is linearized in the same operating points, resulting in parametric FRFs. The optimal parameters are finally obtained by minimizing the discrepancy between the nonparametric and parametric FRFs. The procedure is illustrated by estimating elasticity parameters in a six-axes industrial robot. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest for robot control.

High performance robot manipulators, in terms of cycle time and accuracy, require well designed control methods, based on accurate dynamic models. Robot manipulators are traditionally described by the flexible joint model or the flexible link model. These models only consider elasticity in the rotational direction. When these models are used for control or simulation, the accuracy can be limited due to the model simplifications, since a real manipulator has a distributed flexibility inall directions. This work investigates different methods for the inverse dynamics of a more general manipulator model, called the extended flexible joint model. The inverse dynamics solution is needed for feedforward control, which is often used for high-precision robot manipulator control.

The inverse dynamics of the extended flexible joint model can be computed as the solution of a high-index differential algebraic equation (DAE). One method is to solve the discretized DAE using a constant stepsize constant-order backwards differentiation formula (BDF). This work shows that there is only a small difference between solving theoriginal high-index DAE and the index-reduced DAE. It is also concluded that scaling of the algebraic equations and their derivatives is important.

The inverse dynamics can be solved as an initial-value problem if the zero dynamics of the system is stable, i.e., minimum phase. For unstable zero dynamics, an optimization approach based on the discretized DAE is suggested. An optimization method, using a continuous DAE formulation, is also suggested and evaluated. The solvers are illustrated by simulation, using a manipulator with two actuators and five degrees-of-freedom.

High performance robot manipulators, in terms of cycle time and accuracy, require well designed control methods, based on accurate dynamic models. This work investigates different methods for the inverse dynamics of a general manipulator model, called the extended flexible joint model. This model can describe elasticity in all directions, unlike the traditionally used robot models. The inverse dynamics solution is needed for feedforward control, which is often used for high-precision robot manipulator control. The inverse dynamics of the extended flexible joint model can be computed as the solution of a high index differential algebraic equation (DAE). The obtained DAE is analyzed, and solvers for both minimum phase and nonminimum phase systems are suggested. The solvers are evaluated by simulation, using a manipulator with two actuators and five degrees-of-freedom. Finally, the suggested concept for inverse dynamics is experimentally evaluated using an industrial robot manipulator. In this experimental evalution, an identified model is used in the inverse dynamics computation. Simulations using the same identified model are in good agreement with the experimental results. The conclusion is that the extended flexible joint inverse dynamics method can improve the accuracy for manipulators with significant elasticities,

Feedback linearization is one of the major academic approaches for controlling flexible joint robots. This contribution investigates the discrete-time implementation of the feedback linearization approach for a realistic three-axis robot model. A simulation study of high speed tracking with model uncertainty is performed. It is assumed that full state measurements of the linearizing states are available. The feedback linearization approach is compared to a feedforward approach.

A benchmark problem for robust feedback control of a flexible manipulator is presented. The system to be controlled is a four-mass system subject to input saturation, nonlinear gear elasticity, model uncertainties, and load disturbances affecting both the motor and the arm. The system should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. Four suggested solutions are presented, and even though the solutions are based on different design methods, they give comparable results.

A benchmark problem for robust feedback control of a manipulator is presented. The system to be controlled is an uncertain nonlinear two link manipulator with elastic gear transmissions. The gear transmission is described by nonlinear friction and elasticity. The system is uncertain according to a parametric uncertainty description and due to uncertain disturbances affecting both the motors and the tool. The system should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. The control problem concerns only disturbance rejection. The proposed model is validated by experiments on a real industrial manipulator.