Juan I. Giribet

Indoor navigation using WiFi signals

Every day we use location-dependant services, but there is still a lack of information in terms of a popular indoor location system. In this paper we show methods and some advantages of using already installed infraestructure such as WiFi Access Points to get navigation information. For these purpose an indoor navigation system was implemented using both inertial sensors and WiFi signal strength information. The whole system architectute, both hardware and software, is designed with a modular aproach in order to make easy the test and benchmark of different algotithms and data fusion techniques. Basic algorithms have been implemented to validate the whole system using simulated data through a software-in-the-loop setup.

An approach to benchmarking of loosely coupled low-cost navigation systems

New solutions to the navigation problem related to low-cost integrated navigation systems (INS) are often published. Since these new solutions are generally compared with ad hoc mathematical models that are not fully exposed, one cannot be sure of the relative improvements. In this work, complete mathematical model for a low-cost INS is suggested to be used as a benchmarking. As far as the authors’ knowledge, a benchmarking for low-cost INS has not been previously reported. Shown INS comprises a strapdown inertial navigation system, loosely coupled to a GPS receiver. The INS mathematical model is based upon classical navigation equations and classical sensor models, both from recognized authors. The algorithm that details the INS operation is also presented. The benchmarking is provided as an open-source toolbox for MATLAB. Additionally, this work can be taken as a starting point for new practitioners in the INS field. To validate the INS mathematical model, real-world data sets from three different Micro Electro-Mechanical Systems (MEMS) inertial measurement units (IMU) and a GPS receiver are processed. It is observed that obtained RMS errors from the three INS are coherent with the quality of corresponding MEMS IMU. This confirms that the proposed benchmarking is a suitable tool to evaluate objectively new solutions to low-cost INS.

Weighted Procrustes problems

Abstract Let H be a Hilbert space, L ( H ) the algebra of bounded linear operators on H and W ∈ L ( H ) a positive operator such that W 1 / 2 is in the p-Schatten class, for some 1 ≤ p ∞ . Given A ∈ L ( H ) with closed range and B ∈ L ( H ) , we study the following weighted approximation problem: analyze the existence of m i n X ∈ L ( H ) ‖ A X − B ‖ p , W , where ‖ X ‖ p , W = ‖ W 1 / 2 X ‖ p . In this paper we prove that the existence of this minimum is equivalent to a compatibility condition between R ( B ) and R ( A ) involving the weight W , and we characterize the operators which minimize this problem as W -inverses of A in R ( B ) .

Analysis and design of a tilted rotor hexacopter for fault tolerance

A proof is presented of how a hexagon-shaped hexacopter can be designed to keep the ability to reject disturbance torques in all directions while counteracting the effect of a failure in any of its motors. The method proposed is simpler than previous solutions, because it does not require change of the motor rotation direction or in-flight mechanical reconfiguration of the vehicle. It consists of tilting the rotor a small fixed angle with respect to the vertical axis. Design guidelines are presented to calculate the tilt angle to achieve fault-tolerant attitude control without losing significant vertical thrust. It is also formally proved that the minimum number of unidirectional rotating motors needed to have fault tolerance is 6 and that this can be achieved by tilting their rotors. This proof is essentially a control allocation analysis that recovers in a simple way a result already known: the standard configuration (without tilting the motors) is not fault tolerant. A simulation example illustrates the theory.

Spectrum of J-frame operators

A \(J\)-frame is a frame \(\mathcal{F}\) for a Krein space \((\mathcal{H},[\cdot,\cdot ])\) which is compatible with the indefinite inner product \([\cdot,\cdot ]\) in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in \(\mathcal{H}\). With every \(J\)-frame the so-called \(J\)-frame operator is associated, which is a self-adjoint operator in the Krein space \(\mathcal{H}\). The \(J\)-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of \(J\)-frame operators in a Krein space by a \(2\times 2\) block operator representation. The \(J\)-frame bounds of \(\mathcal{F}\) are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the \(2\times 2\) block representation. Moreover, this \(2\times 2\) block representation is utilized to obtain enclosures for the spectrum of \(J\)-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all \(J\)-frames associated with a given \(J\)-frame operator.

INS/Ultrasound navigation system

The aim of this work is to present a navigation system for GPS denied environments. The system fuses measurements provided by an arrangement of ultrasonic range sensors with inertial measurements and a magnetometer. The core of the navigation computer are two microprocessors, an ARM Cortex M3 processor for low-level tasks, such as sensor acquisition and control, and an ARM Cortex A8 for computationally demanding tasks, as the fusion filter to compute navigation solutions. A brief description of the navigation computer is given, also the navigation algorithm is presented and validated through experimental results.

Shorted operators and minus order

ABSTRACT Let be a Hilbert space, the algebra of bounded linear operators on and a positive operator. Given a closed subspace of , we characterize the shorted operator of W to as the maximum and as the infimum of certain sets, for the minus order . Also, given with closed range, we study the following operator approximation problem considering the minus order: We show that, under certain conditions, the shorted operator of is the minimum of this problem and we characterize the set of solutions.

Formation control for multi-domain autonomous vehicles based on dual quaternions

Unmanned networked multirobot systems have the potential to accomplish complex field tasks with minimum human intervention. Motion coordination of vehicles that operate in different domains (land, sea, air) is one of the problems that need to be addressed to achieve such a goal. This article presents a representation method based on dual quaternions for leader- follower formation control architectures. This representation offers the most compact and computationally efficient screw transformation formalism and can be used to describe rigid body motions because they simultaneously describe positions and orientations with only eight parameters. A controller in dual quaternion formation space is proposed and analyzed. Computer simulation results and experimental tests applied to the task of escorting an UGV with UAVs are shown to verify the functionality of the proposed system.

Hexacopter fault tolerant actuator allocation analysis for optimal thrust

Recently, it was shown that an hexagon shaped hexarotor vehicle with tilted rotors, is capable of fault tolerant attitude and altitude control. In this work, we propose a strategy to select the signals commanded to each rotor in order to achieve a desired torque and vertical force. The proposed strategy is optimal in the sense that minimizes the maximum force exerted by the rotors. A comparison with the commonly used strategy based upon the Moore-Penrose pseudoinverse is carried out. It is shown that, with the optimal strategy proposed here, maneuverability is improved, because the new method takes into account the actuators constraints. Although the optimal strategy is computationally more demanding than the classical method, the additional computational burden is not significant when both strategies are compared in a real application. To show this, both algorithms were programmed in an autopilot based on an ARM Cortex M3 microcontroller, and the experimental results are presented.

Visual Target-Tracking Using a Formation of Unmanned Aerial Vehicles

We present a method to visually track and follow a target using a platoon of three unmanned aerial vehicles for the purpose of surveillance, monitoring or escorting. A coordination control technique that enhances specification and monitoring of high level formation parameters such as position, orientation and size is used as a basis for the coordination. A model of a video camera is employed to obtain relative positions with respect to the target of interest. An open-source simulator of Parrot Ar.Drone quadrotors running on the Robot Operating System environment is used to demonstrate the system functionality. Two test cases are presented to illustrate the validity of the approach.Copyright