This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

Technical Note: modification of the Leuven integrated friction model structure

Friction effects are particularly critical for industrial robots, since they can induce large positioning errors, stick-slip motions, and limit cycles. This paper offers a reasoned overview of the main friction compensation techniques that have been developed in the last years, regrouping them according to the adopted kind of control strategy. Some experimental results are reported, to show how the control performances can be affected not only by the chosen method, but also by the characteristics of the available robotic architecture and of the executed task.

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Friction Compensation in Robotics: an Overview

Models of self-organization have proved useful in revealing what processes may underlie characteristics of swarms. In this study, we review model-based explanations for aspects of the shape and internal structure of groups of fish and of birds travelling undisturbed (without predator threat). Our models attribute specific collective traits to locomotory properties. Fish slow down to avoid collisions and swim at a constant depth, whereas birds fly at low variability of speed and lose altitude during turning. In both the models of fish and birds, the ‘bearing angle’ to the nearest neighbour emerges as a side-effect of the ‘blind angle’ behind individuals and when group size becomes larger, temporary subgroups may increase the complexity of group shape and internal structure. We discuss evidence for model-based predictions and provide a list of new predictions to be tested empirically.

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Schools of fish and flocks of birds: their shape and internal structure by self-organization

Preliminaries External Synchronization of Rigid Joint Robots External Synchronization of Flexible Joint Robots Mutual Synchronization of Rigid Joint Robots Experimental Case Study Extensions.

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Synchronization of Mechanical Systems

This paper presents a reduced-order extended state observer (ESO) based sliding mode control scheme for friction compensation of a three-wheeled omnidirectional mobile robot. Compared with previous works, the proposed control approach is attractive from an implementation point of view. It does not require any explicit friction model, with quite low computation cost. First, a dynamic model with unknown friction forces is given. Then, the controller is designed, consisting of two parts. One part of the control effort is to compensate the friction effects, which are estimated by a reduced-order ESO without using any explicit friction model. The inverse of inertia matrix is also avoided in the proposed reduced-order ESO. The other part of the control effort is designed based on a second-order sliding mode technique known as super-twisting algorithm, in presence of parameter uncertainties. In addition, stability analysis of the designed control system is presented. Extensive experiments are conducted to verify the effectiveness and robustness of the proposed control design in compensating different friction effects.

Extended State Observer-Based Sliding Mode Control of an Omnidirectional Mobile Robot With Friction Compensation

This paper explains a procedure for getting models of robot kinematics and dynamics that are appropriate for robot control design. The procedure consists of the following steps: 1) derivation of robot kinematic and dynamic models and establishing correctness of their structures; 2) experimental estimation of the model parameters; 3) model validation; and 4) identification of the remaining robot dynamics, not covered with the derived model. We give particular attention to the design of identification experiments and to online reconstruction of state coordinates, as these strongly influence the quality of the estimation process. The importance of correct friction modeling and the estimation of friction parameters are illuminated. The models of robot kinematics and dynamics can be used in model-based nonlinear control. The remaining dynamics cannot be ignored if high-performance robot operation with adequate robustness is required. The complete procedure is demonstrated for a direct-drive robotic arm with three rotational joints.

Modeling and identification for high-performance robot control: an RRR-robotic arm case study

A dynamic model of a robot with 3 rotational degrees of freedom is derived in closed form. A systematic procedure for estimation of model dynamic parameters is suggested. It consists of the following steps: (i) identification of friction model parameters for each joint; (ii) calculation of optimal exciting trajectories, required for estimation of the remaining dynamic model parameters; (iii) estimation of these parameters using a least-squares method. The estimated model satisfactory reconstructs experimental control signals, justifying its use in model-based nonlinear control.

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Modeling and identification of an RRR-robot

Presents closed-form kinematic and dynamic models of a robot with three rotational degrees of freedom. The derivation of the models and estimation of their parameters are explained. Relevancy of the models is investigated with a writing task. Validation results, obtained by simulation and experiment, establish correctness of the models and illuminate their practical benefits.

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Closed-form kinematic and dynamic models of an industrial-like RRR robot

In this paper friction induced limit cycles are predicted for a simple motion system of a single motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static Switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field of nonlinear dynamics will be used to investigate the friction induced limit cycles. For a varying controller gain, stable and unstable periodic solutions are computed numerically which, together with the stability analysis of the closed-loop fixed points, result in a bifurcation diagram. For both friction models, the bifurcation analysis indicates the disappearance of the hunting behaviour for controller gains larger than the gain corresponding to the cyclic fold bifurcation point.

/pdf/friction-induced-limit-cycling-hunting-4ntauoafhh.pdf

R. Hensen

Papers

Modeling and identification for high-performance robot control: an RRR-robotic arm case study

Modeling and identification of an RRR-robot

Closed-form kinematic and dynamic models of an industrial-like RRR robot

Friction induced limit cycling : hunting

Friction in motion systems : performance deterioration for regular tasks