Reaction Null Space of a multibody system with applications in robotics

This paper provides an overview of implementation examples based on the Reaction Null Space formalism, developed initially to tackle the problem of satellite-base disturbance of a free-floating space robot, when the robot arm is activated. The method has been applied throughout the years to other unfixed-base systems, e.g. flexible-base and macro/mini robot systems, as well as to the balance control problem of humanoid robots. The paper also includes most recent results about complete dynamical decoupling of the end-link of a fixed-base robot, wherein the end-link is regarded as the unfixed-base. This interpretation is shown to be useful with regard to motion/force control scenarios. Respective implementation results are provided

Uncertainty quantification in ocean state estimation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2013Quantifying uncertainty and error bounds is a key outstanding challenge in ocean state estimation and climate research. It is particularly difficult due to the large dimensionality of this nonlinear estimation problem and the number of uncertain variables involved. The “Estimating the Circulation and Climate of the Oceans” (ECCO) consortium has developed a scalable system for dynamically consistent estimation of global time-evolving ocean state by optimal combination of ocean general circulation model (GCM) with diverse ocean observations. The estimation system is based on the "adjoint method" solution of an unconstrained least-squares optimization problem formulated with the method of Lagrange multipliers for fitting the dynamical ocean model to observations. The dynamical consistency requirement of ocean state estimation necessitates this approach over sequential data assimilation and reanalysis smoothing techniques. In addition, it is computationally advantageous because calculation and storage of large covariance matrices is not required. However, this is also a drawback of the adjoint method, which lacks a native formalism for error propagation and quantification of assimilated uncertainty. The objective of this dissertation is to resolve that limitation by developing a feasible computational methodology for uncertainty analysis in dynamically consistent state estimation, applicable to the large dimensionality of global ocean models. Hessian (second derivative-based) methodology is developed for Uncertainty Quantification (UQ) in large-scale ocean state estimation, extending the gradient-based adjoint method to employ the second order geometry information of the model-data misfit function in a high-dimensional control space. Large error covariance matrices are evaluated by inverting the Hessian matrix with the developed scalable matrix-free numerical linear algebra algorithms. Hessian-vector product and Jacobian derivative codes of the MIT general circulation model (MITgcm) are generated by means of algorithmic differentiation (AD). Computational complexity of the Hessian code is reduced by tangent linear differentiation of the adjoint code, which preserves the speedup of adjoint checkpointing schemes in the second derivative calculation. A Lanczos algorithm is applied for extracting the leading rank eigenvectors and eigenvalues of the Hessian matrix. The eigenvectors represent the constrained uncertainty patterns. The inverse eigenvalues are the corresponding uncertainties. The dimensionality of UQ calculations is reduced by eliminating the uncertainty null-space unconstrained by the supplied observations. Inverse and forward uncertainty propagation schemes are designed for assimilating observation and control variable uncertainties, and for projecting these uncertainties onto oceanographic target quantities. Two versions of these schemes are developed: one evaluates reduction of prior uncertainties, while another does not require prior assumptions. The analysis of uncertainty propagation in the ocean model is time-resolving. It captures the dynamics of uncertainty evolution and reveals transient and stationary uncertainty regimes. The system is applied to quantifying uncertainties of Antarctic Circumpolar Current (ACC) transport in a global barotropic configuration of the MITgcm. The model is constrained by synthetic observations of sea surface height and velocities. The control space consists of two-dimensional maps of initial and boundary conditions and model parameters. The size of the Hessian matrix is O(1010) elements, which would require O(60GB) of uncompressed storage. It is demonstrated how the choice of observations and their geographic coverage determines the reduction in uncertainties of the estimated transport. The system also yields information on how well the control fields are constrained by the observations. The effects of controls uncertainty reduction due to decrease of diagonal covariance terms are compared to dynamical coupling of controls through off-diagonal covariance terms. The correlations of controls introduced by observation uncertainty assimilation are found to dominate the reduction of uncertainty of transport. An idealized analytical model of ACC guides a detailed time-resolving understanding of uncertainty dynamics.This thesis was supported in part by the National Science Foundation (NSF) Collaboration in Mathematical Geosciences (CMG) grant ARC-0934404, and the Department of Energy (DOE) ISICLES initiative under LANL sub-contract 139843-1. Partial funding was provided by the department of Mechanical Engineering at MIT and by the Academic Programs Office at WHOI. My participation in the IMA "Large-scale Inverse Problems and Quantification of Uncertainty" workshop was partially funded by IMA NSF grants

Visual guidance of unmanned aerial manipulators

The ability to fly has greatly expanded the possibilities for robots to perform surveillance, inspection or map generation tasks. Yet it was only in recent years that research in aerial robotics was mature enough to allow active interactions with the environment. The robots responsible for these interactions are called aerial manipulators and usually combine a multirotor platform and one or more robotic arms. The main objective of this thesis is to formalize the concept of aerial manipulator and present guidance methods, using visual information, to provide them with autonomous functionalities. A key competence to control an aerial manipulator is the ability to localize it in the environment. Traditionally, this localization has required external infrastructure of sensors (e.g., GPS or IR cameras), restricting the real applications. Furthermore, localization methods with on-board sensors, exported from other robotics fields such as simultaneous localization and mapping (SLAM), require large computational units becoming a handicap in vehicles where size, load, and power consumption are important restrictions. In this regard, this thesis proposes a method to estimate the state of the vehicle (i.e., position, orientation, velocity and acceleration) by means of on-board, low-cost, light-weight and high-rate sensors. With the physical complexity of these robots, it is required to use advanced control techniques during navigation. Thanks to their redundancy on degrees-of-freedom, they offer the possibility to accomplish not only with mobility requirements but with other tasks simultaneously and hierarchically, prioritizing them depending on their impact to the overall mission success. In this work we present such control laws and define a number of these tasks to drive the vehicle using visual information, guarantee the robot integrity during flight, and improve the platform stability or increase arm operability. The main contributions of this research work are threefold: (1) Present a localization technique to allow autonomous navigation, this method is specifically designed for aerial platforms with size, load and computational burden restrictions. (2) Obtain control commands to drive the vehicle using visual information (visual servo). (3) Integrate the visual servo commands into a hierarchical control law by exploiting the redundancy of the robot to accomplish secondary tasks during flight. These tasks are specific for aerial manipulators and they are also provided. All the techniques presented in this document have been validated throughout extensive experimentation with real robotic platforms.La capacitat de volar ha incrementat molt les possibilitats dels robots per a realitzar tasques de vigilància, inspecció o generació de mapes. Tot i això, no és fins fa pocs anys que la recerca en robòtica aèria ha estat prou madura com per començar a permetre interaccions amb l’entorn d’una manera activa. Els robots per a fer-ho s’anomenen manipuladors aeris i habitualment combinen una plataforma multirotor i un braç robòtic. L’objectiu d’aquesta tesi és formalitzar el concepte de manipulador aeri i presentar mètodes de guiatge, utilitzant informació visual, per dotar d’autonomia aquest tipus de vehicles. Una competència clau per controlar un manipulador aeri és la capacitat de localitzar-se en l’entorn. Tradicionalment aquesta localització ha requerit d’infraestructura sensorial externa (GPS, càmeres IR, etc.), limitant així les aplicacions reals. Pel contrari, sistemes de localització exportats d’altres camps de la robòtica basats en sensors a bord, com per exemple mètodes de localització i mapejat simultànis (SLAM), requereixen de gran capacitat de còmput, característica que penalitza molt en vehicles on la mida, pes i consum elèctric son grans restriccions. En aquest sentit, aquesta tesi proposa un mètode d’estimació d’estat del robot (posició, velocitat, orientació i acceleració) a partir de sensors instal·lats a bord, de baix cost, baix consum computacional i que proporcionen mesures a alta freqüència. Degut a la complexitat física d’aquests robots, és necessari l’ús de tècniques de control avançades. Gràcies a la seva redundància de graus de llibertat, aquests robots ens ofereixen la possibilitat de complir amb els requeriments de mobilitat i, simultàniament, realitzar tasques de manera jeràrquica, ordenant-les segons l’impacte en l’acompliment de la missió. En aquest treball es presenten aquestes lleis de control, juntament amb la descripció de tasques per tal de guiar visualment el vehicle, garantir la integritat del robot durant el vol, millorar de l’estabilitat del vehicle o augmentar la manipulabilitat del braç. Aquesta tesi es centra en tres aspectes fonamentals: (1) Presentar una tècnica de localització per dotar d’autonomia el robot. Aquest mètode està especialment dissenyat per a plataformes amb restriccions de capacitat computacional, mida i pes. (2) Obtenir les comandes de control necessàries per guiar el vehicle a partir d’informació visual. (3) Integrar aquestes accions dins una estructura de control jeràrquica utilitzant la redundància del robot per complir altres tasques durant el vol. Aquestes tasques son específiques per a manipuladors aeris i també es defineixen en aquest document. Totes les tècniques presentades en aquesta tesi han estat avaluades de manera experimental amb plataformes robòtiques real

A high-performance open-source framework for multiphysics simulation and adjoint-based shape and topology optimization

The first part of this thesis presents the advances made in the Open-Source software SU2, towards transforming it into a high-performance framework for design and optimization of multiphysics problems. Through this work, and in collaboration with other authors, a tenfold performance improvement was achieved for some problems. More importantly, problems that had previously been impossible to solve in SU2, can now be used in numerical optimization with shape or topology variables. Furthermore, it is now exponentially simpler to study new multiphysics applications, and to develop new numerical schemes taking advantage of modern high-performance-computing systems. In the second part of this thesis, these capabilities allowed the application of topology optimiza- tion to medium scale fluid-structure interaction problems, using high-fidelity models (nonlinear elasticity and Reynolds-averaged Navier-Stokes equations), which had not been done before in the literature. This showed that topology optimization can be used to target aerodynamic objectives, by tailoring the interaction between fluid and structure. However, it also made ev- ident the limitations of density-based methods for this type of problem, in particular, reliably converging to discrete solutions. This was overcome with new strategies to both guarantee and accelerate (i.e. reduce the overall computational cost) the convergence to discrete solutions in fluid-structure interaction problems.Open Acces