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Analysis and control of the underactuation in continuum soft robots: a kinematic independent approach
No full textThis thesis addresses the challenges involved in formulating the dynamics of continuum soft
robots and their nonlinear control in the underactuated regime. The objectives are twofold: to
advance control-oriented modeling approaches for soft robots and to elucidate how the intrinsic
underactuation of these systems can be explicitly managed within a model-based framework to
ensure guaranteed system performance. Although this work primarily focuses on continuum soft
robots, many theoretical findings apply to a broader class of underactuated Lagrangian systems.
First, we propose a dynamic modeling approach for holonomically constrained serial soft robots
that is inherently recursive and independent of the kinematics used to describe system motion. This
formulation enables the immediate derivation of an inverse dynamics procedure with computational
complexity linear in the number of degrees of freedom. Since no specific kinematic model is
required, the proposed framework represents a first step towards a unified modeling approach for
continuum soft robots, analogous to the Newton-Euler method for rigid manipulators. Additionally,
it makes the kinematics an additional design parameter for control design. We demonstrate
that it is possible to simulate models not handled by popular existing methods. This modeling
framework serves—though not strictly necessary—as a foundational layer for subsequent derivations.
Furthermore, we distribute an expandable open-source library implementing the inverse dynamics
procedure.
We then introduce a transformation of the generalized coordinates to bring the dynamics into a
collocated form, where each input directly affects one, and only one, equation of motion. This
change of coordinates is motivated by the distributed nature of the actuation forces in soft robotics,
which generally influence all degrees of freedom. The coordinates that yield the collocated form,
referred to as actuation coordinates, allow the system properties to be studied as if the actuation
were restricted to only some degrees of freedom. This simplifies control design and analysis and
provides direct access to control techniques for other underactuated robots. Furthermore, these
coordinates have a physical interpretation, corresponding to the coordinates on which the actuators
directly perform work, often making them measurable through proprioceptive sensors.
As the kinematics becomes a design parameter, it is crucial to assess which dynamic model is
best suited for a specific control objective. We address this challenge by introducing a systematic
approach based on nonlinear modal theory, which is independent of both the number of degrees
of freedom and the adopted discretization. The motivation for using modes lies in their ability to
encapsulate intrinsic properties of the dynamics, much as they do in linear systems.
By exploiting the collocated form, we solve the regulation problem, as it has remained an open
challenge. Moreover, shape regulation allows to demonstrate the usefulness of the theoretical tools
developed in previous chapters. We propose several families of feedback control laws and provide
conditions under which they are provably stable, ensuring convergence of the actuation coordinates
to the desired set-point. These regulators, along with their performance when derived from different
discretization techniques, are experimentally validated on a continuum soft robot platform designed
in-house. The experiments rely on findings from previous chapters, providing empirical validation
Feedback Regulation of Elastically Decoupled Underactuated Soft Robots
Full text linkThe intrinsically underactuated and nonlinear nature of continuum soft robots makes the derivation of provably stable feedback control laws a challenging task. Most of the works so far circumvented the issue either by looking at coarse fully-actuated approximations of the dynamics or by imposing quasi-static assumptions. In this letter, we move a step in the direction of controlling generic soft robots taking explicitly into account their underactuation. A class of soft robots that have no direct elastic couplings between the dynamics of actuated and unactuated coordinates is identified. Considering the actuated variables as output, we prove that the system is minimum phase. We then propose regulators that implement different levels of model compensation. The stability of the associated closed-loop systems is formally proven by Lyapunov/LaSalle techniques, taking into account the nonlinear and underactuated dynamics. Simulation results are reported for two models of 2D and 3D soft robots.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Learning & Autonomous Contro
Regulation by Iterative Learning in Continuum Soft Robots
Full text linkThe dynamic uncertainties and disturbances characterizing continuum soft robots call for the derivation of simple and possibly information-free controllers. We propose an iterative learning control law for shape regulation of continuum soft robots consisting of a PD action and a feedforward term, updated to learn the potential forces at the target configuration. We prove that the regulator achieves global asymptotic stabilization of the closed-loop system to the desired set-point. Simulation results validate the proposed control law
P-satI-D Shape Regulation of Soft Robots
Full text linkSoft robots are intrinsically underactuated mechanical systems that operate under uncertainties and disturbances. In these conditions, this letter proposes two versions of PID-like control laws with a saturated integral action for the particularly challenging shape regulation task. The closed-loop system is asymptotically stabilized and matched constant disturbances are rejected using a very reduced amount of system information for control implementation. Stability is assessed on the underactuated dynamic model through the Invariant Set Theorem for two relevant classes of soft robots, i.e., elastically decoupled and elastically dominated soft robots. Extensive simulation results validate the proposed controllers.Learning & Autonomous Contro
Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots
Full text linkContinuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory –called eigenmanifolds– as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high- dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model
Experimental Validation of Functional Iterative Learning Control on a One-Link Flexible Arm
Full text linkPerforming precise, repetitive motions is essential in many robotic and automation systems. Iterative learning con- trol (ILC) allows determining the necessary control command by using a very rough system model to speed up the process. Functional iterative learning control is a novel technique that promises to solve several limitations of classic ILC. It operates by merging the input space into a large functional space, resulting in an over-determined control task in the iteration domain. In this way, it can deal with systems having more outputs than inputs and accelerate the learning process without resorting to model discretizations. However, the framework lacks so far a validation in experiments. This paper aims to provide such experimental validation in the context of robotics. To this end, we designed and built a one-link flexible arm that is actuated by a stepper motor, which makes the development of an accurate model more challenging and the validation closer to the industrial practice. We provide multiple experimental results across several conditions, proving the feasibility of the method in practice
Model-Based Control for Soft Robots With System Uncertainties and Input Saturation
No full textModel-based strategies are a promising solution to the grand challenge of equipping continuum soft robots with motor intelligence. However, finite-dimensional models of these systems are inherently inaccurate, thus posing pressing robustness concerns. Moreover, the actuation space of soft robots is usually limited. This article aims at solving both these challenges by proposing a robust model-based strategy for the shape control of soft robots with system uncertainty and input saturation. The proposed architecture is composed of two key components. First, we propose an observer that estimates deviations between the theoretical model and the soft robot, ensuring that the estimation error converges to zero within finite time. Second, we introduce a sliding mode controller to regulate the soft robot shape while fulfilling saturation constraints. This controller uses the observer's output to compensate for the deviations between the real system and the established model. We prove the convergence of the closed-loop with theoretical analysis and the method's effectiveness with simulations and experiments
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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