This paper introduces the first stiffness controller for continuum robots. The control law is based on an accurate approximation of a continuum robot's coupled kinematic and static force model. To implement a desired tip stiffness, the controller drives the actuators to positions corresponding to a deflected robot configuration that produces the required tip force for the measured tip position. This approach provides several important advantages. First, it enables the use of robot deflection sensing as a means to both sense and control tip forces. Second, it enables stiffness control to be implemented by modification of existing continuum robot position controllers. The proposed controller is demonstrated experimentally in the context of a concentric tube robot. Results show that the stiffness controller achieves the desired stiffness in steady state, provides good dynamic performance, and exhibits stability during contact transitions.

Concentric tube robots are a subset of continuum robots constructed by combining pre-curved elastic tubes. As the tubes are rotated and translated with respect to each other, their curvatures interact elastically, enabling control of the robot's tip configuration as well as the curvature along its length. This technology is projected to be useful in many types of minimally invasive medical procedures. Because these robots are flexible by design, they deflect considerably when applying forces to the external environment. Thus, in contrast to rigid-link robots, their kinematic and static force models are coupled. This paper derives a multi-tube quasistatic model that relates tube rotations and translations together with externally applied loads to robot shape and tip configuration. The model can be applied in robot design, procedure planning as well as control. For validation, the multi-tube model is compared experimentally to a computationally-efficient single-tube approximate model.

Stiffness control of a continuum robot can prevent excessive contact forces during robot navigation inside delicate, uncertain and confined environments. Furthermore, it enables the selection of tip stiffnesses that match varying task requirements. This paper introduces a computationally-efficient approach to continuum-robot stiffness control that is based on writing the forward kinematic model as the product of two transformations. The first transformation calculates the non-contact kinematics of the robot and can be formulated based on the specific type of continuum robot under consideration. The second transformation calculates the tip deflection due to applied forces and is efficiently computed using the special Cosserat rod model. To implement a desired tip stiffness, the two transformations are used to solve for the actuator positions that deform the manipulator so as to generate the required tip force at the measured tip position. The efficacy of the proposed controller is demonstrated experimentally on a concentric-tube continuum robot.

Direct haptic feedback and graphical force feedback have both been hypothesized to improve the performance of robot-assisted surgery. In this study we evaluate the benefits of haptic and graphical force feedback on surgeon performance and tissue exploration behavior during a teleoperated palpation task of artificial tissues. Seven surgeon subjects (four experienced in robot-assisted surgery) used a 7-degree-of-freedom teleoperated surgical robot to identify a comparatively rigid rigid target object (representing a calcified artery) in phantom heart models using the following feedback conditions: (1) direct haptic and graphical feedback, (2) direct haptic only, (3) graphical feedback only, and (4) no feedback. To avoid the problems of force sensing in a minimally invasive surgical environment, we use a position-exchange controller with dynamics compensation for direct haptic feedback and a force estimator displayed via tool-tip tracking bar graph for graphical force feedback. Although the transparency of the system is limited with this approach, results show that direct haptic force feedback minimizes applied forces to the tissue, while coupled haptic and graphical force feedback minimizes subject task error. For experienced surgeons, haptic force feedback substantially reduced task error independent of graphical feedback.

During needle-based procedures, transitions between tissue layers often involve puncture events that produce substantial deformation and tend to drive the needle off course. In this paper, we analyze the mechanics of these rupture events corresponding to unstable crack propagation during the insertion of a sharp needle in an inhomogeneous tissue. The force-deflection curve of the needle prior to a rupture event is modeled by a nonlinear viscoelastic Kelvin model and a stress analysis is used to predict the relationship between rupture force and needle velocity. The model predicts that the force-deflection response of the needle is steeper and the tissue absorbs less energy when the needle moves faster. The force of rupture also decreases for faster insertion under certain conditions. The observed properties are sufficient to show that maximizing needle velocity minimizes tissue deformation and damage, and consequently, results in less needle insertion position error. The model predicts that tissue deformation and absorbed energy asymptotically approach lower bounds as velocity increases. Experiments with porcine cardiac tissue confirm the analytical predictions.

This article presents a model-based compensator for canceling friction in the tendon-driven joints of a haptic-feedback teleoperator. Unlike position-tracking systems, a teleoperator involves an unknown environment force that prevents the use of tracking position error as a feedback to the compensator. Thus, we use a model-based feedforward friction compensator to cancel the friction forces. We provide conditions for selecting compensator parameters to ensure passivity of the teleoperator and demonstrate performance experimentally.

This paper presents a model-based approach to cancel friction in the joints of the manipulators of a force-feedback telerobotic system. Friction compensation can improve the transparency of telerobotic systems, where transparency is quantified in terms of a match between the impedance of the environment and the impedance transmitted to the user. We used Dahl friction models to compensate for physical friction in the device. Experiments performed on a telerobotic system demonstrated that teleoperation transparency is improved by using these models. Further, the stability of the teleoperation is analyzed using passivity theory, and it is shown that the master-slave system remains stable up to a certain level of friction compensation

Passivity theory is applied to the creation of synthetic, complex multidimensional haptic environments. It can be shown that under appropriate conditions, sufficiently high rendering rates can guarantee the passivity of a simulation produced by a haptic device coupled to a discrete-time realization of a nominally passive environment. The creation of a passive, globally defined, virtual environment is either analytically complex or computationally costly. A method is described whereby a passive environment is created from transitions between locally defined force models that encode static conservative force fields. This is applied to the haptic rendering of tool contact with deformable bodies, in which sparse force-deflection responses are used to define local models. Passivity, continuity, and fidelity are provided by response-function interpolation rather than by interpolation of forces, as in previous methods. The work also includes an illustrative example.

A method is described whereby the virtual haptic interaction with deformable elastic objects is created in terms of two processes: a slow process which carries on the simulation, and a fast process to render forces. Passivity theory is used to design an update strategy which reproduces exactly pre-computed responses between a tool and an object. This yields a design procedure for adjustable local models which guarantee the passivity of the interaction while preserving fidelity. Two examples of local models are given and some experimental results are reported.