Rhythmic stabilization of periodic orbits in a wedge

The paper addresses the rhythmic stabilization of periodic orbits in a wedge billiard with actuated edges. The output feedback strategy, based on the sole measurement of impact times, results from the combination of a stabilizing state feedback control law and a nonlinear deadbeat state estimator. It is shown that the robustness of both the control law and the observer leads to a simple rhythmic controller achieving a large basin of attraction. Copyright © 2005 IFAC.

Stabilization of periodic orbits in a wedge billiard

This paper introduces a stabilization problem for an elementary impact control system in the plane. The rich dynamical properties of the wedge billiard, combined to the relevance of the associated stabilization problem for feedback control issues in legged robotics make it a valuable benchmark for energy-based stabilization of impact control systems.

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd. Summary A field programmable gate array (FPGA) based model predictive controller for two phases of spacecraft rendezvous is presented. Linear time-varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer range manoeuvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal-dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft-core processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed-loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze and could be competitive with a pure custom hardware implementation.

Magnetotunnelling spectroscopy: an experimental tool for studying chaos in quantum transport

Resonant tunnelling spectroscopy is used to investigate the energy level spectrum of a wide potential well in the presence of a large magnetic field oriented at angles θ between 0° and 90° to the normal to the plane of the well. In the tilted field geometry, the current-voltage characteristics exhibit a large number of quasiperiodic resonant peaks even though the classical motion of electrons in the potential well is chaotic. The voltage range and spacing of the resonances both change dramatically with θ. We give a quantitative explanation for this behaviour by considering the classical period of unstable periodic orbits within the chaotic sea of the potential well.

A comparison of different failure assessment methodologies applied to the NESC-1 test

Predictions for a 75x205mm surface semi-elliptic defect in the NESC-1 spinning cylinder test have been made using BS PD 6493:1991, the R6 procedure, non-linear cracked body finite element analysis techniques and the local approach to fracture. All the techniques agree in predicting ductile tearing near the inner surface of the cylinder followed by cleavage initiation. However they differ in the amount of ductile tearing, and the exact location and time of any cleavage event. The amount of ductile tearing decreases with increasing sophistication in the analysis, due to the drop in peak crack driving force and more explicit consideration of constraint effects. The local approach predicts a high probability of cleavage in both HAZ and base material after 190s, while the other predictions suggest that cleavage is unlikely in the HAZ due to constraint loss, but likely in the underlying base material. The timing of this event varies from ∼150s for R6 predictions to ∼250-300s using non-linear cracked body analysis.

Pothole detection in asphalt pavement images

Pavement condition assessment is essential when developing road network maintenance programs. In practice, the data collection process is to a large extent automated. However, pavement distress detection (cracks, potholes, etc.) is mostly performed manually, which is labor-intensive and time-consuming. Existing methods either rely on complete 3D surface reconstruction, which comes along with high equipment and computation costs, or make use of acceleration data, which can only provide preliminary and rough condition surveys. In this paper we present a method for automated pothole detection in asphalt pavement images. In the proposed method an image is first segmented into defect and non-defect regions using histogram shape-based thresholding. Based on the geometric properties of a defect region the potential pothole shape is approximated utilizing morphological thinning and elliptic regression. Subsequently, the texture inside a potential defect shape is extracted and compared with the texture of the surrounding non-defect pavement in order to determine if the region of interest represents an actual pothole. This methodology has been implemented in a MATLAB prototype, trained and tested on 120 pavement images. The results show that this method can detect potholes in asphalt pavement images with reasonable accuracy.

Two-orbit switch-pitch structures

The Hoberman 'switch-pitch ' ball is a transformable structure with a single folding and unfolding path. The underlying cubic structure has a novel mechanism that retains tetrahedral symmetry during folding. Here, we propose a generalized class of structures of a similar type that retain their full symmetry during folding. The key idea is that we require two orbits of nodes for the structure: within each orbit, any node can be copied to any other node by a symmetry operation. Each member is connected to two nodes, which may be in different orbits, by revolute joints. We will describe the symmetry analysis that reveals the symmetry of the internal mechanism modes for a switch-pitch structure. To follow the complete folding path of the structure, a nonlinear iterative predictor-corrector algorithm based on the Newton method is adopted. First, a simple tetrahedral example of the class of two-orbit structures is presented. Typical configurations along the folding path are shown. Larger members of the class of structures are also presented, all with cubic symmetry. These switch-pitch structures could have useful applications as deployable structures.