A control design framework for the coupled stability problem in robotics is presented. The proposed framework fundamentally generalizes the conventional passivity-based approaches to the coupled stability problem. In particular, it allows for stabilization of not necessarily passive robot-environment interaction where both the manipulator and the environment are dissipative systems with quadratic supply rates. In contrast with existing results, the proposed framework can be used in combination with an arbitrary robot’s tracking control algorithm, and its stabilizing action when in contact with environment does not affect the robot’s trajectory tracking performance in free space. The framework is based on the recently developed nonplanar conic systems formalism and generalized scattering-based stabilization methods. A detailed design example is presented which illustrates the capabilities of the proposed method.

Tendon-driven mechanisms used in robotic surgery exhibit strong nonlinearities, particularly a static backlash-like hysteresis, in their motion transmission behavior. In this paper, an extension of a previously developed model is proposed that allows for estimation of angular displacements in multi-DOF tendon-driven devices where special attention is given to the coupling effect between DOFs. The proposed model consists of the conventional coupling matrix and a novel elongation matrix which compensates for the coupled hysteretic effect. The model is applied to the problem of position estimation in three DOFs (one pitch and two grasping DOFs) of a da Vinci®surgical instrument. As a further extension, a preliminary dynamic model is also suggested to deal with high-frequency inputs. According to the experimental results obtained, the proposed quasi-static model can describe the transmission behavior with goodness-of-fit of 76-92 per cent, and the estimates are improved by 35-72 per cent in terms of the RMSE for the proposed dynamic model as compared to the conventional rigid model.

In this paper, the design of a novel bilateral telerobotic architecture for rehabilitation purposes is proposed and the related feasibility, stability, and control challenges are studied. The objective is to incorporate the supervision of a local/remote human physiotherapist into haptics-enabled rehabilitation systems and allow the therapist to provide nonpassive nonlinear assistive/resistive forces in response to the patient's movements. This can address a challenge of conventional software-based rehabilitation systems, i.e., limited capability in adjusting the therapy. To guarantee human-robot interaction safety, a new design framework and a stabilizing controller are developed based on the small-gain approach. System stability and transparency are analyzed in the presence of the nonpassive, nonlinear, and nonautonomous behavior of the terminals (the therapist and the patient) and time-varying delays for the case of remote and cloud-based therapy. Several practical considerations have been taken into account to match the clinical needs and minimize the implementation cost. Simulation studies, practical implementation, and experimental evaluations are presented.

In this paper, based on the apparent stiffness analysis of a dual tendon-sheath system, we propose a method for using a surgical instrument of the da Vinci surgical robotic system (from Intuitive Surgical Inc.) for estimation of mechanical properties of tissues. The performance of the method is experimentally evaluated by comparing tissues with different stiffnesses and by localizing tumors in an artificial tissue sample.

Two simplified quasi-static models for the da Vinci instrument are proposed which take into account distributed frictions and compliance of the tendons. These models are derived from static analysis of the interaction of the tendons with a curved surface. The key parameters of the models are identified, and the performance of the models is experimentally evaluated. Experimental results obtained suggest that a weighted combination of the outputs of the two models provides a sufficiently close estimate of the output torque of the da Vinci instrument.

Implementation of haptic feedback in minimally invasive surgical teleoperator systems may lead to improved performance in many common surgical procedures; however, most of the currently available surgical teleoperators do not provide force feedback, mainly because of the associated stability issues. In this paper, we study the effect of a special type of force reflection algorithms, called projection-based force reflection (PBFR) algorithms, on the stability and performance of a dual-arm haptics-enabled teleoperator system for minimally-invasive surgical applications. In particular, the teleoperator system's performance is experimentally evaluated in three common tasks, which are knot tightening, pegboard transfer, and object manipulation, in the presence of negligible as well as non-negligible communication delays. The results obtained indicate that, in almost all cases, the PBFR algorithms demonstrate statistically significant improvement of performance in comparison with conventional direct force feedback.

The projection-based force reflection (PBFR) algorithms were previously demonstrated to substantially improve stability characteristics of the force reflecting teleoperator systems and haptic interfaces without transparency deterioration in the steady state; however, the transient response of the PFBR algorithms suffers from relatively slow force convergence. In particular, the high frequency component of the contact force, which is very important for the haptic perception of stiff surfaces, is typically filtered out. In this paper, a solution to this problem is proposed which is based on the idea to separate different frequency bands in the force reflection signal and consequently apply the projection-based principle to the low-frequency component, while reflecting the high-frequency component directly. It is shown that, for bilateral teleoperators with irregular communication delays, stability can always be achieved by implementing the above described force reflection scheme, if the cut-off frequency of the complementary filters is sufficiently high and a certain weighting coefficient in the force reflection algorithm is sufficiently low. Experimental results demonstrate that substantial simultaneous improvement of stability and transparency is achieved using the proposed method.

The problem of designing of a haptics-enabled teleoperated rehabilitation system in the presence of communication delays is addressed. In a teleoperated rehabilitation system, communication delays introduce phase shift which may result in the task inversion phenomenon. To overcome the task inversion, a new type of projection-based force reflection algorithm is proposed which is suitable for assistive/resistive therapy in the presence of irregular communication delays. Additionally, algorithms for augmented therapy are introduced which combine the projection-based force reflection with a delay-free local virtual therapist. A small-gain design is developed which guarantees stability of the proposed schemes for both assistive and resistive modes of the therapy. Simulations and experimental results are presented which confirm the improvement achieved by the proposed methods.

In master-slave teleoperator systems used for tele-rehabilitation purposes, the passivity can be violated because of the assistive actions of a therapist; moreover, any type of passivation approach to the design of such a system would defeat the purpose of the assistive therapy. In this paper, a design framework is presented that does not rely on passivity considerations. A number of results are given that deal with stability and transparency properties of the tele-rehabilitation system in the case of intrinsically non-passive behaviour of the therapist. In particular, a stabilization scheme for the networked tele-rehabilitation system is proposed which guarantees stability regardless of the specific actions of the therapist. Simulation results are presented which confirm the theoretical developments.

Modeling errors are one of the elements responsible for deficiencies in sensorless collision detection of robotic systems. By providing a specific formulation of manipulator equations, this paper presents a time-variant threshold for observer residues in joint space of a manipulator in order to provide more accurate collision detection ability compared to constant thresholds. The time-variant threshold considers modeling errors in both robot's parameters and its friction forces. Simulation results using real-life collision forces and experiments on the Phantom Omni device are provided to validate the proposed scheme.

For cooperative force-reflecting teleoperation over networks, conventional passivity-based approaches are not always applicable due to possibility of nonpassive slave-slave interactions and irregular communication delays imposed by networks. In this work, we propose a design approach that is based on an advanced version of the small-gain theorem developed previously for complex network-based interconnections. It is shown that, using the proposed design approach, a networked cooperative force-reflecting teleoperator system can be made stable in the presence of irregular communications by adjusting the local control gains appropriately. Experimental results are presented that confirm the validity of the proposed approach.

Developments to the small-gain design approach to networked cooperative force-reflecting teleoperators are presented. Explicit assumptions on the human dynamics are incorporated into the stability analysis, and the conservatism of the small-gain design is eliminated using the projection-based force reflection principle. Results are established that describe the stability properties of the networked cooperative teleoperator system under different conditions on the human dynamics and for different types of the force reflection algorithms. Samples of experimental results are presented.

Results of experimental studies of a teleoperator system with projection-based force reflection algorithms in the presence of communication constraints are presented. It is demonstrated that, using the projection-based force reflection algorithms, the admissible force reflection gain can be substantially increased without loosing the overall stability, which confirms the earlier theoretical results. It is also shown that this improvement is achieved without transparency deterioration.

A general stability result for force-reflecting teleoperator systems with projection-based force reflection algorithms is established. It is shown that the closed-loop system’s gain can be assigned arbitrarily by an appropriate choice of certain weighting function of the projection-based force reflection algorithm. In particular, this allows to achieve stability of the force-reflecting teleoperator system in presence of timevarying irregular delays for arbitrarily large force-reflecting gain and arbitrarily low damping and stiffness of the master. The proposed approach solves, to some extent, the trade-off between stability, manoeuvrability, and high force reflection gain in force-reflecting teleoperator system with network-induced communication constraints.

The problem of stable force-reflecting teleoperation is addressed where the communication between the master and the slave is subject to multiple time-varying, discontinuous, and possibly unbounded communication delays. A new force reflection algorithm is proposed which improves the stability of the system without decreasing its transparency. Based on an estimate of the human forces provided by a high-gain input observer, the proposed algorithm restricts the reflected force in such a way that it eliminates the motion of the master induced by the force reflection signal without changing the human perception of the environmental force. It is shown that the force reflection algorithm proposed allows to achieve stability of the system for arbitrarily high force-reflection gain and arbitrarily low damping/stiffness of the master manipulator.

The problem of stable force-reflecting teleoperation with time-varying communication delay is addressed. A new force reflection algorithm is presented, where the environmental force reflected on the master side can be altered depending on the forces applied by the human operator. This alteration is not felt by the human operator, however, it makes the force reflection safe in the sense it does not destroy the stability of the teleoperator. In particular, using IOS small gain approach, it is shown that the overall stability in the teleoperator system with the force-reflecting algorithm proposed can be achieved theoretically for arbitrarily low damping on the master side and arbitrarily high force-reflection gain. The simulation results are presented that confirm that the proposed scheme allows to decrease master damping significantly, and thus improve the transparency of force-reflecting teleoperation, without sacrificing the overall stability

The problem of force-reflecting teleoperation over Internet protocol networks is addressed. The existence of time-varying communication delay and the possibility of data losses are taken into consideration. Since significant data loss may result in discontinuity of the reference trajectory transmitted through the communication channel, the proposed control scheme includes a filter that provides a smooth approximation of a possibly discontinuous reference trajectory. The stability of the overall system is guaranteed by a version of the input-to-output stable small-gain theorem for functional differential equations. If the communication delay in the forward channel is an "approximately smooth" function of time, the proposed scheme guarantees that the slave manipulator tracks the delayed trajectory of the master within a prescribed small error.

The problem of force-reflecting teleoperation over IP networks is addressed. The existence of time-varying communication delay and possibility of data packets dropouts are taken into consideration. Since significant data dropouts may result in discontinuity of the reference trajectory transmitted through the communication channel, the proposed control scheme includes a filter that provides a smooth approximation of a possibly discontinuous reference trajectory. The stability of the overall system is guaranteed by a version of the IOS small gain theorem for functional-differential equations. It is also shown that, in the case of reliable communication protocols, the proposed scheme guarantees that the slave manipulator tracks the delayed trajectory of the master with a prescribed small error.