Robust stability of second-order systems

It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper

Robotic Manipulation and Capture in Space: A Survey

Space exploration and exploitation depend on the development of on-orbit robotic capabilities for tasks such as servicing of satellites, removing of orbital debris, or construction and maintenance of orbital assets. Manipulation and capture of objects on-orbit are key enablers for these capabilities. This survey addresses fundamental aspects of manipulation and capture, such as the dynamics of space manipulator systems (SMS), i.e., satellites equipped with manipulators, the contact dynamics between manipulator grippers/payloads and targets, and the methods for identifying properties of SMSs and their targets. Also, it presents recent work of sensing pose and system states, of motion planning for capturing a target, and of feedback control methods for SMS during motion or interaction tasks. Finally, the paper reviews major ground testing testbeds for capture operations, and several notable missions and technologies developed for capture of targets on-orbit

Passivity based nonlinear model predictive control (PNMPC) of multi-robot systems for space applications

In the past 2 decades, there has been increasing interest in autonomous multi-robot systems for space use. They can assemble space structures and provide services for other space assets. The utmost significance lies in the performance, stability, and robustness of these space operations. By considering system dynamics and constraints, the Model Predictive Control (MPC) framework optimizes performance. Unlike other methods, standard MPC can offer greater robustness due to its receding horizon nature. However, current literature on MPC application to space robotics primarily focuses on linear models, which is not suitable for highly non-linear multi-robot systems. Although Nonlinear MPC (NMPC) shows promise for free-floating space manipulators, current NMPC applications are limited to unconstrained non-linear systems and do not guarantee closed-loop stability. This paper introduces a novel approach to NMPC using the concept of passivity to multi-robot systems for space applications. By utilizing a passivity-based state constraint and a terminal storage function, the proposed PNMPC scheme ensures closed-loop stability and a superior performance. Therefore, this approach offers an alternative method to the control Lyapunov function for control of non-linear multi-robot space systems and applications, as stability and passivity exhibit a close relationship. Finally, this paper demonstrates that the benefits of passivity-based concepts and NMPC can be combined into a single NMPC scheme that maintains the advantages of each, including closed-loop stability through passivity and good performance through one-line optimization in NMPC

Modeling and Control of a Flexible Space Robot to Capture a Tumbling Debris

RÉSUMÉ La conquête spatiale des 60 dernières années a généré une grande quantité d’objets à la dérive sur les orbites terrestres. Leur nombre grandissant constitue un danger omniprésent pour l’exploitation des satellites, et requiert aujourd’hui une intervention humaine pour réduire les risques de collision. En effet, l’estimation de leur croissance sur un horizon de 200 ans, connue sous le nom de “syndrôme de Kessler”, montre que l’accès à l’Espace sera grandement menacé si aucune mesure n’est prise pour endiguer cette prolifération. Le scientifique J.-C. Liou de la National Aeronautics and Space Administration (NASA) a montré que la tendance actuelle pourrait être stabilisée, voire inversée, si au moins cinq débris massifs étaient désorbités par an, tels que des satellites en fin de vie ou des étages supérieurs de lanceur. Parmi les nombreux concepts proposés pour cette mission, la robotique s’est imposée comme une des solutions les plus prometteuses grâce aux retours d’expérience des 30 dernières années. La Station Spatiale Internationale (ISS) possède déjà plusieurs bras robotiques opérationnels, et de nombreuses missions ont démontré le potentiel d’un tel système embarqué sur un satellite. Pour deux d’entre elles, des étapes fondamentales ont été validées pour le service en orbite,et s’avèrent être similaires aux problématiques de la désorbitation des débris. Cette thèse se concentre sur l’étape de capture d’un débris en rotation par un bras robotique ayant des segments flexibles. Cette phase comprend la planification de trajectoire et le contrôle du robot spatial, afin de saisir le point cible du débris de la façon la plus délicate possible. La validation des technologies nécessaires à un tel projet est quasiment impossible sur Terre, et requiert des moyens démesurés pour effectuer des essais en orbite. Par conséquent, la modélisation et la simulation de systèmes multi-corps flexibles est traitée en détails, et constitue une forte contribution de la thèse. À l’aide de ces modèles, une validation mixte est proposée par des essais expérimentaux, en reproduisant la cinématique en orbite par des manipulateurs industriels contrôlés par une simulation en temps réel. En résumé, cette thèse est construite autour des trois domaines suivants : la modélisation des robots spatiaux, le design de lois de contrôle, et leur validation sur un cas test. Dans un premier temps, la modélisation de robots spatiaux en condition d’apesanteur est développée pour une forme “en étoile”.----------ABSTRACT After 60 years of intensive satellite launches, the number of drifting objects in Earth orbits is reaching a shifting point, where human intervention is becoming necessary to reduce the threat of collision. Indeed, a 200 year forecast, known as the “Kessler syndrome”, states that space access will be greatly compromised if nothing is done to address the proliferation of these debris. Scientist J.-C. Liou from the National Aeronautics and Space Administration (NASA) has shown that the current trend could be reversed if at least five massive objects, such as dead satellites or rocket upper stages, were de-orbited each year. Among the various technical concepts considered for debris removal, robotics has emerged, over the last 30 years, as one of the most promising solutions. The International Space Station (ISS) already possesses fully operational robotic arms, and other missions have explored the potential of a manipulator embedded onto a satellite. During two of the latter, key capabilities have been demonstrated for on-orbit servicing, and prove to be equally useful for the purpose of debris removal. This thesis focuses on the close range capture of a tumbling debris by a robotic arm with light-weight flexible segments. This phase includes the motion planning and the control of a space robot, in order to smoothly catch a target point on the debris. The validation of such technologies is almost impossible on Earth and leads to prohibitive costs when performed on orbit. Therefore, the modeling and simulation of flexible multi-body systems has been investigated thoroughly, and is likewise a strong contribution of the thesis. Based on these models, an experimental validation is proposed by reproducing the on-orbit kinematics on a test bench made up of two industrial manipulators and driven by a real-time dynamic simulation. In a nutshell, the thesis is built around three main parts: the modeling of a space robot, the design of control laws, and their validation on a test case. The first part is dedicated to the flexible modeling of a space robot in conditions of weightlessness. A “star-shaped” multi-body system is considered, meaning that the rigid base carries various flexible appendages and robotic arms, assumed to be open mechanical chains only. The classic Newton-Euler and Lagrangian algorithms are brought together to account for the flexibility and to compute the dynamics in a numerically efficient way. The modeling step starts with the rigid fixed-base manipulators in order to introduce the notations, then, détails the flexible ones, and ends with the moving-base system to represent the space robots

Synchronized Motion Control of Dual Robot Manipulator Systems

Dual manipulator systems are capable of accomplishing a variety of tasks, such as manipulating large and heavy objects and assembling parts, that might be impossible for single manipulators. These collaborative tasks require dual manipulators to be driven by a controller that can coordinate and synchronize the motions of the individual manipulators. Furthermore, many domestic and industrial applications involve the manipulation of objects with unknown properties. For instance, a cooking robot would have to deal with many ingredients of di erent sizes and weights. In this thesis, an adaptive synchronous controller for dual manipulator systems, that is capable of motion synchronization while manipulating objects of unknown properties, is presented. This controller only utilizes position information, hence does not require extra instrumentation, such as force sensors, often not found in industrial manipulators. The performance of the controller is validated through simulations which showed that the inclusion of motion synchronization errors in controller design is critical in accomplishing collaborative tasks. The real-life implementation details are also discussed

Dynamics of Serial Manipulators using Dual Quaternion Algebra

This paper presents two approaches to obtain the dynamical equations of serial manipulators using dual quaternion algebra. The first one is based on the recursive Newton-Euler formulation and uses twists and wrenches instead of 3D vectors, which simplifies the classic procedure by removing the necessity of exhaustive geometrical analyses since wrenches and twists are propagated through high-level algebraic operations. Furthermore, the proposed formulation works for arbitrary types of joints and does not impose any particular convention for the propagation of twists. The second approach, based on Gauss's Principle of Least Constraint (GPLC), takes into account elements of the dual quaternion algebra and provides a linear relationship between twists derivatives and joint accelerations, which can be particularly useful in robot control. Differently from other approaches based on the GPLC, which have representational singularities or require constraints, our method does not have those drawbacks. We present a thorough methodology to obtain the computational cost of both algorithms and compared them with their classic counterparts. Although our current formulations are more computationally expensive, they are more general than their counterparts in the state of the art. Simulation results showed that both methods are as accurate as the classic recursive Newton-Euler algorithm.Comment: Submitted for publication (currently under review

Stabilization of Mobile Manipulators

The focus of this work is to generate a method of stabilization in a system generated through the marriage of a mobile robot and a manipulator. While the stability of a rigid manipulator is a solved problem, upon the introduction of flexibilities into the manipulator base structure there is the simultaneous introduction of an unmodeled, induced, oscillatory disturbance to the manipulator system from the mobile base suspension and mounting. Under normal circumstances, the disturbance can be modeled through experimentation and then a form of vibration suppression control can be employed to damp the induced oscillations in the base. This approach is satisfactory for disturbances that are measured, however the hardware necessary to measure the induced oscillations in the manipulator base is generally not included in mobile manipulation systems. Because of this lack of sensing hardware it becomes difficult to directly compensate for the induced disturbances in the system. Rather than developing a direct method for compensation, efforts are made to find postures of the manipulator where the flexibilities of the system are passive. In these postures the manipulator behaves as if it is on a rigid base, this allows the use of higher feedback gains and simpler control architectures.Ph.D

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

From Underactuation to Quasi‐Full Actuation: A Unifying Control Framework for Rigid and Elastic Joint Robot

The quest for animal-like performance in robots has driven the integration of elastic elements in their drive trains, sparking a revolution in robot design. Elastic robots can store and release potential energy, providing distinct advantages over traditional robots, such as enhanced safety in human-robot interaction, resilience to mechanical shocks, improved energy efficiency in cyclic tasks, and dynamic motion capabilities. Exploiting their full potential, however, necessitates novel control methods. This thesis advances the field of nonlinear control for underactuated systems and utilizes the results to push the boundaries of motion and interaction performance of elastic robots. Through real-life experiments and applications, the proposed controllers demonstrate that compliant robots hold promise as groundbreaking robotic technology. To achieve these objectives, we first derive a simultaneous phase space and input transformation that enables a specific class of underactuated Lagrangian systems to be treated as if fully actuated. These systems can be represented as the interconnection of actuated and underactuated subsystems, with the kinetic energy of each subsystem depending only on its own velocity. Elastic robots are typical representatives. We refer to the transformed system as quasi-fully actuated due to weak constraints on the new inputs. Fundamental aspects of the transforming equations are 1) the same Lagrangian function characterizes both the original and transformed systems, 2) the transformed system establishes a passive mapping between inputs and outputs, and 3) the solutions of both systems are in a one-to-one correspondence, describing the same physical reality. This correspondence allows us to study and control the behavior of the quasi-fully actuated system instead of the underactuated one. Thus, this approach unifies the control design for rigid and elastic joint robots, enabling the direct application of control results inherited from the fully-actuated case while ensuring closed-loop system stability and passivity. Unlike existing methods, the quasi-full actuation concept does not rely on inner control loops or the neglect and cancellation of dynamics. Notably, as joint stiffness values approach infinity, the control equivalent of a rigid robot is recovered. Building upon the quasi-full actuation concept, we extend energy-based control schemes such as energy shaping and damping injection, Euler-Lagrange controllers, and impedance control. Moreover, we introduce Elastic Structure Preserving (ESP) control, a passivity-based control scheme designed for robots with elastic or viscoelastic joints, guided by the principle of ``do as little as possible''. The underlying hope is that reducing the system shaping, i.e., having a closed-loop dynamics match in some way the robot's intrinsic structure, will award high performance with little control effort. By minimizing the system shaping, we obtain low-gain designs, which are favorable concerning robustness and facilitate the emergence of natural motions. A comparison with state-of-the-art controllers highlights the minimalistic nature of ESP control. Additionally, we present a synthesis method, based on purely geometric arguments, for achieving time-optimal rest-to-rest motions of an elastic joint with bounded input. Finally, we showcase the remarkable performance and robustness of the proposed ESP controllers on DLR David, an anthropomorphic robot implemented with variable impedance actuators. Experimental evidence reveals that ESP designs enable safe and compliant interaction with the environment and rigid-robot-level accuracy in free motion. Additionally, we introduce a control framework that allows DLR David to perform commercially relevant tasks, such as pick and place, teleoperation, hammer drilling into a concrete block, and unloading a dishwasher. The successful execution of these tasks provides compelling evidence that compliant robots have a promising future in commercial applications