Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Tracking control for a cascade perturbed control system using the active disturbance rejection paradigm

In this paper the stability of a closed-loop cascade control system in the trajectory tracking task is addressed. The considered plant consists of underlying second-order fully actuated perturbed dynamics and the first order system which describes dynamics of the input. The main theoretical result presented in the paper concerns stability conditions formulated based on the Lyapunov analysis for the cascade control structure taking advantage of the active rejection disturbance approach. In particular, limitations imposed on a feasible set of an observer bandwidth are discussed. In order to illustrate characteristics of the closed-loop control system simulation results are presented. Furthermore, the controller is verified experimentally using a two-axis telescope mount. The obtained results confirm that the considered control strategy can be efficiently applied for mechanical systems when a high tracking precision is required.Comment: 17 pages, 8 figures, 2 table

Control of Flexible Manipulator Robots Based on Dynamic Confined Space of Velocities: Dynamic Programming Approach

Linear Parameter Varying models-based Model Predictive Control (LPV-MPC) has stood out in manipulator robots because it presents well-rejection to dynamic uncertainties in flexible joints. However, it has become too weak when the MPC's optimization problem does not include kinematic constraints-based conditions. This paper uses dynamic confined space of velocities (DCSV) to include these conditions as a recursive polytopic constraint, guaranteeing optimal dependency on a simplex scheduling parameter. To this end, the local frame's velocities and torque/force preload of joints (related to violation of kinematic constraints) are associated with different time scale dynamics such that DCSV correlates them as a polytope. So, a classical LPV-MPC will be updated using a dynamic programming approach according to the DCSV-based polytope. As a result, one lemma about DCSV-based recursive polytope and a five-step procedure for two decoupled close-loop schemes with different time scales compose the LPV-MPC proposed method. Numerical validation shows that even for relevant flexibility situations, trajectory tracking performance is improved by tuning finite horizons and optimization problem constraints regarding DCSV's behavior

Adaptive fuzzy sliding mode algorithm-based decentralised control for a permanent magnet spherical actuator

<p>The dynamic model of multi-degree-of-freedom permanent magnet (PM) spherical actuators is multivariate and nonlinear due to strong inter-axis couplings, which affects the trajectory tracking performance of the system. In this paper, a decentralised control strategy based on adaptive fuzzy sliding mode (AFSM) algorithm is developed for a PM spherical actuator to enhance its trajectory tracking performance. In this algorithm, the coupling terms are separated as subsystems from the entire system. The AFSM algorithm is applied in such a way that the fuzzy logic systems are used to approximate the subsystem with uncertainties. A sliding mode term is introduced to compensate for the effect of coupling terms and fuzzy approximation error. The stability of the proposed method is guaranteed by choosing the appropriate Lyapunov function. Both simulation and experimental results show that the proposed control algorithm can effectively handle various uncertainties and inter-axis couplings, and improve the trajectory tracking precision of the spherical actuator.</p

An Omnidirectional Aerial Platform for Multi-Robot Manipulation

The objectives of this work were the modeling, control and prototyping of a new fully-actuated aerial platform. Commonly, the multirotor aerial platforms are under-actuated vehicles, since the total propellers thrust can not be directed in every direction without inferring a vehicle body rotation. The most common fully-actuated aerial platforms have tilted or tilting rotors that amplify the aerodynamic perturbations between the propellers, reducing the efficiency and the provided thrust. In order to overcome this limitation a novel platform, the ODQuad (OmniDirectional Quadrotor), has been proposed, which is composed by three main parts, the platform, the mobile and rotor frames, that are linked by means of two rotational joints, namely the roll and pitch joints. The ODQuad is able to orient the total thrust by moving only the propellers frame by means of the roll and pitch joints. Kinematic and dynamic models of the proposed multirotor have been derived using the Euler- Lagrange approach and a model-based controller has been designed. The latter is based on two control loops: an outer loop for vehicle position control and an inner one for vehicle orientation and roll-pitch joint control. The effectiveness of the controller has been tested by means of numerical simulations in the MATLAB c SimMechanics environment. In particular, tests in free motion and in object transportation tasks have been carried out. In the transportation task simulation, a momentum based observer is used to estimate the wrenches exchanged between the vehicle and the transported object. The ODQuad concept has been tested also in cooperative manipulation tasks. To this aim, a simulation model was considered, in which multiple ODQuads perform the manipulation of a bulky object with unknown inertial parameters which are identified in the first phase of the simulation. In order to reduce the mechanical stresses due to the manipulation and enhance the system robustness to the environment interactions, two admittance filters have been implemented: an external filter on the object motion and an internal one local for each multirotor. Finally, the prototyping process has been illustrated step by step. In particular, three CAD models have been designed. The ODQuad.01 has been used in the simulations and in a preliminary static analysis that investigated the torque values for a rough sizing of the roll-pitch joint actuators. Since in the ODQuad.01 the components specifications and the related manufacturing techniques have not been taken into account, a successive model, the ODQuad.02, has been designed. The ODQuad.02 design can be developed with aluminum or carbon fiber profiles and 3D printed parts, but each component must be custom manufactured. Finally, in order to shorten the prototype development time, the ODQuad.03 has been created, which includes some components of the off-the-shelf quadrotor Holybro X500 into a novel custom-built mechanical frame

Nonlinear Control Strategies for Outdoor Aerial Manipulators

In this thesis, the design, validation and implementation of nonlinear control strategies for aerial manipulators {i.e. aerial robots equipped with manipulators{ is studied, with special emphasis on the internal coupling of the system and its resilience against external disturbances. For the rst, di erent decentralised control strategies {i.e. using di erent control typologies for each one of the subsystems{ that indirectly take into account this coupling have been analysed. As a result, a nonlinear strategy composed of two controllers is proposed. A higher priority is given to the manipulation accuracy, relaxing the platform tracking, and hence obtaining a solution improving the manipulation capabilities with the surrounding environment. To validate these results, thorough stability and robustness analyses are provided, both theoretically and in simulation. On the other hand, a signi cant e ort has been devoted to improving the response and applicability of robot manipulators used in ight via control. In particular, the design of controllers for lightweight exible manipulators {that reduce the consequences of incidents involving unforeseen contacts{ is analysed. Although their inherent nature perfectly ts for aerial manipulation applications, the added exibility produces unwanted behaviours, such as second-order modes and uncertainties. To cope with them, an adaptable position nonlinear control strategy is proposed. To validate this contribution, the stability of the approach is studied in theory and its capabilities are proven in several experimental scenarios. In these, the robustness of the solution against unforeseen impacts and contact with uncharacterised interfaces is demonstrated. Subsequently, this strategy has been enriched with {multiaxis{ force control capabilities thanks to the inclusion of an outer control loop modifying the manipulator reference. Accordingly, this additional applicationfocused capability is added to the controlled system without loosing the modulated response of the inner-loop position strategy. It is also worth noting that, thanks to the cascade-like nature of the modi cation, the transition between position and force control modes is inherently smooth and automatic. The stability of this expanded strategy has been theoretically analysed and the results validated in a set of experimental scenarios. To validate the rst nonlinear approach with realistic outdoor simulations before its implementation, a computational uid dynamics analysis has been performed to obtain an explicit model of the aerodynamic forces and torques applied to the blunt-body of the aerial platform in ight. The results of this study have been compared to the most common alternative nowadays, being highlighted that the proposed model signi cantly surpasses this option in terms of accuracy. Moreover, it is worth underscoring that this characterisation could be also employed in the future to develop control solutions with enhanced rejection capabilities against wind conditions. Finally, as the focus of this thesis is on the use of novel control strategies on real aerial manipulation outdoors to improve their accuracy while performing complex tasks, a modular autopilot solution to be able to implement them has been also developed. This general-purpose autopilot allows the implementation of new algorithms, and facilitates their theory-to-experimentation transition. Taking into account this perspective, the proposed tool employs the simple and widely-known MAS interface and the highly reliable PX4 autopilot as backup, thus providing a redundant approach to handle unexpected incidents in ight.En esta tesis se ha estudiado el diseño, validación e implementación de estrategias de control no lineales para robots manipuladores aéreos –esto es, robots aéreos equipados con un sistema de manipulación robótica–, dándose especial énfasis a las interacciones internas del sistema y a su resiliencia frente a efectos externos. Para lo primero, se han analizado diferentes estrategias de control descentralizado –es decir, que usan tipologías de control diferentes para cada uno de los subsistemas–, pero que tienen indirectamente en consideración la interacción entre manipulación y vuelo. Como resultado de esta línea, se propone una estretegia de control conformada por dos controladores. Estos se coordinan de tal forma que se le da prioridad a la manipulación sobre el seguimiento de posiciones del vehículo, produciéndose un sistema de control que mejora la precisión de las interacciones entre el sistema manipulador y el entorno. Para validar estos resultados, se ha analizado su estabilidad y robustez tanto teóricamente como mediante simulaciones numéricas. Por otro lado, se ha buscado mejorar la respuesta y aplicabilidad de los manipuladores que se usan en vuelo mediante su control. Dentro de esta tendencia, la tesis se ha centrado en el diseño de controladores para manipuladores ligeros flexibles, ya que estos permiten reducir el peso del sistema completo y reducen el riesgo de incidentes debidos a contactos inesperados. Sin embargo, la flexibilidad de estos produce comportamientos indeseados durante la operación, como la aparición de modos de segundo orden y cierta incentidumbre en su comportamiento. Para reducir su impacto en la precisión de las tareas de manipulación, se ha desarrollado un controlador no lineal adaptable. Para validar estos resultados, se ha analizado la estabilidad del sistema teóricamente y se han desarrollado una serie de experimentos. En ellos, se ha comprobado su robustez ante impactos inesperados y contactos con elementos no caracterizados. Posteriormente, esta estrategia para manipuladores flexibles ha sido ampliada al añadir un bucle externo que posibilita el control en fuerzas en varias direcciones. Esto permite, mediante un único controlador, mantener la suave respuesta de la estrategia. Además cabe destacar que, al contar esta estrategia con un diseño en cascade, la transición entre los segmentos de desplazamiento del brazo y de aplicación de fuerzas es fluida y automática. La estabilidad de esta estrategia ampliada ha sido analizada teóricamente y los resultados han sido validados experimentalmente. Para validar la primera estrategia mediante simulaciones que representen fielmente las condiciones en exteriores antes de su implementación, ha sido necesario realizar un estudio mediante mecánica de fluidos computacional para obtener un modelo explícito de las fuerzas y momentos aerodinámicos a los que se efrenta la plataforma en vuelo. Los resultados de este estudio han sido comparados con la alternativa más empleada actualmente, mostrándose que los avances del método propuesto son sustanciales. Asimismo, es importante destacar que esta caracterización podría también usarse en el futuro para desarrollar controladores con una respuesta mejorada ante perturbaciones aerodinámicas, como en el caso de volar con viento. Finalmente, al ser esta una tesis centrada en las estrategias de control novedosas en sistemas reales para la mejora de su rendimiento en misiones complejas, se ha desarrollado un autopiloto modular fácilmente modificable para implementarlas. Este permite validar experimentalmente nuevos algoritmos y facilita la transición entre teoría y práctica. Para ello, esta herramienta se basa en una interfaz sencilla ampliamente conocida por los investigadores de robótica, Simulink®, y cuenta con un autopiloto de respaldo, PX4, para enfrentarse a los incidentes inesperados que pudieran surgir en vuelo

Two-link lower limb exoskeleton model control enhancement using computed torque

Robotic technology has recently been used to help stroke patients with gait and balance rehabilitation. Rehabilitation robots such as gait trainers are designed to assist patients in systematic, repetitive training sessions to speed up their recovery from injuries. Several control algorithms are commonly used on exoskeletons, such as proportional, integral and derivative (PID) as linear control. However, linear control has several disadvantages when applied to the exoskeleton, which has the problem of uncertainties such as load and stiffness variations of the patient’s lower limb. To improve the lower limb exoskeleton for the gait trainer, the computed torque controller (CTC) is introduced as a control approach in this study. When the dynamic properties of the system are only partially known, the computed torque controller is an essential nonlinear controller. A mathematical model forms the foundation of this controller. The suggested control approach’s effectiveness is evaluated using a model or scaled-down variation of the method. The performance of the suggested calculated torque control technique is then evaluated and contrasted with that of the PID controller. Because of this, the PID controller’s steady-state error in the downward direction can reach 5.6%, but the CTC can lower it to 2.125%