Journal of Intelligent and Robotic Systems 34: 331–333, 2002. 331

Guest Editorial:Flexible-Joint and Flexible-Link Robots

Flexible robots (manipulators) are distinguished in flexible-joint and flexible-link manipulators. Flexible joints result from drive shaft elasticity, gear defor-mations and torque sensors. The presence of flexibility in the joints and/or thelinks leads to poorly damped oscillations whenever the robot structure’s resonantfrequencies are excited. Thus, joint and link flexibilities have to be taken into ac-count in designing the control loops, especially in situations with high load/robotmass ratios. The research effort on flexible-joint and flexible-link robots rangesfrom modeling and estimation to adaptation mechanisms and intelligent/robustcontrol [1–11]. Given the dynamic nature of flexible robots (flexural dynamics)the theoretical analysis and the practical implementation of such methodologiespresent new challenges. A usual approach followed by researchers is the partition-ing of the system dynamics into slow (rigid body) and fast (flexural motion) dynam-ics, and designing separate controllers. A particular problem that has to be faced inthis type of robots is the non-minimum phase behavior of the system which maylead to unstable control (e.g., when using optimal feedback control). The aboveproblem is still under investigation and research workers are trying new emerg-ing control technologies including intelligent control schemes and soft-computing(fuzzy/neural network)-based control.

This Special Issue of the Journal of Intelligent and Robotic Systems containseight papers that address many of the issues mentioned above. Five of these papershave been invited especially for this issue and the other three papers were selectedfrom the normal channel of submitted papers.

The paper by El Maraghy, Lahdhiri and Ciuca proposes a robust linear con-troller for a flexible joint robot. First, a comprehensive model is developed whichaccounts for the stick-slip friction, the nonlinear elastic elements, model uncer-tainties and noise measurements. Then, the robust linear controller is designedfollowing the LQG/LTR approach. The simulation study showed that the proposedmodel/controller possesses excellent tracking and regulation abilities.

The next paper, by Khalil and Besnard, provides a general method to calibratethe geometric and flexural parameters of flexible-joint and flexible-link robots. Thedescription of the rigid model is based on the notation of Khalil and Kleinfinger,and is used to describe the shape of the links and define the flexibility parameters.The flexible transformation matrices are used to obtain the associated generalizedJacobian matrix, while the Newton–Euler method is employed to compute the

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forces and moments applied on the links and joints. The overall model is used forthe calibration in a way analogous to that used for the calibration of the geometricparameters.

The third paper, by Benosman, Boyer, Le Vey and Primault, is concernedwith the modeling and control of flexible-link manipulators. The presentation startswith the Newton–Euler model of a flexible link using the modal floating frameapproach. An extension of the control models to the case of fast dynamics and finitedeformations is presented. Using these models the end-effector tracking problem istreated for the single-link and the planar multi-link case. A set of numerical resultsare provided which illustrate the effectiveness of the control schemes.

The paper of Wilson, Robinett III, Parker and Starr proposes an augmentedsliding mode control (SMC) scheme for flexible link robots, which ensures a goodperformance in the rigid body motion and provides sufficient damping in the mea-sured flexible body modes. The new issue in the method is that the control lawdesign neglects the flexible body generalized accelerations, but the robot remainsstable even when flexible body generalized accelerations, unmodeled dynamics,disturbances and model uncertainties are present. The effectiveness of the controlscheme is verified in a slewing flexible link.

In the paper of S.-H. Lee and C.-W. Lee a hybrid control scheme is proposed forstabilizing the vibrations of a 2-link flexible robot and maintaining the robustnessof rigid-robot variable structure control (VSC) when controlling the joint angles.This scheme employs virtual control forces which play a principal role in gener-ating hybrid trajectories to stabilize the flexible vibrations. Simulation results areprovided which show the robustness superiority of the proposed hybrid controlscheme over the conventional composite control scheme.

The paper of Deng, F. Sun and Z. Sun presents a new neuro-fuzzy controlscheme for the time-delay adaptive control of flexible manipulators. The principalidea is to make the flexible system acting as a minimum phase system, via a suitableoutput redefinition. The controller is composed by a conventional observer-basedlinear control part and an adaptive time delay dynamic neuro-fuzzy control part forthe trajectory tracking task. The satisfying performance achieved by the proposedcontroller is demonstrated by a simulation example.

The paper by Feliu, Somolimos, Garcia and Sanchez provides a comparativestudy of two control schemes designed for a novel 3-DOF flexible arm. This armwas designed to have simple dynamics in order to facilitate its control and minimizethe sensing effort requirements. A compliance matrix is used to model the oscil-lations of the structure. Simulated results are presented and a comparison betweencontrolled and non-controlled tip responses is included.

Finally, the paper by Tzafestas, Kotsis and Pimenides treats the optimal regu-lator control problem for a 6-DOF flexible link parallel manipulator of the Stewarttype for the case where a nonlinear rigid model of the flexible manipulator iscombined with a linear rigid observer, and the case where a nonlinear flexiblemanipulator model is combined with a linear flexible observer. The simulation

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experiments showed that the second case gives better results than the first case(faster trajectory tracking, higher accuracy), and that in overall, optimal control isa good method for controlling parallel robots.

The above contributions show the current research tendency in the field of flex-ible robots as well as the type of results and performance that can be expected andrealized. I wish to express my sincere thanks to the authors for their contributionsand I hope that the issue will stimulate further research work in this field.

SPYROS TZAFESTASNational Technical University of Athens

References

1. Bayo, E.: A finite-element approach to control the end-point motion of a single-link flexiblerobot, J. Robotic Systems (1987), 63–75.

2. Christoforou, E. G. and Damaren, C. J.: The control of flexible-link robots manipulating largepayloads: Theory and experiments, J. Robotic Systems 17(5) (2000), 255–271.

3. Kanoh, K., Tzafestas, S. G., Lee, H. G., and Kalat, J.: Modeling and control of flexible robotarms, in: Proc. of the 25th IEEE Conf. on Decision and Control, Athens, December 1986,pp. 10–12.

4. Krikochoritis, T. E. and Tzafestas, S. G.: Control of flexible joint robots using neural networks,IMA J. Math. Control Inform. 18 (2001), 269–280.

5. Moallem, M., Khorasani, K., and Patel, R. V.: Inversion-based sliding control of a flexible-linkmanipulator, Internat. J. Control 71(3) (1998), 477–490.

6. Qu, Z.: Input–output robust tracking control design for flexible joint robots, IEEE Trans.Automat. Control 40(1) (1995), 78–83.

7. Spong, M. W.: Modeling and Control of elastic joint robots, J. Dynamic Systems Meas. Control109 (1987), 310–319.

8. Tomei, P.: Tracking control of flexible joint robots with uncertain parameters and disturbances,IEEE Trans. Automat. Control 39(5) (1994), 1037–1072.

9. Tzafestas, S. G. and Kanoh, K.: Dynamic studies of flexible robot manipulators, in: Proc.IMACS/IFAC Internat. Symp. on Modelling and Simulation of Distributed Parameter Sys-tems, Hiroshima, October 1987; also in: T. Futagami, S. G. Tzafestas and Y. Sunahara (eds),Distributed–Parameter Systems: Modelling and Simulation, North-Holland, Amsterdam, 1989,pp. 329–344.

10. Tzafestas, S. G., Desypris, S. N., and Kostis, D. L.: Singular perturbation-based control offlexible joint robots, Systems Analysis Modelling Simulation 38(2) (2000), 477–494.

11. Zagorianos, A., Kostis, D., and Tzafestas, S. G.: Robust adaptive linearization control offlexible joint robots, in: Proc. of the First ECPD Internat. Conf. on Advanced Robotics andIntelligent Automation, Athens, Greece, 1995, pp. 220–227.