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

Experimental Evaluation of the Projection-based Force Reflection Algorithms for Haptic Interaction with Virtual Environment

Haptic interaction with virtual environments is currently a major and growing area of research with a number of emerging applications, particularly in the field of robotics. Digital implementation of the virtual environments, however, introduces errors which may result in instability of the haptic displays. This thesis deals with experimental investigation of the Projection-Based Force Reflection Algorithms (PFRAs) for haptic interaction with virtual environments, focusing on their performance in terms of stability and transparency. Experiments were performed to compare the PFRA in terms of performance for both non-delayed and delayed haptic interactions with more conventional haptic rendering methods, such as the Virtual Coupling (VC) and Wave Variables (WV). The results demonstrated that the PFRA is more stable, guarantees higher levels of transparency, and is less sensitive to decrease in update rates

Input-to-state stability of infinite-dimensional control systems

We define the notion of local ISS-Lyapunov function and prove, that existence of a local ISS-Lyapunov function implies local ISS (LISS) of the system. Then we consider infinite-dimensional systems generated by differential equations in Banach spaces. We prove, that an interconnection of such systems is ISS if all the subsystems are ISS and the small-gain condition holds. Next we show that a system is LISS provided its linearization is ISS. In the second part of the thesis we deal with infinite-dimensional impulsive systems. We prove, that existence of an ISS Lyapunov function (not necessarily exponential) for an impulsive system implies ISS of the system over impulsive sequences satisfying nonlinear fixed dwell-time condition. Also we prove, that an impulsive system, which possesses an exponential ISS Lyapunov function is uniform ISS over impulse time sequences, satisfying the generalized average dwell-time condition. Then we generalize small-gain theorems to the case of impulsive systems

Estimation de vitesse de rotation par mesures de direction

This thesis addresses the general question of estimating the angular rate of a rigid body from on-board direction sensors (e.g. magnetometers, Sun sensors). The objective is to replace rate gyros which are very expensive compared to direction sensors, prone to saturation during high rate rotations and subject to failure. In a first part of the thesis, we address the specific cases of single-axis and slightly perturbed axis rotations.In a second part, we address the general case by an asymptotic non-linear observer. We build the observer from two non-collinear vector measurements or from a single vector measurements. The knowledge of the inertial coordinates of the reference vectors is not necessary. We then extend the observer to further estimate unknown torques and inertia parameters. The Euler’s equations play a central role in all the works developed in this thesis. It appears that, at least for the illustrative cases considered, rate gyros could be replaced with an estimation algorithm employing direction sensors which are much cheaper,more rugged and more resilient sensors.Cette thèse étudie l’estimation de vitesse de rotation d’un corps rigide à partir de mesures de directions (par exemple champ magnétique, direction du soleil) embarquées. L’objectif est de remplacer les gyromètres qui sont chers comparés aux autres capteurs inertiels et sujets à des saturations et à des dysfonctionnements. Dans une première partie de la thèse, on traite les cas spécifiques d’une rotation à axe fixe ou légèrement variable. Dans une seconde partie, on traite le cas d’une rotation quelconque par un observateur asymptotique non-linéaire. On construit l’observateur à partir de mesures de deux vecteurs de référence non colinéaires, ou bien d’un seul vecteur. La connaissance des coordonnées inertielles des vecteurs de référence n’est pas nécessaire. On étend ensuite l’observateur pour estimer en plus le couple et les paramètres d’inertie. Les équations d’Euler jouent un rôle central dans les travaux présentés ici. Il apparaît que, du moins pour les illustrations considérées, les gyromètres peuvent être remplacés par un algorithme d’estimation basé sur des capteurs de direction qui sont bien moins chers et plus robustes

Generating timed trajectories foran autonomous robot

Tese de Doutoramento Programa Doutoral em Engenharia Electrónica e ComputadoresThe inclusion of timed movements in control architectures for mobile navigation has received an increasing attention over the last years. Timed movements allow modulat- ing the behavior of the mobile robot according to the elapsed time, such that the robot reaches a goal location within a specified time constraint. If the robot takes longer than expected to reach the goal location, its linear velocity is increased for compen- sating the delay. Timed movements are also relevant when sequences of missions are considered. The robot should follow the predefined time schedule, so that the next mission is initiated without delay. The performance of the architecture that controls the robot can be validated through simulations and field experiments. However, ex- perimental tests do not cover all the possible solutions. These should be guided by a stability analysis, which might provide directions to improve the architecture design in cases of inadequate performance of the architecture. This thesis aims at developing a navigation architecture and its stability analysis based on the Contraction Theory. The architecture is based on nonlinear dynamical systems and must guide a mobile robot, such that it reaches a goal location within a time constraint while avoiding unexpected obstacles in a cluttered and dynamic real environment. The stability analysis based on the Contraction Theory might provide conditions to the dynamical systems parameters, such that the dynamical systems are designed as contracting, ensuring the global exponential stability of the architecture. Furthermore, Contraction Theory provides solutions to analyze the success of the mis- sion as a stability problem. This provides formal results that evaluate the performance of the architecture, allowing the comparison to other navigation architectures. To verify the ability of the architecture to guide the mobile robot, several experi- mental tests were conducted. The obtained results show that the proposed architecture is able to drive mobile robots with timed movements in indoor environments for large distances without human intervention. Furthermore, the results show that the Con- traction Theory is an important tool to design stable control architectures and to analyze the success of the robotic missions as a stability problem.A inclusão de movimentos temporizados em arquitecturas de controlo para navegação móvel tem aumentado ao longo dos últimos anos. Movimentos temporizados permitem modular o comportamento do robô de tal forma que ele chegue ao seu destino dentro de um tempo especificado. Se o robô se atrasar, a sua velocidade linear deve ser aumen- tada para compensar o atraso. Estes movimentos são também importantes quando se consideram sequências de missões. O robô deve seguir o escalonamento da sequência, de tal forma que a próxima missão seja iniciada sem atraso. O desempenho da arqui- tectura pode ser validado através de simulações e experiências reais. Contudo, testes experimentais não cobrem todas as possíveis soluções. Estes devem ser conduzidos por uma análise de estabilidade, que pode fornecer direcções para melhorar o desempenho da arquitectura. O objectivo desta tese é desenvolver uma arquitectura de navegação e analisar a sua estabilidade através da teoria da Contracção. A arquitectura é baseada em sistemas dinâmicos não lineares e deve controlar o robô móvel num ambiente real, desordenado e dinâmico, de tal modo que ele chegue à posição alvo dentro de uma restrição de tempo especificada. A análise de estabilidade baseada na teoria da Contracção pode fornecer condições aos parâmetros dos sistemas dinâmicos de modo a desenha-los como contracções, e assim garantir a estabilidade exponencial global da arquitectura. Esta teoria fornece ainda soluções interessantes para analisar o sucesso da missão como um problema de estabilidade. Isto providencia resultados formais que avaliam o desem- penho da arquitectura e permitem a comparação com outras arquitecturas. Para verificar a habilidade da arquitectura em controlar o robô móvel, foram con- duzidos vários testes experimentais. Os resultados obtidos mostram que a arquitectura proposta é capaz de controlar robôs móveis com movimentos temporizados em ambi- entes interiores durante grandes distâncias e sem intervenção humana. Além disso, os resultados mostram que a teoria da Contracção é uma ferramenta importante para desenhar arquitecturas de controlo estáveis e para analisar o sucesso das missões efec- tuadas pelo robô como um problema de estabilidade.Portuguese Science and Technology Foundation (FCT) SFRH/BD/68805/2010

A sensitivity trade-off arising in small-gain design for nonlinear systems: an iISS framework

International audienceThis note investigates the trade-off arising in disturbance attenuation for nonlinear feedback systems in the framework of integral input-to-state stability. Similarly to the linear case, we show that if a gain tuning on one subsystem is used to drastically reduce the effect of its exogenous disturbances, then the other subsystem's disturbance attenuation is qualitatively the same as in open loop