Robust H-infinity finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This technical note addresses the robust H∞ finite-horizon output feedback control problem for a class of uncertain discrete stochastic nonlinear time-varying systems with both sensor and actuator saturations. In the system under investigation, all the system parameters are allowed to be time-varying, the parameter uncertainties are assumed to be of the polytopic type, and the stochastic nonlinearities are described by statistical means which can cover several classes of well-studied nonlinearities. The purpose of the problem addressed is to design an output feedback controller, over a given finite-horizon, such that the H∞ disturbance attenuation level is guaranteed for the nonlinear stochastic polytopic system in the presence of saturated sensor and actuator outputs. Sufficient conditions are first established for the robust H∞ performance through intensive stochastic analysis, and then a recursive linear matrix inequality (RLMI) approach is employed to design the desired output feedback controller achieving the prescribed H∞ disturbance rejection level. Simulation results demonstrate the effectiveness of the developed controller design scheme.This work was supported under Australian Research Council’s Discovery Projects funding scheme (project DP0880494) and by the German Science Foundation (DFG) within the priority programme 1305: Control Theory of Digitally Networked Dynamical Systems. Recommended by Associate Editor H. Ito

Control of Cooperative Haptics-Enabled Teleoperation Systems with Application to Minimally Invasive Surgery

Robot-Assisted Minimally Invasive Surgical (RAMIS) systems frequently have a structure of cooperative teleoperator systems where multiple master-slave pairs are used to collaboratively execute a task. Although multiple studies indicate that haptic feedback improves the realism of tool-tissue interaction to the surgeon and leads to better performance for surgical procedures, current telesurgical systems typically do not provide force feedback, mainly because of the inherent stability issues. The research presented in this thesis is directed towards the development of control algorithms for force reflecting cooperative surgical teleoperator systems with improved stability and transparency characteristics. In the case of cooperative force reflecting teleoperation over networks, conventional passivity based approaches may have limited applicability due to potentially non-passive slave-slave interactions and irregular communication delays imposed by the network. In this thesis, an alternative small gain framework for the design of cooperative network-based force reflecting teleoperator systems is developed. Using the small gain framework, control algorithms for cooperative force-reflecting teleoperator systems are designed that guarantee stability in the presence of multiple network-induced communication constraints. Furthermore, the design conservatism typically associated with the small-gain approach is eliminated by using the Projection-Based Force Reflection (PBFR) algorithms. Stability results are established for networked cooperative teleoperator systems under different types of force reflection algorithms in the presence of irregular communication delays. The proposed control approach is consequently implemented on a dual-arm (two masters/two slaves) robotic MIS testbed. The testbed consists of two Haptic Wand devices as masters and two PA10-7C robots as the slave manipulators equipped with da Vinci laparoscopic surgical instruments. The performance of the proposed control approach is evaluated in three different cooperative surgical tasks, which are knot tightening, pegboard transfer, and object manipulation. The experimental results obtained indicate that the PBFR algorithms demonstrate statistically significant performance improvement in comparison with the conventional direct force reflection algorithms. One possible shortcoming of using PBFR algorithms is that implementation of these algorithms may lead to attenuation of the high-frequency component of the contact force which is important, in particular, for haptic perception of stiff surfaces. In this thesis, a solution to this problem is proposed which is based on the idea of separating the different frequency bands in the force reflection signal and consequently applying the projection-based principle to the low-frequency component, while reflecting the high-frequency component directly. The experimental results demonstrate that substantial improvement in transient fidelity of the force feedback is achieved using the proposed method without negative effects on the stability of the system

Expert-in-the-Loop Multilateral Telerobotics for Haptics-Enabled Motor Function and Skills Development

Among medical robotics applications are Robotics-Assisted Mirror Rehabilitation Therapy (RAMRT) and Minimally-Invasive Surgical Training (RAMIST) that extensively rely on motor function development. Haptics-enabled expert-in-the-loop motor function development for such applications is made possible through multilateral telerobotic frameworks. While several studies have validated the benefits of haptic interaction with an expert in motor learning, contradictory results have also been reported. This emphasizes the need for further in-depth studies on the nature of human motor learning through haptic guidance and interaction. The objective of this study was to design and evaluate expert-in-the-loop multilateral telerobotic frameworks with stable and human-safe control loops that enable adaptive “hand-over-hand” haptic guidance for RAMRT and RAMIST. The first prerequisite for such frameworks is active involvement of the patient or trainee, which requires the closed-loop system to remain stable in the presence of an adaptable time-varying dominance factor. To this end, a wave-variable controller is proposed in this study for conventional trilateral teleoperation systems such that system stability is guaranteed in the presence of a time-varying dominance factor and communication delay. Similar to other wave-variable approaches, the controller is initially developed for the Velocity-force Domain (VD) based on the well-known passivity assumption on the human arm in VD. The controller can be applied straightforwardly to the Position-force Domain (PD), eliminating position-error accumulation and position drift, provided that passivity of the human arm in PD is addressed. However, the latter has been ignored in the literature. Therefore, in this study, passivity of the human arm in PD is investigated using mathematical analysis, experimentation as well as user studies involving 12 participants and 48 trials. The results, in conjunction with the proposed wave-variables, can be used to guarantee closed-loop PD stability of the supervised trilateral teleoperation system in its classical format. The classic dual-user teleoperation architecture does not, however, fully satisfy the requirements for properly imparting motor function (skills) in RAMRT (RAMIST). Consequently, the next part of this study focuses on designing novel supervised trilateral frameworks for providing motor learning in RAMRT and RAMIST, each customized according to the requirements of the application. The framework proposed for RAMRT includes the following features: a) therapist-in-the-loop mirror therapy; b) haptic feedback to the therapist from the patient side; c) assist-as-needed therapy realized through an adaptive Guidance Virtual Fixture (GVF); and d) real-time task-independent and patient-specific motor-function assessment. Closed-loop stability of the proposed framework is investigated using a combination of the Circle Criterion and the Small-Gain Theorem. The stability analysis addresses the instabilities caused by: a) communication delays between the therapist and the patient, facilitating haptics-enabled tele- or in-home rehabilitation; and b) the integration of the time-varying nonlinear GVF element into the delayed system. The platform is experimentally evaluated on a trilateral rehabilitation setup consisting of two Quanser rehabilitation robots and one Quanser HD2 robot. The framework proposed for RAMIST includes the following features: a) haptics-enabled expert-in-the-loop surgical training; b) adaptive expertise-oriented training, realized through a Fuzzy Interface System, which actively engages the trainees while providing them with appropriate skills-oriented levels of training; and c) task-independent skills assessment. Closed-loop stability of the architecture is analyzed using the Circle Criterion in the presence and absence of haptic feedback of tool-tissue interactions. In addition to the time-varying elements of the system, the stability analysis approach also addresses communication delays, facilitating tele-surgical training. The platform is implemented on a dual-console surgical setup consisting of the classic da Vinci surgical system (Intuitive Surgical, Inc., Sunnyvale, CA), integrated with the da Vinci Research Kit (dVRK) motor controllers, and the dV-Trainer master console (Mimic Technology Inc., Seattle, WA). In order to save on the expert\u27s (therapist\u27s) time, dual-console architectures can also be expanded to accommodate simultaneous training (rehabilitation) for multiple trainees (patients). As the first step in doing this, the last part of this thesis focuses on the development of a multi-master/single-slave telerobotic framework, along with controller design and closed-loop stability analysis in the presence of communication delays. Various parts of this study are supported with a number of experimental implementations and evaluations. The outcomes of this research include multilateral telerobotic testbeds for further studies on the nature of human motor learning and retention through haptic guidance and interaction. They also enable investigation of the impact of communication time delays on supervised haptics-enabled motor function improvement through tele-rehabilitation and mentoring

Stability of Bilateral Teleoperators with Projection-Based Force Reflection Algorithms

Abstract-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

Therapist-in-the-Loop robotics-assisted mirror rehabilitation therapy: An Assist-as-Needed framework

framework for robotics-assisted mirror rehabilitation therapy integrated with adaptive Assist-as-Needed (ANN) training, to be adjusted based on the impairment and disability level of the patient’s affected limb. Closed-loop system stability has been investigated using a combination of the Circle Criterion and the Small-Gain Theorem to account both for time-delay and the time-varying adaptive ANN training. Experiments to investigate the performance of the proposed framework are reported. I

Posture-Dependent Projection-Based Force Reflection Algorithms for Bilateral Teleoperators

It was previously established that the projection-based force reflection (PBFR) algorithms improve the overall stability of a force reflecting teleoperation system. The idea behind the PBFR algorithms is to identify the component of the reflected force which is compensated by interaction with the operator\u27s hand, and subsequently attenuate the residual component of the reflected force. If there is no a priori information regarding the behaviour of the human operator, the PBFR gain is selected equal to sufficiently small constant in order to guarantee stability for a wide range of human operator responses. Small PBRF gains, however, may deteriorate the transparency of a teleoperator system. In this thesis, a new method for selecting the PBFR gain is introduced which depends on human postures. Using an online human posture estimation, the introduced posture-dependent PBFR algorithm has been applied to a teleoperation system with force feedback. It is experimentally demonstrated that the developed method for selection of the PBFR gain based on human postures improves the transparency of the teleoperator system while the stability is preserved. Finally, preliminary results that deal with an extension of the developed methods towards a more realistic model of the human arm with 4 degrees of freedom and three dimensional movements are presented

Safe Haptics-enabled Patient-Robot Interaction for Robotic and Telerobotic Rehabilitation of Neuromuscular Disorders: Control Design and Analysis

Motivation: Current statistics show that the population of seniors and the incidence rate of age-related neuromuscular disorders are rapidly increasing worldwide. Improving medical care is likely to increase the survival rate but will result in even more patients in need of Assistive, Rehabilitation and Assessment (ARA) services for extended periods which will place a significant burden on the world\u27s healthcare systems. In many cases, the only alternative is limited and often delayed outpatient therapy. The situation will be worse for patients in remote areas. One potential solution is to develop technologies that provide efficient and safe means of in-hospital and in-home kinesthetic rehabilitation. In this regard, Haptics-enabled Interactive Robotic Neurorehabilitation (HIRN) systems have been developed. Existing Challenges: Although there are specific advantages with the use of HIRN technologies, there still exist several technical and control challenges, e.g., (a) absence of direct interactive physical interaction between therapists and patients; (b) questionable adaptability and flexibility considering the sensorimotor needs of patients; (c) limited accessibility in remote areas; and (d) guaranteeing patient-robot interaction safety while maximizing system transparency, especially when high control effort is needed for severely disabled patients, when the robot is to be used in a patient\u27s home or when the patient experiences involuntary movements. These challenges have provided the motivation for this research. Research Statement: In this project, a novel haptics-enabled telerobotic rehabilitation framework is designed, analyzed and implemented that can be used as a new paradigm for delivering motor therapy which gives therapists direct kinesthetic supervision over the robotic rehabilitation procedure. The system also allows for kinesthetic remote and ultimately in-home rehabilitation. To guarantee interaction safety while maximizing the performance of the system, a new framework for designing stabilizing controllers is developed initially based on small-gain theory and then completed using strong passivity theory. The proposed control framework takes into account knowledge about the variable biomechanical capabilities of the patient\u27s limb(s) in absorbing interaction forces and mechanical energy. The technique is generalized for use for classical rehabilitation robotic systems to realize patient-robot interaction safety while enhancing performance. In the next step, the proposed telerobotic system is studied as a modality of training for classical HIRN systems. The goal is to first model and then regenerate the prescribed kinesthetic supervision of an expert therapist. To broaden the population of patients who can use the technology and HIRN systems, a new control strategy is designed for patients experiencing involuntary movements. As the last step, the outcomes of the proposed theoretical and technological developments are translated to designing assistive mechatronic tools for patients with force and motion control deficits. This study shows that proper augmentation of haptic inputs can not only enhance the transparency and safety of robotic and telerobotic rehabilitation systems, but it can also assist patients with force and motion control deficiencies