NEW METHODS OF UNDERACTUATED ROBOT ANALYSIS, DESIGN AND CONTROL FOR CYCLIC TASKS

Ph.DDOCTOR OF PHILOSOPH

Instantaneous Momentum-Based Control of Floating Base Systems

In the last two decades a growing number of robotic applications such as autonomous drones, wheeled robots and industrial manipulators started to be employed in several human environments. However, these machines often possess limited locomotion and/or manipulation capabilities, thus reducing the number of achievable tasks and increasing the complexity of robot-environment interaction. Augmenting robots locomotion and manipulation abilities is a fundamental research topic, with a view to enhance robots participation in complex tasks involving safe interaction and cooperation with humans. To this purpose, humanoid robots, aerial manipulators and the novel design of flying humanoid robots are among the most promising platforms researchers are studying in the attempt to remove the existing technological barriers. These robots are often modeled as floating base systems, and have lost the assumption -- typical of fixed base robots -- of having one link always attached to the ground. From the robot control side, contact forces regulation revealed to be fundamental for the execution of interaction tasks. Contact forces can be influenced by directly controlling the robot's momentum rate of change, and this fact gives rise to several momentum-based control strategies. Nevertheless, effective design of force and torque controllers still remains a complex challenge. The variability of sensor load during interaction, the inaccuracy of the force/torque sensing technology and the inherent nonlinearities of robot models are only a few complexities impairing efficient robot force control. This research project focuses on the design of balancing and flight controllers for floating base robots interacting with the surrounding environment. More specifically, the research is built upon the state-of-the-art of momentum-based controllers and applied to three robotic platforms: the humanoid robot iCub, the aerial manipulator OTHex and the jet-powered humanoid robot iRonCub. The project enforces the existing literature with both theoretical and experimental results, aimed at achieving high robot performances and improved stability and robustness, in presence of different physical robot-environment interactions

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

Robust hybrid control for autonomous vehicle motion planning

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 141-150).This dissertation focuses on the problem of motion planning for agile autonomous vehicles. In realistic situations, the motion planning problem must be solved in real-time, in a dynamic and uncertain environment. The fulfillment of the mission objectives might also require the exploitation of the full maneuvering capabilities of the vehicle. The main contribution of the dissertation is the development of a new computational and modelling framework (the Maneuver Automaton), and related algorithms, for steering underactuated, nonholonomic mechanical systems. The proposed approach is based on a quantization of the system's dynamics, by which the feasible nominal system trajectories are restricted to the family of curves that can be obtained by the interconnection of suitably defined primitives. This can be seen as a formalization of the concept of "maneuver", allowing for the construction of a framework amenable to mathematical programming. This motion planning framework is applicable to all time-invariant dynamical systems which admit dynamic symmetries and relative equilibria. No other assumptions are made on the dynamics, thus resulting in exact motion planning techniques of general applicability. Building on a relatively expensive off-line computation phase, we provide algorithms viable for real-time applications. A fundamental advantage of this approach is the ability to provide a mathematical foundation for generating a provably stable and consistent hierarchical system, and for developing the tools to analyze the robustness of the system in the presence of uncertainty and/or disturbances.(cont.) In the second part of the dissertation, a randomized algorithm is proposed for real-time motion planning in a dynamic environment. By employing the optimal control solution in a free space developed for the maneuver automaton (or for any other general system), we present a motion planning algorithm with probabilistic convergence and performance guarantees, and hard safety guarantees, even in the face of finite computation times. The proposed methodologies are applicable to a very large class of autonomous vehicles: throughout the dissertation, examples, simulation and experimental results are presented and discussed, involving a variety of mechanical systems, ranging from simple academic examples and laboratory setups, to detailed models of small autonomous helicopters.by Emilio Frazzoli.Ph.D

Conception d’un quadrirotor à rotors inclinables pour le suivi de trajectoires agressives

RÉSUMÉ Les quadrirotors sont des plateformes robotiques aériennes peu coûteuses et agiles. Plusieurs applications sont envisageables avec ces robots tels que l’exploration des mines ou les opérations de reconnaissance et sauvetage. Ces missions nécessitent de naviguer dans des environnements encombrés et imprédictibles. Le véhicule utilisé doit pouvoir éviter rapidement des obstacles tout en circulant à haute vitesse. Le quadrirotor étant sous-actionné est limité dans son agressivité puisqu’il doit s’incliner avant d’accélérer. De plus, les contrôleurs conventionnels utilisés ne prédisent pas le comportement qu’aura le véhicule durant la trajectoire en utilisant sa dynamique ce qui l’empêche de planifier assidument les manœuvres complexes. Dans ce contexte, l’objectif principal de ce mémoire est de s’affranchir de ces deux limitations en développant un quadrirotor capable d’incliner ses moteurs pour accélérer plus rapidement et d’utiliser un contrôleur prédictif pour le suivi de trajectoire. Plus spécifiquement, une modification au design conventionnel du quadrirotor est proposée par l’ajout d’un seul actuateur pour permettre des manœuvres agressives dans un seul axe. Puis, un ILQR qui est un contrôleur prédictif sans optimisation numérique, est développé. Celui-ci tient compte de l’état à jour du quadrirotor pour la linéarisation et la résolution du problème de contrôle optimal. En premier lieu, le modèle dynamique du quadrirotor à moteurs inclinables est présenté. Puis, une loi de contrôle basé sur un schéma de contrôle en cascade avec une boucle régulant la dynamique en translation à l’aide d’un ILQR et une autre la dynamique en rotation avec un régulateur PD sont implémentées. Ensuite, la solution proposée est testée en simulation et comparée aux approches conventionnelles tant en termes de conception mécanique qu’en asservissement. L’erreur en suivi de trajectoire est diminuée de plus de 1483% avec un impact supérieur de l’ajout de l’inclinaison des moteurs. Enfin, un prototype expérimental est conçu avec des pièces électroniques et mécaniques standards et largement accessibles. La différence entre le design conventionnel et le quadrirotor à moteurs inclinables est étudiée sur des trajectoires agressives. L’erreur diminue de plus de 26% avec l’ajout d’un actionneur alors qu’en simulation pour la même trajectoire l’erreur diminue de 38% ce qui indique que la même tendance est conservée.----------ABSTRACT Quadrotors are cost-effective and agile aerial robotic platforms. Numerous applications are possible with these robots like mines exploration or search and rescue operations. Nevertheless, these missions require navigating through cluttered and unpredictable environments. The vehicle used for these operations must be able to avoid newly located obstacles fast while travelling at high speeds for time critical missions. Quadrotors are underactuated systems and therefore limited in their overall maneuvers because they need to tilt their whole body before accelerating in a direction. Also, conventional controllers used with these systems don’t predict the behavior of the vehicle during a trajectory by using the systems dynamics which prevents them from planning diligently complex maneuvers. In this context, the main objective of this master thesis is to mitigate these two limitations by developing a quadrotor able to tilt his motors thrust to accelerate faster and to use a predictive controller for the trajectory tracking problem. Specifically, a modification to the conventional quadrotor mechanical system is proposed by adding a single actuator to enable aggressive motions in a single axis. Then, an ILQR, which is a predictive controller and does not require parameter optimization, is developed. The latter is a state- dependent controller who behaves as a nonlinear controller by considering the known updated state of the vehicle to solve the optimal control problem. First, the dynamic model of the quadrotor with tilting motors is found. Then, a control law based on a cascade control scheme with a loop for the translational dynamics regulated by an ILQR controller and another loop for the rotational dynamics with a PD controller is implemented. Afterwards, the proposed solution is tested in simulations and compared with conventional approaches in terms of mechanical design and control. Trajectory tracking error is reduced by more than 1483% with the tilting motors modification having a superior impact on performance. Finally, an experimental prototype is designed with standard electronic and mechanical pieces available off-the-shelf. The difference between the conventional design and the quadrotor with tilting motors is studied on this custom-made quadrotor on aggressive trajectories. The error has decreased by more than 26% by adding an actuator while in simulation for the same trajectory this error decrease by 38% which indicates that the same trend is maintained

Model-Based Control of Flying Robots for Robust Interaction under Wind Influence

Model-Based Control of Flying Robots for Robust Interaction under Wind Influence The main goal of this thesis is to bridge the gap between trajectory tracking and interaction control for flying robots in order to allow physical interaction under wind influence by making aerial robots aware of the disturbance, interaction, and faults acting on them. This is accomplished by reasoning about the external wrench (force and torque) acting on the robot, and discriminating (distinguishing) between wind, interactions, and collisions. This poses the following research questions. First, is discrimination between the external wrench components even possible in a continuous real-time fashion for control purposes? Second, given the individual wrench components, what are effective control schemes for interaction and trajectory tracking control under wind influence? Third, how can unexpected faults, such as collisions with the environment, be detected and handled efficiently and effectively? In the interest of the first question, a fourth can be posed: is it possible to obtain a measurement of the wind speed that is independent of the external wrench? In this thesis, model-based methods are applied in the pursuit of answers to these questions. This requires a good dynamics model of the robot, as well as accurately identified parameters. Therefore, a systematic parameter identification procedure for aerial robots is developed and applied. Furthermore, external wrench estimation techniques from the field of robot manipulators are extended to be suitable for aerial robots without the need of velocity measurements, which are difficult to obtain in this context. Based on the external wrench estimate, interaction control techniques (impedance and admittance control) are extended and applied to flying robots, and a thorough stability proof is provided. Similarly, the wrench estimate is applied in a geometric trajectory tracking controller to compensate external disturbances, to provide zero steady-state error under wind influence without the need of integral control action. The controllers are finally combined into a novel compensated impedance controller, to facilitate the main goal of the thesis. Collision detection is applied to flying robots, providing a low level reflex reaction that increases safety of these autonomous robots. In order to identify aerodynamic models for wind speed estimation, flight experiments in a three-dimensional wind tunnel were performed using a custom-built hexacopter. This data is used to investigate wind speed estimation using different data-driven aerodynamic models. It is shown that good performance can be obtained using relatively simple linear regression models. In this context, the propeller aerodynamic power model is used to obtain information about wind speed from available motor power measurements. Leveraging the wind tunnel data, it is shown that power can be used to obtain the wind speed. Furthermore, a novel optimization-based method that leverages the propeller aerodynamics model is developed to estimate the wind speed. Essentially, these two methods use the propellers as wind speed sensors, thereby providing an additional measurement independent of the external force. Finally, the novel topic of simultaneously discriminating between aerodynamic, interaction, and fault wrenches is opened up. This enables the implementation of novel types of controllers that are e.g. compliant to physical interaction, while compensating wind disturbances at the same time. The previously unexplored force discrimination topic has the potential to even open a new research avenue for flying robots

Bayesian Learning for Data-Efficient Control

Applications to learn control of unfamiliar dynamical systems with increasing autonomy are ubiquitous. From robotics, to finance, to industrial processing, autonomous learning helps obviate a heavy reliance on experts for system identification and controller design. Often real world systems are nonlinear, stochastic, and expensive to operate (e.g. slow, energy intensive, prone to wear and tear). Ideally therefore, nonlinear systems can be identified with minimal system interaction. This thesis considers data efficient autonomous learning of control of nonlinear, stochastic systems. Data efficient learning critically requires probabilistic modelling of dynamics. Traditional control approaches use deterministic models, which easily overfit data, especially small datasets. We use probabilistic Bayesian modelling to learn systems from scratch, similar to the PILCO algorithm, which achieved unprecedented data efficiency in learning control of several benchmarks. We extend PILCO in three principle ways. First, we learn control under significant observation noise by simulating a filtered control process using a tractably analytic framework of Gaussian distributions. In addition, we develop the ‘latent variable belief Markov decision process’ when filters must predict under real-time constraints. Second, we improve PILCO’s data efficiency by directing exploration with predictive loss uncertainty and Bayesian optimisation, including a novel approximation to the Gittins index. Third, we take a step towards data efficient learning of high-dimensional control using Bayesian neural networks (BNN). Experimentally we show although filtering mitigates adverse effects of observation noise, much greater performance is achieved when optimising controllers with evaluations faithful to reality: by simulating closed-loop filtered control if executing closed-loop filtered control. Thus, controllers are optimised w.r.t. how they are used, outperforming filters applied to systems optimised by unfiltered simulations. We show directed exploration improves data efficiency. Lastly, we show BNN dynamics models are almost as data efficient as Gaussian process models. Results show data efficient learning of high-dimensional control is possible as BNNs scale to high-dimensional state inputs