Robotic manipulation of a rotating chain

This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in $\mathbb{R}^3$. Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.Comment: 12 pages, 9 figure

Time-Optimal Path Tracking via Reachability Analysis

Given a geometric path, the Time-Optimal Path Tracking problem consists in finding the control strategy to traverse the path time-optimally while regulating tracking errors. A simple yet effective approach to this problem is to decompose the controller into two components: (i)~a path controller, which modulates the parameterization of the desired path in an online manner, yielding a reference trajectory; and (ii)~a tracking controller, which takes the reference trajectory and outputs joint torques for tracking. However, there is one major difficulty: the path controller might not find any feasible reference trajectory that can be tracked by the tracking controller because of torque bounds. In turn, this results in degraded tracking performances. Here, we propose a new path controller that is guaranteed to find feasible reference trajectories by accounting for possible future perturbations. The main technical tool underlying the proposed controller is Reachability Analysis, a new method for analyzing path parameterization problems. Simulations show that the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201

A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis

Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based methods are fast but difficult to implement and suffer from robustness issues, while CO-based approaches are more robust but at the same time significantly slower. Here we propose a new approach to TOPP based on Reachability Analysis (RA). The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small Linear Programs (LPs). The resulting algorithm is faster than NI-based methods and as robust as CO-based ones (100% success rate), as confirmed by extensive numerical evaluations. Moreover, the proposed approach offers unique additional benefits: Admissible Velocity Propagation and robustness to parametric uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure

Homotopy groups of EChG24∧A1E_{C}^{hG_{24}}\wedge A_1

Let $A_1$ be any spectrum in a class of finite spectra whose mod $2$ cohomology is isomorphic to a free module of rank one over the subalgebra $\mathcal{A}(1)$ of the Steenrod algebra. Let $E_{C}$ be the second Morava-$E$ theory associated to a universal deformation of the formal completion of the supersingular elliptic curve $(C) : y^{2}+y = x^{3}$ defined over $\mathbb{F}_{4}$ and $G_{24}$ a maximal finite subgroup of automorphism group $\mathbb{S}_{C}$ of the formal completion of $C$. In this paper, we compute the homotopy groups of $E_{C}^{hG_{24}}\wedge A_1$ by means of the homotopy fixed point spectral sequence.Comment: 82 pages, 29 figure

An ecological perspective on the motivational trajectories of high school students learning English in rural areas in Vietnam : A thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Applied Linguistics at Massey University, Palmerston North, New Zealand.

This study explores the motivational trajectories of four students learning English at a rural high school in Southern Vietnam. It draws on a person-in-context relational view of motivation (Ushioda, 2009) as the overarching theoretical framework and uses ecological systems theory (Bronfenbrenner, 1993) as an analytical tool to develop insights into the ways motivation is implicated in a multiplicity of settings and social relationships. Specifically, it aims to identify motivational affordances for these students, the synergistic effects across settings on their language learning motivation, and their motivational trajectories within and across settings and relationships. The study utilises a qualitative case study design, relying primarily on interviews from social practice perspectives and observations. The data collection, spanning approximately one and a half years, comprised two main phases, one on-site and one off-site. In the first phase, data were gathered in different settings, including the school, the participants’ homes as a site for private tuition, and other more informal public spaces such as food stores. In the second phase, Skype interviews and Facebook exchanges were the main means of data collection. The findings suggest that while language affordances were evident in both formal and informal learning settings, students developed diverse individual motivational trajectories. Their motivational constructions resulted from a synergy of environmental and idiosyncratic elements pertinent to their own language learning conditions, social relationships, and personal appraisals of such affordances and learning opportunities. These relationships and students’ agentive use of resources were shaped and reshaped by their interactions with significant others within and across settings. Sociocultural features related to the school systems, local and national education policies, family traditions, cultural values, and future prospects also have synergistic impacts on their L2 motivation. The present study illustrates the value of interpreting the situated and dynamic nature of L2 motivation using an ecological paradigm. It also points to the need to adopt a set of data collection methods, tools, and data sources that diverge from more conventional means to explore L2 motivation. The study offers a fresh theoretical and methodological approach for future research geared towards lifewide adaptive perspectives on English language teaching and learning