9 research outputs found

    Nonholonomic Rolling Nonprehensile Manipulation Primitive

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    This chapter reviews the problem of nonholonomic rolling in nonprehen- sile manipulation tasks through two challenging and illustrative examples: the robotic hula-hoop and the ballbot system. The hula-hoop consists of an actuated stick and an unactuated hoop. First, the corresponding kinematic model is derived. Second, the dynamic model is derived through the Lagrange-D’Alembert equations. Then a control strategy is designed to rotate the hoop at some desired constant speed whereas positioning it over a desired point on the stick surface. A stability analysis, which guarantees ultimate boundedness of all signals of interest, is carried out. The ball-bot is an underactuated and nonholonomic constrained mobile robot whose upward equilibrium point must be stabilised by active controls. Coordinate-invariant equations of motion are derived for the ballbot. The linearised equations of motion are then derived, followed by the detailed controllability analysis. Excluding the rotary degree of freedom of the ball in the inertial vertical direction, the linear system turns out to be controllable. It follows that the nonlinear system is locally controllable, and a proportional-derivative type controller is designed to locally exponentially stabilise the upward equilibrium point and the translation of the ball. Numerical simulations for these two examples illustrate the effectiveness of the proposed methods. This chapter is based on the works presented in [1–4]

    Position Control of the Single Spherical Wheel Mobile Robot by Using the Fuzzy Sliding Mode Controller

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    A spherical wheel robot or Ballbot—a robot that balances on an actuated spherical ball—is a new and recent type of robot in the popular area of mobile robotics. This paper focuses on the modeling and control of such a robot. We apply the Lagrangian method to derive the governing dynamic equations of the system. We also describe a novel Fuzzy Sliding Mode Controller (FSMC) implemented to control a spherical wheel mobile robot. The nonlinear nature of the equations makes the controller nontrivial. We compare the performance of four different fuzzy controllers: (a) regulation with one signal, (b) regulation and position control with one signal, (c) regulation and position control with two signals, and (d) FSMC for regulation and position control with two signals. The system is evaluated in a realistic simulation and the robot parameters are chosen based on a LEGO platform, so the designed controllers have the ability to be implemented on real hardware

    A Two-Stage Trajectory Optimization Strategy for Articulated Bodies with Unscheduled Contact Sequences

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    In this letter, we propose a two-stage strategy for optimal control problems of robotic mechanical systems that proves to be more robust, and yet more efficient, than straightforward solution strategies. Specifically, we focus on a simplified humanoid model, represented as a two-dimensional articulated serial chain of rigid bodies, in the tasks of getting up (sitting down) from (to) the supine and prone postures. Interactions with the environment are integral parts of these motions, and a priori unscheduled contact sequences are discovered by the solver itself, opportunistically making or breaking contacts with the ground through feet, knees, hips, elbows, and hands. The present investigation analyzes the effects on the computational performance of: 1) the explicit introduction of contact forces among the optimization variables, 2) the substitution of undesired contact forces with geometric constraints that prevent interpenetrations, and 3) the splitting of the planning problem into two consecutive phases of increasing complexity. To the best of our knowledge, these tests represent the only quantitative analysis of the performances achievable with different solution strategies for optimization-based, whole-body dynamic motion planning in the presence of contacts

    Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

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    Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially

    Conception d'un générateur d'inertie rotationnelle variable à trois degrés de liberté

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    Ce mémoire présente la démarche de conception d’un générateur d’inertie à trois degrés de liberté. Un tel dispositif, conçu pour être tenu en main, utilise une ou plusieurs masses au sein d’un bâti, qui sont réorientées afin d’induire des couples à un utilisateur. Ceci influence l’effort requis par l’utilisateur et modifie sa perception de l’inertie déplacée. Pour y parvenir, un modèle réduit à un degré de liberté est élaboré puis implémenté dans un prototype. Avec une commande en couple, un rendu haptique plus que satisfaisant est obtenu, permettant des inerties jusqu’à 10 fois l’inertie intrinsèque. Par la suite, cinq concepts de générateurs à trois degrés de liberté sont modélisés et simulés. Trois de ceux-ci s’avèrent impossible ou complexes à mettre en oeuvre, laissant deux possibilités : utiliser trois roues d’inertie, ou réaliser un gyroscope à deux axes avec une roue d’inertie centrale. En simulation, le second offre une plus grande efficacité au niveau des requis des moteurs et surtout au niveau de la masse. Il est donc sélectionné pour le développement d’un prototype. Les différentes sections du modèle CAO, les instruments de mesure, et le modèle de contrôle en temps-réel sont détaillés. Avec toutes ces composantes fonctionnelles, des résultats intermédiaires sont obtenus. Le modèle dynamique est d’abord validé comme étant précis à l’aide de capteurs d’efforts, puis il est vérifié que le dispositif est en mesure de suivre des consignes de couple. Enfin la commande de génération d’inertie est implémentée. Des problèmes surviennent comme la limitation des mouvements par les câbles d’alimentation et l’instabilité inhérente du gyroscope. Ils empêchent d’utiliser l’appareil comme prévu, soit avec une roue tournant à haute vitesse. En démarrant le dispositif à 0 RPM, il réussit à simuler des inerties entre 0.5 fois et 1.5 fois son inertie intrinsèque. Ces variations sont de bonne qualité au niveau haptique, et sont suffisantes pour ressentir l’effet du dispositif. Enfin, pour améliorer ses capacités, il est suggéré de retourner vers le concept à trois roues d’inertie.This thesis presents the synthesis and design of a three-degree-of-freedom inertia generator. Such a device, intended as a hand-held apparatus, uses one or many masses within a frame which are accelerated in order to render torques to a user. This influences the effort required by the user to move the device, and modifies their perception of its inertia. To achieve this, a simplified one-degree-of-freedom model is first elaborated and implemented in a prototype. With a torque command, a satisfying haptic rendering is obtained, capable of rendering nearly 10 times the intrinsic inertia of the device. Then, five three-degree-of-freedom torque generation concepts are modelled. Three of those are impossible or too complex to implement, leaving only two options : using three orthogonal flywheels, or using a double gimbal gyroscope with one central flywheel. When compared in simulations, the gyroscope concept offers a better efficiency in terms of mass and motor capabilities. As such, it is selected for the prototype. Then, details are given on the various components of the CAD model, the measuring tools, and the real-time model used for the control. Using these, a series of results are obtained. The dynamic model is first validated as accurate using force/torque sensors. Then the device’s ability to produce torque profiles is confirmed. Finally, its inertia generation capabilities are tested. Problems arise due to movement limitations from the power cables and the instability inherent to the gyroscope. They prevent the device to be used as intended, i.e., with the flywheel initially rotating with a large velocity. Instead, by setting it initially at 0 RPM, the device is able to render inertias equivalent to 0.5 to 1.5 its intrinsic inertia. The haptic quality of these renderings is very good, and they are sufficient to demonstrate the validity of the concept as a whole. Finally, to improve the capabilities of the device, it is suggested to use the three flywheels concept instead.

    Optical tracking control of a differentially-driven wheeled robot

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    Mobile robotics has become an increasingly ubiquitous technology in modern times. A typical example is the wheeled mobile robot (WMR). In order for a WMR to function effectively, it must demonstrate excellent tracking control and localisation capabilities. This is achieved by having accurate and responsive control algorithms as well as high-precision sensor systems. However, this often requires complicated algorithms and expensive equipment. This thesis proposes a system to show that good tracking performance can be achieved with moderately simple control algorithm and relatively inexpensive hardware. The platform used in this research was a differentially-driven wheeled robot constructed using the Lego MindstormsNXT system. Positional tracking was provided by two Avago optical laser sensors commonly found on the computer mouse. The main programming environments were MATLAB and Simulink, along with several other open-source applications. In the first part of the thesis, a PID-based system is presented along with the two control schemes. The first is a purely kinematic model and the second includes dynamic constraints. For both versions, a cascaded PID design was employed and settings were manually tuned. The final mathematical models were computationally simulated and their respective results were analysed and compared. Hardware validation was not conducted for this phase of the research as the simulation results suggested that the PID-based system may not produce the desired level of tracking performance. The second part of the thesis explores a model reference adaptive control system. Lyapunov's direct method was used to achieve stability and convergence in the system. In contrast to the PID-based model, a vastly more accurate geometric localisation technique was applied. The research identified a number of shortcomings in current geometric localisation methods and suggested ways to mitigate them. In addition, a novel approach for detecting faulty sensor readings was introduced in conjunction with the development of a semi-redundant system. The eventual theoretical model was tested using computer simulation, and the outcome was contrasted with the results of the PID-based system. This was followed by the construction of a prototype in order to verify the validity of the proposed model. Various configurations of the adaptive model were tested and compared: the two localisation methods, use of single and dual sensors, and application of semi-redundancy. The thesis concludes with the analysis of results of the prototype testing. The theoretical propositions in the thesis were shown to be amply validated. Suggestions for future research work are also presented

    Intrinsic Euler-Lagrange dynamics and control analysis of the ballbot

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    Research on bipedal locomotion has shown that a dynamic walking gait is energetically more efficient than a statically stable one. Analogously, even though statically stable multi-wheeled robots are easier to control, they are energetically less efficient and have low accelerations to avoid tipping over. In contrast, the ballbot is an underactuated, nonholonomically constrained mobile robot, upward equilibrium point of whose body has to stabilized by active controls. In this work, we derive coordinate-invariant equations of motion for the ballbot. We present the linearized equations of motion followed by its controllability analysis. Excluding the rotary degree of freedom of the ball in the inertial vertical direction, the linear system turns out to be controllable. It follows that the nonlinear system is locally controllable and we provide a proportional-derivative type controller that locally exponentially stabilizes the upward equilibrium point as well as the translation of the ball. The basin of attraction turns out to be large in the simulation studies
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