Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Obstacle avoidance routing scheme through optimal sink movement for home monitoring and mobile robotic consumer devices

In recent years, ZigBee has been proven to be an excellent solution to create scalable and flexible home automation networks. In a home automation network, consumer devices typically collect data from a home monitoring environment and then transmit the data to an end user through multi-hop communication without the need for any human intervention. However, due to the presence of typical obstacles in a home environment, error-free reception may not be possible, particularly for power constrained devices. A mobile sink based data transmission scheme can be one solution but obstacles create significant complexities for the sink movement path determination process. Therefore, an obstacle avoidance data routing scheme is of vital importance to the design of an efficient home automation system. This paper presents a mobile sink based obstacle avoidance routing scheme for a home monitoring system. The mobile sink collects data by traversing through the obstacle avoidance path. Through ZigBee based hardware implementation and verification, the proposed scheme successfully transmits data through the obstacle avoidance path to improve network performance in terms of life span, energy consumption and reliability. The application of this work can be applied to a wide range of intelligent pervasive consumer products and services including robotic vacuum cleaners and personal security robots1.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Investigating music tempo as a feedback mechanism for closed-loop BCI control

The feedback mechanism used in a brain-computer interface (BCI) forms an integral part of the closed-loop learning process required for successful operation of a BCI. However, ultimate success of the BCI may be dependent upon the modality of the feedback used. This study explores the use of music tempo as a feedback mechanism in BCI and compares it to the more commonly used visual feedback mechanism. Three different feedback modalities are compared for a kinaesthetic motor imagery BCI: visual, auditory via music tempo, and a combined visual and auditory feedback modality. Visual feedback is provided via the position, on the y-axis, of a moving ball. In the music feedback condition, the tempo of a piece of continuously generated music is dynamically adjusted via a novel music-generation method. All the feedback mechanisms allowed users to learn to control the BCI. However, users were not able to maintain as stable control with the music tempo feedback condition as they could in the visual feedback and combined conditions. Additionally, the combined condition exhibited significantly less inter-user variability, suggesting that multi-modal feedback may lead to more robust results. Finally, common spatial patterns are used to identify participant-specific spatial filters for each of the feedback modalities. The mean optimal spatial filter obtained for the music feedback condition is observed to be more diffuse and weaker than the mean spatial filters obtained for the visual and combined feedback conditions.

Optimal infinity-quasiconformal immersions

For a Hamiltonian K ∈ C2(RN × n) and a map u:Ω ⊆ Rn − → RN, we consider the supremal functional (1) The “Euler−Lagrange” PDE associated to (1)is the quasilinear system (2) Here KP is the derivative and [ KP ] ⊥ is the projection on its nullspace. (1)and (2)are the fundamental objects of vector-valued Calculus of Variations in L∞ and first arose in recent work of the author [N. Katzourakis, J. Differ. Eqs. 253 (2012) 2123–2139; Commun. Partial Differ. Eqs. 39 (2014) 2091–2124]. Herein we apply our results to Geometric Analysis by choosing as K the dilation function which measures the deviation of u from being conformal. Our main result is that appropriately defined minimisers of (1)solve (2). Hence, PDE methods can be used to study optimised quasiconformal maps. Nonconvexity of K and appearance of interfaces where [ KP ] ⊥ is discontinuous cause extra difficulties. When n = N, this approach has previously been followed by Capogna−Raich ? and relates to Teichmüller’s theory. In particular, we disprove a conjecture appearing therein.

Optimal power management strategy for energy storage with stochastic loads

In this paper, a power management strategy (PMS) has been developed for the control of energy storage in a system subjected to loads of random duration. The PMS minimises the costs associated with the energy consumption of specific systems powered by a primary energy source and equipped with energy storage, under the assumption that the statistical distribution of load durations is known. By including the variability of the load in the cost function, it was possible to define the optimality criteria for the power flow of the storage. Numerical calculations have been performed obtaining the control strategies associated with the global minimum in energy costs, for a wide range of initial conditions of the system. The results of the calculations have been tested on a MATLAB/Simulink model of a rubber tyre gantry (RTG) crane equipped with a flywheel energy storage system (FESS) and subjected to a test cycle, which corresponds to the real operation of a crane in the Port of Felixstowe. The results of the model show increased energy savings and reduced peak power demand with respect to existing control strategies, indicating considerable potential savings for port operators in terms of energy and maintenance costs.