On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Vision-based control of multi-agent systems

Scope and Methodology of Study: Creating systems with multiple autonomous vehicles places severe demands on the design of decision-making supervisors, cooperative control schemes, and communication strategies. In last years, several approaches have been developed in the literature. Most of them solve the vehicle coordination problem assuming some kind of communications between team members. However, communications make the group sensitive to failure and restrict the applicability of the controllers to teams of friendly robots. This dissertation deals with the problem of designing decentralized controllers that use just local sensor information to achieve some group goals.Findings and Conclusions: This dissertation presents a decentralized architecture for vision-based stabilization of unmanned vehicles moving in formation. The architecture consists of two main components: (i) a vision system, and (ii) vision-based control algorithms. The vision system is capable of recognizing and localizing robots. It is a model-based scheme composed of three main components: image acquisition and processing, robot identification, and pose estimation.Using vision information, we address the problem of stabilizing groups of mobile robots in leader- or two leader-follower formations. The strategies use relative pose between a robot and its designated leader or leaders to achieve formation objectives. Several leader-follower formation control algorithms, which ensure asymptotic coordinated motion, are described and compared. Lyapunov's stability theory-based analysis and numerical simulations in a realistic tridimensional environment show the stability properties of the control approaches

Dynamic Modeling and Control of Spherical Robots

In this work, a rigorous framework is developed for the modeling and control of spherical robotic vehicles. Motivation for this work stems from the development of Moball, which is a self-propelled sensor platform that harvests kinetic energy from local wind fields. To study Moball's dynamics, the processes of Lagrangian reduction and reconstruction are extended to robotic systems with symmetry-breaking potential energies, in order to simplify the resulting dynamic equations and expose mathematical structures that play an important role in subsequent control-theoretic tasks. These results apply to robotic systems beyond spherical robots. A formulaic procedure is introduced to derive the reduced equations of motion of most spherical robots from inspection of the Lagrangian. This adaptable procedure is applied to a diverse set of robotic systems, including multirotor aerial vehicles. Small time local controllability (STLC) results are derived for barycentric spherical robots (BSR), which are spherical vehicles whose locomotion depends on actuating the vehicle's center of mass (COM) location. STLC theorems are introduced for an arbitrary BSR on flat, sloped, or smooth terrain. I show that STLC depends on the surjectivity of a simple steering matrix. An STLC theorem is also derived for a class of commonly encountered multirotor vehicles. Feedback linearizing and PID controllers are proposed to stabilize an arbitrary spherical robot to a desired trajectory over smooth terrain, and direct collocation is used to develop a feedforward controller for Moball specifically. Moball's COM is manipulated by a novel system of magnets and solenoids, which are actuated by a "ballistic-impulse" controller that is also presented. Lastly, a motion planner is developed for energy-harvesting vehicles. This planner charts a path over smooth terrain while balancing the desire to achieve scientific objectives, avoid hazards, and the imperative of exposing the vehicle to environmental sources of energy such as local wind fields and topology. Moball's design details and experimental results establishing Moball's energy-harvesting performance (7W while rolling at a speed of 2 m/s), are contained in an Appendix.</p

A Large Scale Inertial Aided Visual Simultaneous Localization And Mapping (SLAM) System For Small Mobile Platforms

In this dissertation we present a robust simultaneous mapping and localization scheme that can be deployed on a computationally limited, small unmanned aerial system. This is achieved by developing a key frame based algorithm that leverages the multiprocessing capacity of modern low power mobile processors. The novelty of the algorithm lies in the design to make it robust against rapid exploration while keeping the computational time to a minimum. A novel algorithm is developed where the time critical components of the localization and mapping system are computed in parallel utilizing the multiple cores of the processor. The algorithm uses a scale and rotation invariant state of the art binary descriptor for landmark description making it suitable for compact large scale map representation and robust tracking. This descriptor is also used in loop closure detection making the algorithm efficient by eliminating any need for separate descriptors in a Bag of Words scheme. Effectiveness of the algorithm is demonstrated by performance evaluation in indoor and large scale outdoor dataset. We demonstrate the efficiency and robustness of the algorithm by successful six degree of freedom (6 DOF) pose estimation in challenging indoor and outdoor environment. Performance of the algorithm is validated on a quadcopter with onboard computation

Geometric methods for designing optimal filters on Lie groups

In control theory, the problem of having available good measurements is of primary importance in order to perform good tracking and control. Unfortunately, in real-life applications, sensing systems do not provide direct measurements about the pose (and its rate) of mechanical systems, while, in other situations, measurements are so noisy that require pre-processing to filter out disturbances and biases. These problems could be faced by using filters and observers. In this thesis, we apply a second-order optimal minimum-energy filter constructed on Lie groups to several planar bodies. We start by studying the application of the filter to the matrix Lie group TSE(2), i.e. the tangent bundle of the Special Euclidean group SE(2); moreover, a comparison with the extended Kalman filter is presented. After that, we consider the Chaplygin sleigh case, that is a mechanical system with a nonholonomic constraint. Then, we move our attention to the case of an articulated convoy with hooking constraints. Finally, we apply the filter to a real case scenario consisting of a scaled model representing a parking truck semi-trailer system. Particular attention is posed to the description of the geometric structure that underlies the dynamics and to the choice of the measurement equation, the affine connection, and the other parameters that define the filters. Simulations show the effectiveness of the proposed filters. The use of Lie groups theory for designing the filters is challenging, but the accuracy of the results, obtained considering the geometric structure and the symmetries of the system justifies the effort

Parameter tuning and cooperative control for automated guided vehicles

For several practical control engineering applications it is desirable that multiple systems can operate independently as well as in cooperation with each other. Especially when the transition between individual and cooperative behavior and vice versa can be carried out easily, this results in ??exible and scalable systems. A subclass is formed by systems that are physically separated during individual operation, and very tightly coupled during cooperative operation. One particular application of multiple systems that can operate independently as well as in concert with each other is the cooperative transportation of a large object by multiple Automated Guided Vehicles (AGVs). AGVs are used in industry to transport all kinds of goods, ranging from small trays of compact and video discs to pallets and 40-tonne coils of steel. Current applications typically comprise a ??eet of AGVs, and the vehicles transport products on an individual basis. Recently there has been an increasing demand to transport very large objects such as sewer pipes, rotor blades of wind turbines and pieces of scenery for theaters, which may reach lengths of over thirty meters. A realistic option is to let several AGVs operate together to handle these types of loads. This Ph.D. thesis describes the development, implementation, and testing of distributed control algorithms for transporting a load by two or more Automated Guided Vehicles in industrial environments. We focused on the situations where the load is connected to the AGVs by means of (semi-)rigid interconnections. Attention was restricted to control on the velocity level, which we regard as an intermediate step for achieving fully automatic operation. In our setup the motion setpoint is provided by an external host. The load is assumed to be already present on the vehicles. Docking and grasping procedures are not considered. The project is a collaboration between the company FROG Navigation Systems (Utrecht, The Netherlands) and the Control Systems group of the Technische Universiteit Eindhoven. FROG provided testing facilities including two omni-directional AGVs. Industrial AGVs are custom made for the transportation tasks at hand and come in a variety of forms. To reduce development times it is desirable to follow a model-based control design approach as this allows generalization to a broad class of vehicles. We have adopted rigid body modeling techniques from the ??eld of robotic manipulators to derive the equations of motion for the AGVs and load in a systematic way. These models are based on physical considerations such as Newton's second law and the positions and dimensions of the wheels, sensors, and actuators. Special emphasis is put on the modeling of the wheel-??oor interaction, for which we have adopted tire models that stem from the ??eld of vehicle dynamics. The resulting models have a clear physical interpretation and capture a large class of vehicles with arbitrary wheel con??gurations. This ensures us that the controllers, which are based on these models, are applicable to a broad class of vehicles. An important prerequisite for achieving smooth cooperative behavior is that the individual AGVs operate at the required accuracy. The performance of an individual AGV is directly related to the precision of the estimates for the odometric parameters, i.e. the effective wheel diameters and the offsets of the encoders that measure the steering angles of the wheels. Cooperative transportation applications will typically require AGVs that are highly maneuverable, which means that all the wheels of an individual AGV ahould be able to steer. Since there will be more than one steering angle encoder, the identi??cation of the odometric parameters is substantially more dif??cult for these omni-directional AGVs than for the mobile wheeled robots that are commonly seen in literature and laboratory settings. In this thesis we present a novel procedure for simultaneously estimating effective wheel diameters and steering angle encoder offsets by driving several pure circle segments. The validity of the tuning procedure is con??rmed by experiments with the two omni-directional test vehicles with varying loads. An interesting result is that the effective wheel diameters of the rubber wheels of our AGVs increase with increasing load. A crucial aspect in all control designs is the reconstruction of the to-be-controlled variables from measurement data. Our to-be-controlled variables are the planar motion of the load and the motions of the AGVs with respect to the load, which have to be reconstruct from the odometric sensor information. The odometric sensor information consists of the drive encoder and steering encoder readings. We analyzed the observability of an individual AGV and proved that it is theoretically possible to reconstruct its complete motion from the odometric measurements. Due to practical considerations, we pursued a more pragmatic least-squares based observer design. We show that the least-squares based motion estimate is independent of the coordinate system that is being used. The motion estimator was subsequently analyzed in a stochastic setting. The relation between the motion estimator and the estimated velocity of an arbitrary point on the vehicle was explored. We derived how the covariance of the velocity estimate of an arbitrary point on the vehicle is related to the covariance of the motion estimate. We proved that there is one unique point on the vehicle for which the covariance of the estimated velocity is minimal. Next, we investigated how the local motion estimates of the individual AGVs can be combined to yield one global estimate. When the load and AGVs are rigidly interconnected, it suf??ces that each AGVs broadcasts its local motion estimate and receives the estimates of the other AGVs. When the load is semi-rigidly interconnected to the AGVs, e.g. by means of revolute or prismatic joints, then generally each AGV needs to broadcasts the corresponding information matrix as well. We showed that the information matrix remains constant when the load is connected to the AGV with a revolute joint that is mounted at the aforementioned unique point with the smallest velocity estimate covariance. This means that the corresponding AGV does not have to broadcast its information matrix for this special situation. The key issue in the control design for cooperative transportation tasks is that the various AGVs must not counteract each others' actions. The decentralized controller that we derived makes the AGVs track an externally provided planar motion setpoint while minimizing the interconnection forces between the load and the vehicles. Although the control design is applicable to cooperative transportation by multiple AGVs with arbitrary semi-rigid AGV-load interconnections, it is noteworthy that a particularly elegant solution arises when all interconnections are completely rigid. Then the derived local controllers have the same structure as the controllers that are normally used for individual operation. As a result, changing a few parameter settings and providing the AGVs with identical setpoints is all that is required to achieve cooperative behavior on the velocity level for this situation. The observer and controller designs for the case that the AGVs are completely rigidly interconnected to the load were successfully implemented on the two test vehicles. Experi ments were carried out with and without a load that consisted of a pallet with 300 kg pave stones. The results were reproducible and illustrated the practical validity of the observer and controller designs. There were no substantial drawbacks when the local observers used only their local sensor information, which means that our setup can also operate satisfactory when the velocity estimates are not shared with the other vehicles

Safe navigation and human-robot interaction in assistant robotic applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Dexterous robotic motion planning using intelligent algorithms

The fundamental purpose of robots is to help humans in a variety of difficult tasks, enabling people to increase their capabilities of strength, energy, speed, memory, and to operate in hazardous environments and many other applications. Service robots, more precisely mobile manipulators, incorporate one or two robotic arms and a mobile base, and must accomplish complex manipulations tasks, interacting with tools or objects and navigating through cluttered environments. To this end, the motion planning problem plays a key role in the ahead calculation of robot movements to interact with its world and achieve the established goals. The objective of this work is to design various motion planning methods in order to improve the autonomy of MANFRED-2, which is a mobile robot fully developed by the Robotics Lab research group of the Systems Engineering and Automation Department of the Carlos III University of Madrid. Mobile robots need to calculate accurate paths in order to navigate and interact with objects throughout their surrounding area. In this work, we have developed motion planning algorithms for both navigation and manipulation. The presented algorithms for path planning are based on the Fast Marching Square method and include a replanner with subgoals, an anytime triangular planner, and a nonholonomic approach. The replanner with subgoals starts by generating a smooth and safe global path with the Fast Marching Square method. Then, this path is divided into multiple subpaths separated by equidistant nodes (defined by topological or metric constraints). After that, the obstacles information is progressively added and modifications are made only when the original path is unreachable. The most important advantage with respect to similar approaches is that the generated sub-paths are always efficient in terms of smoothness and safeness. Besides, the computational cost is low enough to use the algorithm in real-time. The anytime triangular planner, such as “Anytime” algorithms, quickly finds a feasible but not necessarily optimal motion plan which is incrementally improved. One important characteristic that this type of algorithms must satisfy is that the path must be generated in real-time. The planner relies on the Fast Marching Square method over a triangular mesh structure. Different variants are introduced and compared under equal circumstances that produce different paths in response time and quality, which leads us to an additional consideration. As in the field of benchmarking it is becoming increasingly difficult to compare new planners approaches because of the lack of a general benchmarking platform, improvements to existing approaches are suggested. Finally, the nonholonomic approach is presented. It is based on the Fast Marching Square method and its application to car-like robots. In order to apply the proposed method, a three dimensional configuration space of the environment is considered. The first two dimensions are given by the position of the robot, and the third one by its orientation. This means that we operate over the configuration space instead of the bi-dimensional environment map. Besides, the trajectory is computed along the configuration space taking into account the dimensions of the vehicle. In this way, it is possible to guarantee the absence of collisions. The proposed method is consistent at local and global scale because it guarantees a motion path solution, if it exists, and does not require global replanning supervision when a local trap is detected. Once a mobile robot has reached a goal location, it usually triggers the servomotors enclosed inside its robotic arm to manipulate a target. The manipulation algorithms presented in this work include the adaptation of trajectories, a planner with adaptive dimensionality, and an implementation of a dimensionality reduction approach inside a nuclear device. The adaptation of manipulation trajectories enables the robot to accomplish a task in different locations by using Evolution Strategies and forward kinematics. This approach avoids all the inconveniences that inverse kinematics imply, as well as the convergence problems in singular kinematic configurations. The planner with adaptive dimensionality reduces the complexity of high-dimensional path planning. First, a Rapidly-exploring Random Tree trajectory is generated using the full degrees of freedom of the robotic arm. Then, a geometry as a closed tube is built around the path line and the Fast Marching Square method is applied from start to goal using three dimensions inside the surface. The resulted three dimensional path is converted to full degrees of freedom with the inverse kinematics of the robot. The result is a smoother and safer path, visually more human friendly. Additionally, the search space is reduced, and therefore, also the planning time and the memory requirements. The application inside the nuclear device, similarly to the previous approach, reduces the degrees of freedom of the problem (but this time to two dimensions due to the mostly planar nature of the robot). The manipulation path is smooth and safe in an environment where safety must be the primarily objective. The motion planning algorithms have been tested in numerous experiments. The fast response of the methods allows its application in real-time tasks.El propósito fundamental de los robots es ayudar a los humanos en tareas difíciles, lo que permite a las personas incrementar sus capacidades de fuerza, energía, velocidad y memoria para trabajar en entornos peligrosos y en una inmensa variedad de aplicaciones. Los robots de servicio, puntualmente los manipuladores móviles, incorporan uno o dos brazos robóticos y una base móvil, y deben ser capaces de realizar tareas complejas de manipulación, interactuando con herramientas u objetos y navegando a través de entornos con obstáculos. Para este fin, el problema de la planificación de movimientos juega un rol clave en el cálculo anticipado de los movimientos del robot, para interactuar con su mundo y realizar las tareas establecidas. El objetivo de este trabajo es diseñar diversos métodos de planificación de movimiento con el fin de mejorar la autonomía de MANFRED-2, un robot móvil que fue desarrollado completamente en el grupo de investigación del Laboratorio de Robótica del Departamento de Ingeniería de Sistemas y Automatización de la Universidad Carlos III de Madrid. Los robots móviles necesitan calcular de antemano trayectorias precisas para poder navegar e interactuar con objetos en su entorno. En este trabajo, hemos desarrollado algoritmos de planificación de movimiento para navegación y manipulación robótica. Los algoritmos presentados para la planificación de trayectorias de navegación se basan en el método de Fast Marching Square (FM2) e incluyen un replanificador con sub-objetivos, un planificador triangular de tipo interrumpible (en inglés este enfoque es mejor conocido como Anytime), y un enfoque no holonómico. El replanificador con submetas comienza generando una trayectoria global de curvas suaves y segura con FM2, entonces este camino es dividido en múltiples subtrayectorias separadas por nodos equidistantes (definidos por restricciones topológicas o métricas). Después de esto, se actualiza progresivamente el entorno con obstáculos detectados por los sensores; sólo se realizan cambios cuando la trayectoria original resulta inalcanzable. La ventaja más importante con respecto a enfoques similares es que las sub-trayectorias generadas son siempre eficientes en términos de suavidad y seguridad. Además, el coste computacional es lo suficientemente bajo como para utilizar el algoritmo en tiempo real. El planificador triangular interrumpible, como algoritmo “Anytime”, encuentra rápidamente una trayectoria de navegación válida, pero no necesariamente ópti ma, a continuación, de forma incremental se va mejorando según haya tiempo hasta llegar al óptimo. La capacidad más resaltante de este tipo de algoritmos es la de generar trayectorias en tiempo real. El planificador se basa en el uso de FM2 sobre una estructura de malla triangular. Se presentan diferentes formas de construir el mallado y se comparan en igualdad de circunstancias los diferentes caminos producidos en tiempo de respuesta y calidad, lo que generó una contribución adicional. Debido a la falta de una plataforma general de evaluación robusta, en el campo de la evaluación de trayectorias es cada vez más difícil comparar nuevos planificadores, por consiguiente se sugieren mejoras a los enfoques existentes. Finalmente, se presenta el enfoque no holónomo, que se basa en FM2 y su aplicación en robots móviles con sistemas de dirección similares a la de los coches. Para aplicar el método propuesto, se considera un espacio de configuración tridimensional del entorno, donde las dos primeras dimensiones vienen dadas por la posición del robot y la tercera dimensión, por su orientación. Esto quiere decir, que operamos en el espacio de configuraciones en vez de en el mapa bidimensional del entorno. Además, la trayectoria se calcula en el espacio de configuraciones teniendo en cuenta las dimensiones del vehículo, de esta manera es posible garantizar la ausencia de colisiones. El método propuesto es consistente a nivel local y global, ya que si existe una solución se garantiza encontrarla, y no requiere de supervisión global para reiniciar una planificación cuando se detecta un bloqueo a nivel local. Una vez que el robot móvil ha alcanzado la ubicación requerida, se suelen accionar los servomotores que están dentro del brazo robótico para manipular un objeto. Los algoritmos de manipulación presentados en este trabajo incluyen la adaptación de trayectorias, un planificador con dimensionalidad adaptable, y una implementación de un método de reducción de la dimensionalidad dentro de un dispositivo nuclear. La adaptación de las trayectorias de manipulación permite al robot realizar una misma tarea con diferentes ubicaciones y orientaciones haciendo uso de una Evolution Strategy y la cinemática directa del robot, este enfoque evita todos los inconvenientes que implican utilizar la cinemática inversa, así como los problemas de convergencia en configuraciones cinemáticas singulares. El planificador con dimensionalidad adaptativa reduce la complejidad de la planificación de trayectorias de manipulación con muchas dimensiones; en primer lugar, una trayectoria RRT se genera utilizando todos los grados de libertad (DOF) del brazo robótico, a continuación, una figura geométrica en forma de tubo cerrado se construye alrededor de la línea de la trayectoria y se aplica FM2 dentro de la superficie desde el inicio hasta el objetivo utilizando tres dimensiones, la ruta 3D resultante se convierte con la cinemática inversa del robot. El resultado es un camino más suave y seguro, más amigable a la vista humana. Además, debido a que el espacio de búsqueda se reduce, también se reduce el tiempo de planificación y los requerimientos de memoria. La aplicación en el interior del dispositivo nuclear, de manera similar al enfoque anterior, reduce los DOF del problema pero esta vez a dos dimensiones aprovechando la naturaleza mayormente plana del robot utilizado. La trayectoria de manipulación es suave y segura, lo que es conveniente en un entorno donde la seguridad debe ser el objetivo principal. Los algoritmos de planificación de movimiento resultantes han sido probados en numerosos experimentos. La respuesta rápida de los métodos permite su aplicación en tiempo real.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Carlos Balaguer Bernaldo de Quirós.- Secretario: Carlos Sagüés Blázquiz.- Vocal: Pedro Lim