Paths In Plane Research Articles

Large, non-saturating magnetoresistance in single layer chemical vapor deposition graphene with an h-BN capping layer

We report large, non-saturating magnetoresistance (MR) of ∼140% in single layer chemical vapor deposition (CVD) graphene with an h-BN capping layer at room temperature at B = 9 T. Based on the classical model developed by Parish and Littlewood, our results show that the MR is proportional to the average mobility <μ > and decreases with increasing temperature. In contrast, in a large-area, extremely homogenous single layer epitaxial graphene (EG) device, the MR is saturating and is inversely proportional to <μ>, which is consistent with the finite resistance network picture. By comparing the results obtained from CVD graphene with an h-BN capping layer with those from the EG device, we show that the non-saturating linear characteristics come from multi-channel current paths in a two-dimensional plane due to the intrinsic grain boundaries and domains of CVD graphene by capping an h-BN layer that increase the <μ> of CVD graphene. Our results on CVD graphene with an h-BN capping layer pave the way for industrial schemes of graphene-based and air-stable magnetic field sensors with a linear, large response at room temperature.

Planar path following nonlinear controller design for an autonomous airship

This paper investigates the planar path following control problem for an autonomous airship taking actuator saturation, actuator dynamics, parameter variation, and wind field into account. Firstly, improved nonlinear models of the airship are introduced and the control objective is formulated. Then, a command filtered backstepping controller combined with nonlinear disturbance observer is derived based on Lyapunov stability theory. The command filter is adopted to approximate the magnitude and rate saturations of actuator. The first-order inertia term is used to approximate the actuator dynamics. And, the nonlinear disturbance observer is employed to handle the disturbance caused by parameter variations and wind field. To guarantee the controller still works when saturations occur, the compensation terms are also designed. It is proved that the proposed controller can drive the airship to track a predefined path under actuator saturation, parameter variations and wind field. Besides, the proposed approach is able to avoid the complex analytic computation of command derivatives which is required in traditional backstepping method. Finally, simulations are carried out to illustrate effectiveness of the proposed controller.

Fast-Marching Methods for Curvature Penalized Shortest Paths

We introduce numerical schemes for computing distances and shortest paths with respect to several planar paths models, featuring curvature penalization and data-driven velocity: the Dubins car, the Euler/Mumford elastica, and a two variants of the Reeds–Shepp car. For that purpose, we design monotone and causal discretizations of the associated Hamilton–Jacobi–Bellman PDEs, posed on the three-dimensional domain $${\mathbb R}^2 \times {\mathbb S}^1$$ . Our discretizations involve sparse, adaptive and anisotropic stencils on a cartesian grid, built using techniques from lattice geometry. A convergence proof is provided, in the setting of discontinuous viscosity solutions. The discretized problems are solvable in a single pass using a variant of the fast-marching algorithm. Numerical experiments illustrate the applications of our schemes in motion planning and image segmentation.

The Memo Slide: An explorative study into a novel mechanical follow-the-leader mechanism.

Follow-the-leader propagation allows for the insertion of flexible surgical instruments along curved paths, reducing the access required for natural orifice transluminal endoscopic surgery. Currently, the most promising follow-the-leader instruments use the alternating memory method containing two mechanical memory-banks for controlling the motion of the flexible shaft, which reduces the number of actuators to a minimum. These instruments do, however, require concentric structures inside the shaft, limiting its miniaturization. The goal of this research was, therefore, to develop a mechanism conforming the principles of the alternating memory method that could be located at the controller-side instead of inside the shaft of the instrument, which is positioned outside the patient and is therefore less restricted in size. First, the three-dimensional motion of the shaft was decoupled into movement in a horizontal and vertical plane, which allowed for a relatively simple planar alternating memory mechanism design for controlling planar follow-the-leader motion. Next, the planar movement of the alternating memory mechanism was discretized, increasing its resilience to errors. The resulting alternating memory mechanism was incorporated and tested in a proof-of-concept prototype called the MemoSlide. This prototype does not include a flexible shaft, but was fully focused on proving the function of the alternating memory mechanism. Evaluation of the MemoSlide shows the mechanism to work very well, being able to transfer any planar path that lays within its physical boundaries along the body of the mechanism without accumulating errors.

Non-integer-period motion generation of a planar four-bar mechanism using wavelet series

In this paper, on the basis of the theory of the Haar wavelet series, the early proposed method, which is used to solve the problem of planar four-bar path synthesis, is extended to motion generation synthesis of a planar four-bar mechanism. By analysing the wavelet coefficients between the rigid-body rotation angle and the connecting rod rotation angle of its corresponding basic dimensional type, the internal relationships are determined. Based on this finding, an output feature parameters database of planar four-bar motion generation including 101,408 sets of the basic dimensional type was established. Using the fuzzy identification method and theoretical formulas to compute the actual size and installing positions parameters of a planar four-bar mechanism, the synthesis of a planar four-bar motion generation mechanism can be achieved using the established numerical atlas, fuzzy identification method and theoretical formulas.

Absorption and diffusion of oxygen in the Ti3Al alloy

The absorption and diffusion of oxygen in the Ti3Al alloy are studied by the projector augmented wave within the density functional theory. The highest absorption energies are shown to correspond to the sites in the octahedra formed by six titanium atoms, and the presence of aluminum in the nearest neighbors leads to a substantial decrease in the binding energy of oxygen in the alloy by approximately 1.5 eV. The energy barriers of oxygen diffusion between various interstices in the crystal lattice of the alloy are estimated, and the preferred migration paths in the (0001) plane and the [0001] direction are determined. It is found that the migration barrier from the most preferred octahedral O1 site to distorted tetrahedral Ti-site (2.42 eV) is a key barrier and limits the oxygen diffusion in the alloy. The calculated temperature diffusion coefficient of oxygen in the Ti3Al alloy and the activation energies determined in two directions agree with the experimental data.

Joint Probability Method to Time-dependent Reliability for Planar Path Mechanisms

Joint Probability Method to Time-dependent Reliability for Planar Path Mechanisms

Hierarchical Robust Path Following Control of Fully Submerged Hydrofoil Vessels

This paper investigates the hierarchical path following control of a fully submerged hydrofoil vessel (FSHV) in the presence of additive disturbances. Roll dynamics is particularly considered for planar path following in both kinematics and rigid-body dynamics. A coordinated turn aided line-of-sight (LOS) guidance methodology is proposed for the guidance system design. In this approach, an adaptive LOS guidance algorithm is presented to calculate the command course angle. An adaptive estimator is designed to estimate the sideslip angle caused by the drift forces of ocean currents. The command bank angle is calculated based on the dynamics of the cross-track error and the coordinated turn constraint, which highly improves the maneuverability of the FSHV. A robust integral of the sign of the error feedback control is proposed as the autopilot to cope with attitude tracking of the lateral dynamics. The cascade characteristics of the guidance system and the autopilot are discussed; uniform asymptotic stability of the overall closed-loop system is achieved via cascade system theory. Simulation results validate the effectiveness of the hierarchical control strategy, and disturbance attenuation can be guaranteed for the composite guidance and control of the FSHV.

Planar maneuvering control of underwater snake robots using virtual holonomic constraints

This paper investigates the problem of planar maneuvering control for bio-inspired underwater snake robots that are exposed to unknown ocean currents. The control objective is to make a neutrally buoyant snake robot which is subject to hydrodynamic forces and ocean currents converge to a desired planar path and traverse the path with a desired velocity. The proposed feedback control strategy enforces virtual constraints which encode biologically inspired gaits on the snake robot configuration. The virtual constraints, parametrized by states of dynamic compensators, are used to regulate the orientation and forward speed of the snake robot. A two-state ocean current observer based on relative velocity sensors is proposed. It enables the robot to follow the path in the presence of unknown constant ocean currents. The efficacy of the proposed control algorithm for several biologically inspired gaits is verified both in simulations for different path geometries and in experiments.

Optimizing Steady Turns for Gliding Trajectories

Dubins planners provide minimum-length planar paths between waypoints for turning constrained vehicles. For a no-thrust or glider aircraft, Dubins paths have been extrapolated to three dimensions by augmenting the planar path with a constant flight-path angle in each path segment. Best-glide flight maximizes the horizontal distance traveled per unit altitude loss, but steeper flight-path angles result in a maximum heading change per unit altitude loss. This paper investigates combinations of bank and flight-path angles yielding maximum ranges for gliding Dubins trajectories. Starting from the extrema flight-path angles usually applied in the literature, it is shown that the maximum range along each flight radial from an initial point (that is, the footprint) is obtained at a maximum glidepath angle for a given turn radius. This result is applied in a novel three-dimensional maximum-range Dubins path. Three-dimensional Dubins examples with different heading constraints are presented. The impact of constraining solutions to a single pair of turning bank and flight-path angles is analyzed.

Scattering and delay time for 1D asymmetric potentials: The step-linear and the step-exponential case

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U 0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. For both the linear and the exponential barrier we provide an explicit formula for the delay time τ ( E ) as a function of the peak energy E. We display the resonant behavior of τ ( E ) at energies close to U 0. By analyzing the asymptotic behavior for large energies of the eigenfunctions of the continuous spectrum we also show that, as expected, τ ( E ) approaches the classical value for E → ∞, thus diverging for the step-linear case and vanishing for the step-exponential one.

Inverse kinematic and dynamic analysis of planar path generating adjustable mechanism

Path generating adjustable mechanisms with continuous adjustment have been studied in literature, wherein the synthesis has been commonly based on the position kinematics of the mechanism. Many real life applications would, however, demand that the coupler point traces the path at specified velocity and acceleration, thus necessitating development of inverse velocity and acceleration analyses. Further, the inverse dynamic analysis needs to be carried out from the viewpoint of mechanical design and motion control of the mechanism. In this paper, inverse kinematic and dynamic analysis of a path generating four-bar mechanism with continuous one-parameter adjustment is presented. The kinematic analysis is presented for both, the non-singular and singular configurations of the mechanism. Newton's equations of motion are solved by introducing a set of generalized unknowns, resulting in explicit formulae for all the unknowns. The dynamic analysis approach is general and is applicable to any multi-degree-of-freedom single-loop planar mechanism with revolute joints. Results are presented for illustrative examples and future extension of the presented work is discussed.

Continental growth and mantle hydration as intertwined feedback cycles in the thermal evolution of Earth

A model of Earth’s continental coverage and mantle water budget is discussed along with its thermal evolution. The model links a thermal evolution model based on parameterized mantle convection with a model of a generic subduction zone that includes the oceanic crust and a sedimentary layer as carriers of water. Part of the subducted water is used to produce continental crust while the remainder is subducted into the mantle. The total length of the subduction zones is calculated from the total surface area of continental crust assuming randomly distributed continents. The mantle viscosity is dependent of temperature and the water concentration. Sediments are generated by continental crust erosion, and water outgassing at mid-oceanic ridges closes the water cycle. We discuss the strongly coupled, non-linear model using a phase plane defined by the continental coverage and mantle water concentration. Fixed points are found in the phase plane at which the rates of change of both variables are zero. These fixed points evolve with time, but in many cases, three fixed points emerge of which two are stable and an intermediate point is unstable with respect to continental coverage. With initial conditions from a Monte-Carlo scheme we calculate evolution paths in the phase plane and find a large spread of final states that all have a mostly balanced water budget. The present day observed 40% continental surface coverage is found near the unstable fixed point. Our evolution model suggests that Earth’s continental coverage formed early and has been stable for at least 1.5Gyr. The effect of mantle water regassing (and mantle viscosity depending on water concentration) is found to lower the present day mantle temperature by about 120K, but the present day mantle viscosity is affected little. The water cycle thus complements the well-known thermostat effect of viscosity and mantle temperature. Our results further suggest that the biosphere could impact the feedback cycles by its effects on continental weathering and erosion and may be the reason for the present day steady state of continental coverage and mantle water concentration.

Path planning with obstacle avoidance by [formula omitted] PH quintic splines

We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths having no intersection with the obstacles of a given scenario. Variations of the shortest piecewise linear path with angle-based criteria are proposed and discussed. In the second part of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider the class of curves with Pythagorean structures, because they provide an exact computation of fundamental geometric quantities. A selection of test cases demonstrates the quality of the new motion planning scheme.

Planar Path Following of Underwater Snake Robots in the Presence of Ocean Currents

This letter presents a control system that enables an underwater snake robot to converge towards and follow a straight path in the presence of constant irrotational ocean currents. The robot is assumed to be neutrally buoyant, fully submerged and moving in a virtual plane with a sinusoidal gait and limited link angles. The proposed control approach uses a heading controller that exponentially stabilises the heading of the robot towards the desired heading, which is obtained by an integral line-of-sight guidance law. Uniform semiglobal exponential stability of the control system is formally proved using cascaded systems and Lyapunov theory. Simulations are presented that illustrate and validate the theoretical results.

Multiple homoclinic solutions for a one-dimensional Schrödinger equation

In this paper we study the problem of the existence of homoclinic solutions to a Schrodinger equation of the form \[ x''-V(t)x+x^3=0, \] where is a stepwise potential. The technique of proof is based on a topological method, relying on the properties of the transformation of continuous planar paths (the S.A.P. method), together with the application of the classical Conley-Wazewski's method.

Path-Following Control of an AUV: Fully Actuated Versus Under-actuated Configuration

AbstractThe problem of motion control of underwater vehicles in both the fully actuated and under-actuated configurations is often confronted by the marine technology community. This paper presents a nonlinear control method for autonomous underwater vehicles (AUVs) traveling along a planned planar path in both actuation configurations. The common objectives of path-following control for both fully actuated and under-actuated vehicles are described, and the differences in the necessary path-following control designs are analyzed, showing that the side-slip angle of the vehicle plays an important role in the evolution of the dynamics of AUVs with different actuation configurations. Based on the presented analysis, nonlinear controllers for the two types of AUV configurations are proposed, and the inherent characteristics of under-actuation and full actuation are revealed by a dedicated analysis of numerical simulation paradigms, the results of which will be instrumental in guiding marine technology engineers in the practical design and control of AUVs.

Generic Path Planning Algorithm for Mobile Robots Based on Bézier Curves

The availability of an efficient and reliable path planning strategy is a great benefit to mobile robots. Being able to intelligently connect a series of waypoints is a crucial requirement for the execution of autonomous navigation tasks. Several performance indices can be used to evaluate the goodness of a path, including its length and smoothness. In this paper, the authors focus on planar path planning for mobile robots; Bézier curves are employed, optimizing the computed path with respect to length and curvature, the latter used as a measure of smoothness. Due to the complexity of the objective function, optimization is performed by means of a direct search method. The proposed approach aims at generating paths offering advantages to mobile robots navigation in terms of controllability and reducing the related power consumption. The performed tests show that the presented method allows to achieve interesting results, suggesting its viability as a suitable path planning strategy for different kinds of mobile robots.

A tangential microslip model for circularly and elliptically loaded structures

It is well known that the noise and vibration control of structures is a continuing challenge. With many structures this is commonly achieved through passive vibration damping, often using viscoelastic materials. It is sometimes, however, that the use of such materials is not permitted as their properties change over time, or when they are subjected to low and high temperature environments. For these structures and structural elements, it is often that clamping or applied boundary conditions are critical for providing the energy dissipation through microslip. This makes it necessary to understand the level of damping that arises from the clamping zones. In general, the estimation of damping is complicated in that most structures are not unidirectionally loaded and can have a planar path of motion (e.g. gas turbine blades, circular motion valves). Although it is typical during experiments and simulations to reduce a structure into a single axis of excitation, this can often be an over simplification which does not describe the dynamics of the system; but should be included. This paper presents a biaxial planar motion tangential microslip model that accounts for the vibratory loads arising from circular and elliptical motion. This model vectorially decouples and reduces the planar vibratory circular and elliptical motion into two separate independent tangential microslip models. The models account for tip loading and for centroid loading within the microslip region of the clamping zone. Each analytical microslip model is presented and is compared to numerical simulations using finite elements. The analytical models are then coupled to demonstrate the net effect that various eccentricities have on the overall energy dissipation within the structure. The coupled models are then compared to numerical simulations using finite elements through ANSYS.

Three-Dimensional Nonlinear Differential Geometric Path-Following Guidance Law

A three-dimensional nonlinear guidance law for path-following is proposed using differential geometry of space curves. The proposed guidance law makes a vehicle converge to and then follow a given desired path of general shape, which does not require strict restrictions on initial position and velocity. To take the advantages of the look-ahead effect for precise and robust path-following, the proposed guidance law takes the form of pure pursuit guidance, which is designed to align the velocity of the vehicle with the look-ahead vector. The look-ahead angle and the radially shifted distance are designed using differential geometry of the desired path. The proposed guidance law generates the normal acceleration command required for exact path-following and finally overcomes the limitations of previously developed look-ahead point-based methods in the case of general three-dimensional path-following. Stability analysis on the guidance law to follow constant-curvature planar paths is performed. The performance of the proposed guidance law is demonstrated by numerical simulations for various types of desired paths.