Nonholonomic Rolling Nonprehensile Manipulation Primitive

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]

A bead on a hoop rotating about a horizontal axis: a 1-D ponderomotive trap

We describe a simple mechanical system that operates as a ponderomotive particle trap, consisting of a circular hoop and a frictionless bead, with the hoop rotating about a horizontal axis lying in the plane of the hoop. The bead in the frame of the hoop is thus exposed to an effective sinusoidally-varying gravitational field. This field's component along the hoop is a zero at the top and bottom. In the same frame, the bead experiences a time-independent centrifugal force that is zero at the top and bottom as well. The system is analyzed in the ideal case of small displacements from the minimum, and the motion of the particle is shown to satisfy the Mathieu equation. In the particular case that the axis of rotation is tangential to the hoop, the system is an exact analog for the rf Paul ion trap. Various complicating factors such as anharmonic terms, friction and noise are considered. A working model of the proposed system has been constructed, using a ball-bearing rolling in a tube along the outside of a section of a bicycle rim. The apparatus demonstrates in detail the operation of an rf Paul trap by reproducing the dynamics of trapped atomic ions and illustrating the manner in which the electric potential varies with time.Comment: Second external review for AJP, 28 pages double spaced, 11 figure

PERFORMANCE OF PID CONTROLLER OF NONLINEAR SYSTEM USING SWARM INTELLIGENCE TECHNIQUES

In this paper swarm intelligence based PID controller tuning is proposed for a nonlinear ball and hoop system. Particle swarm optimization (PSO), Artificial bee colony (ABC), Bacterial foraging optimization (BFO) is some example of swarm intelligence techniques which are focused for PID controller tuning. These algorithms are also tested on perturbed ball and hoop model. Integral square error (ISE) based performance index is used for finding the best possible value of controller parameters. Matlab software is used for designing the ball and hoop model. It is found that these swarm intelligence techniques have easy implementation & lesser settling & rise time compare to conventional methods

Cartan-Hannay-Berry Phases and Symmetry

We give a systematic treatment of the treatment of the classical Hannay-Berry phases for mechanical systems in terms of the holonomy of naturally constructed connections on bundles associated to the system. We make the costructions using symmetry and reduction and, for moving systems, we use the Cartan connection. These ideas are woven with the idea of Montgomery [1988] on the averaging of connections to produce the Hannay-Berry connection

Information, information processing and gravity

I discuss fundamental limits placed on information and information processing by gravity. Such limits arise because both information and its processing require energy, while gravitational collapse (formation of a horizon or black hole) restricts the amount of energy allowed in a finite region. Specifically, I use a criterion for gravitational collapse called the hoop conjecture. Once the hoop conjecture is assumed a number of results can be obtained directly: the existence of a fundamental uncertainty in spatial distance of order the Planck length, bounds on information (entropy) in a finite region, and a bound on the rate of information processing in a finite region. In the final section I discuss some cosmological issues related to the total amount of information in the universe, and note that almost all detailed aspects of the late universe are determined by the randomness of quantum outcomes. This paper is based on a talk presented at a 2007 Bellairs Research Institute (McGill University) workshop on black holes and quantum information.Comment: 7 pages, 5 figures, revte

Reduction, Symmetry and Phases in Mechanics

Various holonomy phenomena are shown to be instances of the reconstruction procedure for mechanical systems with symmetry. We systematically exploit this point of view for fixed systems (for example with controls on the internal, or reduced, variables) and for slowly moving systems in an adiabatic context. For the latter, we obtain the phases as the holonomy for a connection which synthesizes the Cartan connection for moving mechanical systems with the Hannay-Berry connection for integrable systems. This synthesis allows one to treat in a natural way examples like the ball in the slowly rotating hoop and also non-integrable mechanical systems

Hoop/column antenna deployment mechanism overview

The hoop/column antenna program is directed toward the development of a cost effective, large area, self deploying reflector antenna system. Large surface area antenna systems are required in future space missions involving improved land communications, Earth resources observation, and the study of intergalactic energy sources. The hoop/column antenna is a concept where a large antenna system can be packaged within the Space Transportation System (Shuttle) payload bay, launched into Earth orbit where it is released either for deployment as an Earth observation or communications antenna, or boosted into deep space as an intergalactic energy probe. Various mechanisms and support structures are described that are required to deploy the hoop, which is used to support the antenna reflective surface, and the column that is used to position the antenna feeds and the reflector. It also describes a proof-of-concept model (15 meters in diameter) that is currently being ground tested to determine the adequacy of the deployment mechanisms