Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

Control Of Nonh=holonomic Systems

Many real-world electrical and mechanical systems have velocity-dependent constraints in their dynamic models. For example, car-like robots, unmanned aerial vehicles, autonomous underwater vehicles and hopping robots, etc. Most of these systems can be transformed into a chained form, which is considered as a canonical form of these nonholonomic systems. Hence, study of chained systems ensure their wide applicability. This thesis studied the problem of continuous feed-back control of the chained systems while pursuing inverse optimality and exponential convergence rates, as well as the feed-back stabilization problem under input saturation constraints. These studies are based on global singularity-free state transformations and controls are synthesized from resulting linear systems. Then, the application of optimal motion planning and dynamic tracking control of nonholonomic autonomous underwater vehicles is considered. The obtained trajectories satisfy the boundary conditions and the vehicles\u27 kinematic model, hence it is smooth and feasible. A collision avoidance criteria is set up to handle the dynamic environments. The resulting controls are in closed forms and suitable for real-time implementations. Further, dynamic tracking controls are developed through the Lyapunov second method and back-stepping technique based on a NPS AUV II model. In what follows, the application of cooperative surveillance and formation control of a group of nonholonomic robots is investigated. A designing scheme is proposed to achieves a rigid formation along a circular trajectory or any arbitrary trajectories. The controllers are decentralized and are able to avoid internal and external collisions. Computer simulations are provided to verify the effectiveness of these designs

Whole-Body MPC for a Dynamically Stable Mobile Manipulator

Autonomous mobile manipulation offers a dual advantage of mobility provided by a mobile platform and dexterity afforded by the manipulator. In this paper, we present a whole-body optimal control framework to jointly solve the problems of manipulation, balancing and interaction as one optimization problem for an inherently unstable robot. The optimization is performed using a Model Predictive Control (MPC) approach; the optimal control problem is transcribed at the end-effector space, treating the position and orientation tasks in the MPC planner, and skillfully planning for end-effector contact forces. The proposed formulation evaluates how the control decisions aimed at end-effector tracking and environment interaction will affect the balance of the system in the future. We showcase the advantages of the proposed MPC approach on the example of a ball-balancing robot with a robotic manipulator and validate our controller in hardware experiments for tasks such as end-effector pose tracking and door opening

Integration of vertical COM motion and angular momentum in an extended Capture Point tracking controller for bipedal walking

In this paper, we demonstrate methods for bipedal walking control based on the Capture Point (CP) methodology. In particular, we introduce a method to intuitively derive a CP reference trajectory from the next three steps and extend the linear inverted pendulum (LIP) based CP tracking controller introduced in [1], generalizing it to a model that contains vertical CoM motions and changes in angular momentum. Respecting the dynamics of general multibody systems, we propose a measurement-based compensation of multi-body effects, which leads to a stable closed-loop dynamics of bipedal walking robots. In addition we propose a ZMP projection method, which prevents the robots feet from tilting and ensures the best feasible CP tracking. The extended CP controller’s performance is validated in OpenHRP3 [2] simulations and compared to the controller proposed in [1]

Motion Planning and Control for the Locomotion of Humanoid Robot

This thesis aims to contribute on the motion planning and control problem of the locomotion of humanoid robots. For the motion planning, various methods were proposed in different levels of model dependence. First, a model free approach was proposed which utilizes linear regression to estimate the relationship between foot placement and moving velocity. The data-based feature makes it quite robust to handle modeling error and external disturbance. As a generic control philosophy, it can be applied to various robots with different gaits. To reduce the risk of collecting experimental data of model-free method, based on the simplified linear inverted pendulum model, the classic planning method of model predictive control was explored to optimize CoM trajectory with predefined foot placements or optimize them two together with respect to the ZMP constraint. Along with elaborately designed re-planning algorithm and sparse discretization of trajectories, it is fast enough to run in real time and robust enough to resist external disturbance. Thereafter, nonlinear models are utilized for motion planning by performing forward simulation iteratively following the multiple shooting method. A walking pattern is predefined to fix most of the degrees of the robot, and only one decision variable, foot placement, is left in one motion plane and therefore able to be solved in milliseconds which is sufficient to run in real time. In order to track the planned trajectories and prevent the robot from falling over, diverse control strategies were proposed according to the types of joint actuators. CoM stabilizer was designed for the robots with position-controlled joints while quasi-static Cartesian impedance control and optimization-based full body torque control were implemented for the robots with torque-controlled joints. Various scenarios were set up to demonstrate the feasibility and robustness of the proposed approaches, like walking on uneven terrain, walking with narrow feet or straight leg, push recovery and so on

Planning and Control Strategies for Motion and Interaction of the Humanoid Robot COMAN+

Despite the majority of robotic platforms are still confined in controlled environments such as factories, thanks to the ever-increasing level of autonomy and the progress on human-robot interaction, robots are starting to be employed for different operations, expanding their focus from uniquely industrial to more diversified scenarios. Humanoid research seeks to obtain the versatility and dexterity of robots capable of mimicking human motion in any environment. With the aim of operating side-to-side with humans, they should be able to carry out complex tasks without posing a threat during operations. In this regard, locomotion, physical interaction with the environment and safety are three essential skills to develop for a biped. Concerning the higher behavioural level of a humanoid, this thesis addresses both ad-hoc movements generated for specific physical interaction tasks and cyclic movements for locomotion. While belonging to the same category and sharing some of the theoretical obstacles, these actions require different approaches: a general high-level task is composed of specific movements that depend on the environment and the nature of the task itself, while regular locomotion involves the generation of periodic trajectories of the limbs. Separate planning and control architectures targeting these aspects of biped motion are designed and developed both from a theoretical and a practical standpoint, demonstrating their efficacy on the new humanoid robot COMAN+, built at Istituto Italiano di Tecnologia. The problem of interaction has been tackled by mimicking the intrinsic elasticity of human muscles, integrating active compliant controllers. However, while state-of-the-art robots may be endowed with compliant architectures, not many can withstand potential system failures that could compromise the safety of a human interacting with the robot. This thesis proposes an implementation of such low-level controller that guarantees a fail-safe behaviour, removing the threat that a humanoid robot could pose if a system failure occurred

Kontextsensitive Körperregulierung für redundante Roboter

In the past few decades the classical 6 degrees of freedom manipulators' dominance has been challenged by the rise of 7 degrees of freedom redundant robots. Similarly, with increased availability of humanoid robots in academic research, roboticists suddenly have access to highly dexterous platforms with multiple kinematic chains capable of undertaking multiple tasks simultaneously. The execution of lower-priority tasks, however, are often done in task/scenario specific fashion. Consequently, these systems are not scalable and slight changes in the application often implies re-engineering the entire control system and deployment which impedes the development process over time. This thesis introduces an alternative systematic method of addressing the secondary tasks and redundancy resolution called, context aware body regulation. Contexts consist of one or multiple tasks, however, unlike the conventional definitions, the tasks within a context are not rigidly defined and maintain some level of abstraction. For instance, following a particular trajectory constitutes a concrete task while performing a Cartesian motion with the end-effector represents an abstraction of the same task and is more appropriate for context formulation. Furthermore, contexts are often made up of multiple abstract tasks that collectively describe a reoccurring situation. Body regulation is an umbrella term for a collection of schemes for addressing the robots' redundancy when a particular context occurs. Context aware body regulation offers several advantages over traditional methods. Most notably among them are reusability, scalability and composability of contexts and body regulation schemes. These three fundamental concerns are realized theoretically by in-depth study and through mathematical analysis of contexts and regulation strategies; and are practically implemented by a component based software architecture that complements the theoretical aspects. The findings of the thesis are applicable to any redundant manipulator and humanoids, and allow them to be used in real world applications. Proposed methodology presents an alternative approach for the control of robots and offers a new perspective for future deployment of robotic solutions.Im Verlauf der letzten Jahrzehnte wich der Einfluss klassischer Roboterarme mit 6 Freiheitsgraden zunehmend denen neuer und vielfältigerer Manipulatoren mit 7 Gelenken. Ebenso stehen der Forschung mit den neuartigen Humanoiden inzwischen auch hoch-redundante Roboterplattformen mit mehreren kinematischen Ketten zur Verfügung. Diese überaus flexiblen und komplexen Roboter-Kinematiken ermöglichen generell das gleichzeitige Verfolgen mehrerer priorisierter Bewegungsaufgaben. Die Steuerung der weniger wichtigen Aufgaben erfolgt jedoch oft in anwendungsspezifischer Art und Weise, welche die Skalierung der Regelung zu generellen Kontexten verhindert. Selbst kleine Änderungen in der Anwendung bewirken oft schon, dass große Teile der Robotersteuerung überarbeitet werden müssen, was wiederum den gesamten Entwicklungsprozess behindert. Diese Dissertation stellt eine alternative, systematische Methode vor um die Redundanz neuer komplexer Robotersysteme zu bewältigen und vielfältige, priorisierte Bewegungsaufgaben parallel zu steuern: Die so genannte kontextsensitive Körperregulierung. Darin bestehen Kontexte aus einer oder mehreren Bewegungsaufgaben. Anders als in konventionellen Anwendungen sind die Aufgaben nicht fest definiert und beinhalten eine gewisse Abstraktion. Beispielsweise stellt das Folgen einer bestimmten Trajektorie eine sehr konkrete Bewegungsaufgabe dar, während die Ausführung einer Kartesischen Bewegung mit dem Endeffektor eine Abstraktion darstellt, die für die Kontextformulierung besser geeignet ist. Kontexte setzen sich oft aus mehreren solcher abstrakten Aufgaben zusammen und beschreiben kollektiv eine sich wiederholende Situation. Durch die Verwendung der kontextsensitiven Körperregulierung ergeben sich vielfältige Vorteile gegenüber traditionellen Methoden: Wiederverwendbarkeit, Skalierbarkeit, sowie Komponierbarkeit von Konzepten. Diese drei fundamentalen Eigenschaften werden in der vorliegenden Arbeit theoretisch mittels gründlicher mathematischer Analyse aufgezeigt und praktisch mittels einer auf Komponenten basierenden Softwarearchitektur realisiert. Die Ergebnisse dieser Dissertation lassen sich auf beliebige redundante Manipulatoren oder humanoide Roboter anwenden und befähigen diese damit zur realen Anwendung außerhalb des Labors. Die hier vorgestellte Methode zur Regelung von Robotern stellt damit eine neue Perspektive für die zukünftige Entwicklung von robotischen Lösungen dar

Practical stabilization of a mobile robot using saturated control

This paper presents a new, practically stabilizing, hybrid control algorithm for a unicycle type of mobile robot. The design of this algorithm is based on a set of performance requirements and it is tested numerically and experimentally. The resulting controller is compared to three other recently developed controllers, considering (a limited amount of) measurement and input time-delays, model deviations, parameter uncertainty and measurement noise