Pierre E. Dupont

A survey of models, analysis tools and compensation methods for the control of machines with friction

Abstract While considerable progress has been made in friction compensation, this is, apparently, the first survey on the topic. In particular, it is the first to bring to the attention of the controls community the important contributions from the tribology, lubrication and physics literatures. By uniting these results with those of the controls community, a set of models and tools for friction compensation is provided which will be of value to both research and application engineers. The successful design and analysis of friction compensators depends heavily upon the quality of the friction model used, and the suitability of the analysis technique employed. Consequently, this survey first describes models of machine friction, followed by a discussion of relevant analysis techniques and concludes with a survey of friction compensation methods reported in the literature. An overview of techniques used by practising engineers and a bibliography of 280 papers is included.

Design and Control of Concentric-Tube Robots

A novel approach toward construction of robots is based on a concentric combination of precurved elastic tubes. By rotation and extension of the tubes with respect to each other, their curvatures interact elastically to position and orient the robots tip, as well as to control the robots shape along its length. In this approach, the flexible tubes comprise both the links and the joints of the robot. Since the actuators attach to the tubes at their proximal ends, the robot itself forms a slender curve that is well suited for minimally invasive medical procedures. This paper demonstrates the potential of this technology. Design principles are presented and a general kinematic model incorporating tube bending and torsion is derived. Experimental demonstration of real-time position control using this model is also described.

Single state elastoplastic friction models

For control applications involving small displacements and velocities, friction modeling and compensation can be very important. In particular, the modeling of presliding displacement (motion prior to fully developed slip) can play a pivotal role. In this paper, it is shown that existing single-state friction models exhibit a nonphysical drift phenomenon which results from modeling presliding as a combination of elastic and plastic displacement. A new class of single state models is defined in which presliding is elastoplastic: under loading, frictional displacement is first purely elastic and then transitions to plastic. The new model class is demonstrated to substantially reduce drift while preserving the favorable properties of existing models (e.g., dissipativity) and to provide a comparable match to experimental data.

A Steerable Needle Technology Using Curved Concentric Tubes

A new approach to steerable needle design is proposed for use in minimally invasive surgery. The technology is based on sets of curved concentric tubes. By rotating and extending the tubes with respect to each other, the position and orientation of the needle tip, as well as the shape of the inserted length, can be controlled. A mechanics model is presented for computing the shape of the needle. Forward and inverse kinematic equations are also derived. In addition, experimental results are presented as validation of the approach

Analysis of Rigid-Body Dynamic Models for Simulation of Systems With Frictional Contacts

The use of Coulombs friction law with the principles of classical rigid-body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations, compliant contact models, while increasing the dimensionality of the state vector, can resolve these problems. The simplicity and efficiency of rigid-body models, however, provide strong motivation for their use during those portions of a simulation when the rigid-body solution is unique and stable. In this paper, we use singular perturbation analysis in conjunction with linear complementarity theory to establish conditions under which the solution predicted by the rigid-body dynamic model is stable. We employ a general model of contact compliance to derive stability criteria for planar mechanical systems. In particular, we show that for cases with one sliding contact, there is always at most one stable solution. Our approach is not directly applicable to transitions between rolling and sliding where the Coulomb friction law is discontinuous. To overcome this difficulty, we introduce a smooth nonlinear friction law, which approximates Coulomb friction. Such a friction model can also increase the efficiency of both rigid-body and compliant contact simulation. Numerical simulations for the different models and comparison with experimental results are also presented.

Avoiding stick-slip through PD control

Addresses the question of how to achieve steady motion at very low velocities using proportional-derivative (PD) control. Most prior work in control has used friction models which depend only on the current value of velocity. This type of analysis indicates that stick-slip can be avoided only through velocity feedback. The tribology literature, however, indicates that friction also depends on the history of motion. By including this dependence, a second regime of stable motion is revealed which is associated with position feedback gains above a critical value. Two experimentally-based dynamic friction models are compared using a linearized stability analysis. In accord with experiment, a state variable friction model exhibits asymptotically stable motion for any system stiffness (position feedback gain) exceeding a critical value. This property is not exhibited by a time-lag friction model. >

GPU Based Real-time Instrument Tracking with Three Dimensional Ultrasound

Real-time 3D ultrasound can enable new image-guided surgical procedures, but high data rates prohibit the use of traditional tracking techniques. We present a new method based on the modified Radon transform that identifies the axis of instrument shafts as bright patterns in planar projections. Instrument rotation and tip location are then determined using fiducial markers. These techniques are amenable to rapid execution on the current generation of personal computer graphics processor units (GPU). Our GPU implementation detected a surgical instrument in 31 ms, sufficient for real-time tracking at the 26 volumes per second rate of the ultrasound machine. A water tank experiment found instrument tip position errors of less than 0.2 mm, and an in vivo study tracked an instrument inside a beating porcine heart. The tracking results showed good correspondence to the actual movements of the instrument.

Elasto-plastic friction model: contact compliance and stiction

The presliding displacement and stiction properties of friction models are investigated. It is found that existing single-state-variable friction models possess either stiction or presliding displacement. Next, those models with continuous states are interpreted as examples of Prandlts elasto-plastic material model. A class of general one-state models is derived that is stable, dissipative and exhibits both stiction and presliding displacement.

Real-Time Three-Dimensional Ultrasound for Guiding Surgical Tasks

Objective: As a stand-alone imaging modality, two-dimensional (2D) ultrasound (US) can only guide basic interventional tasks due to the limited spatial orientation information contained in these images. High-resolution real-time three-dimensional (3D) US can potentially overcome this limitation, thereby expanding the applications for US-guided procedures to include intracardiac surgery and fetal surgery, while potentially improving results of solid organ interventions such as image-guided breast, liver or prostate procedures. The following study examines the benefits of real-time 3D US for performing both basic and complex image-guided surgical tasks. Materials and Methods: Seven surgical trainees performed three tasks in an acoustic testing tank simulating an image-guided surgical environment using 2D US, biplanar 2D US, and 3D US for guidance. Surgeon-controlled US imaging was also tested. The evaluation tasks were (1) bead-in-hole navigation; (2) bead-to-bead navigation; and (3) clip fixation. Performance measures included completion time, tool tip trajectory, and error rates, with endoscope-guided performance serving as a gold-standard reference measure for each subject. Results: Compared to 2D US guidance, completion times decreased significantly with 3D US for both bead-in-hole navigation (50%, p = 0.046) and bead-to-bead navigation (77%, p = 0.009). Furthermore, tool-tip tracking for bead-to-bead navigation demonstrated improved navigational accuracy using 3D US versus 2D US (46%, p = 0.040). Biplanar 2D imaging and surgeon-controlled 2D US did not significantly improve performance as compared to conventional 2D US. In real-time 3D mode, surgeon-controlled imaging and changes in 3D image presentation made by adjusting the perspective of the 3D image did not diminish performance. For clip fixation, completion times proved excessive with 2D US guidance (< 240 s). However, with real-time 3D US imaging, completion times and error rates were comparable to endoscope-guided performance. Conclusions: Real-time 3D US can guide basic surgical tasks more efficiently and accurately than 2D US imaging. Real-time 3D US can also guide more complex surgical tasks which may prove useful for procedures where optical imaging is suboptimal, as in fetal surgery or intracardiac interventions.

Mechanics of Dynamic Needle Insertion into a Biological Material

During needle-based procedures, transitions between tissue layers often lead to rupture events that involve large forces and tissue deformations and produce uncontrollable crack extensions. In this paper, the mechanics of these rupture events is described, and the effect of insertion velocity on needle force, tissue deformation, and needle work is analyzed. Using the J integral method from fracture mechanics, rupture events are modeled as sudden crack extensions that occur when the release rate J of strain energy concentrated at the tip of the crack exceeds the fracture toughness of the material. It is shown that increasing the velocity of needle insertion will reduce the force of the rupture event when it increases the energy release rate. A nonlinear viscoelastic Kelvin model is then used to predict the relationship between the deformation of tissue and the rupture force at different velocities. The model predicts that rupture deformation and work asymptotically approach minimum values as needle velocity increases. Consequently, most of the benefit of using a higher needle velocity can be achieved using a finite velocity that is inversely proportional to the relaxation time of the tissue. Experiments confirm the analytical predictions with multilayered porcine cardiac tissue.