State estimation of a cheetah spine and tail using an inertial sensor network

The cheetah (Acinonyx jubatus) is by far the most manoeuvrable and agile terrestrial animal. Little is known, in terms of biomechanics, about how it achieves these incredible feats of manoeuvrability. The transient motions of the cheetah all involve rapid flicking of its tail and flexing of its spine. The aim of the research was to develop tools (hardware and software) that can be used to gain a better understanding of the cheetah tail and spine by capturing its motion. A mechanical rig was used to simulate the tail and spine motion. This insight may inspire and aid in the design of bio-inspired robotic platforms. A previous assumption was that the tail is heavy and acts as a counter balance or rudder, yet this was never tested. Contrary to this assumption, necropsy results determined that the tail was in fact light with a relatively low inertia value. Fur from the tail was used in wind tunnel experiments to determine the drag coefficient of a cheetah tail. No researchers have actively sought to track the motion of a cheetah's spine and tail during rapid manoeuvres via placing multiple sensors on a cheetah. This requires the development of a 3D dynamic model of the spine and tail to accurately study the motion of the cheetah. A wireless sensor network was built and three different filters and state estimation algorithms were designed and validated with a mechanical rig and camera system. The sensor network consists of three sensors on the tail (base, middle and tip) as well as a hypothetical collar sensor (GPS and WiFi were not implemented)

Head Tracking for 3D Audio Using a GPS-Aided MEMS IMU

Audio systems have been developed which use stereo headphones to project sound in three dimensions. When using these 3D audio systems, audio cues sound like they are originating from a particular direction. There is a desire to apply 3D audio to general aviation applications, such as projecting control tower transmissions in the direction of the tower or providing an audio orientation cue for VFR pilots who find themselves in emergency zero-visibility conditions. 3D audio systems, however, require real-time knowledge of the pilot\u27s head orientation in order to be effective. This research describes the development and testing of a low-cost head tracking system for 3D audio rendering applied in general aviation. The system uses a low-cost MEMS IMU combined with a low-cost, single frequency GPS receiver. Real-time data from both of these systems was sent to a laptop computer where a real-time Kalman filter was implemented in MATLAB to solve for position velocity, and attitude. The attitude information was then sent to a 3D audio system for sound direction rendering. The system was flight tested on board a Raytheon C-12C aircraft. The accuracy of the system was measured by comparing its output to truth data from a high-accuracy post-processed navigation-grade INS/DGPS solution. Results showed that roll and pitch error were accurate to within 1-2 degrees, but that heading error was dependent upon the flight trajectory. During straight-and-level flight, the heading error would drift up to 10-15 degrees because of heading unobservability. However, even with heading error, the ability of a pilot to determine the correct direction of a 3D audio cue was significantly improved when using the developed head tracking system over using the navigation-grade INS/GPS system fixed to the aircraft

A practical method for implementing an attitude and heading reference system

This paper describes a practical and reliable algorithm for implementing an Attitude and Heading Reference System (AHRS). This kind of system is essential for real time vehicle navigation, guidance and control applications. When low cost sensors are used, efficient and robust algorithms are required for performance to be acceptable. The proposed method is based on an Extended Kalman Filter (EKF) in a direct configuration. In this case, the filter is explicitly derived from both the kinematic and rror models. The selection of this kind of EKF configuration can help in ensuring a tight integration of the method for its use in filter-based localization and mapping systems in autonomous vehicles. Experiments with real data show that the proposed method is able to maintain an accurate and drift-free attitude and heading estimation. An additional result is to show that there is no ostensible reason for preferring that the filter have an indirect configuration over a direct configuration for implementing an AHRS system.Postprint (published version

Design and Analysis of an Attitude Determination and Control Subsystem (ADCS) for AFIT\u27s 6U Standard Bus

The design and testing of AFIT\u27s 6U Attitude Determination and Control Subsystem (ADCS) are explored to establish 3-axis attitude control. The development of AFIT\u27s 6U CubeSat standard bus is an on-going research effort designed to create in-house CubeSat bus components and software. The 6U chassis measures approximately 11 x 24 x 37 cu cm and can have a mass up to 12 kg. The larger bus size (as compared to the more common 3U CubeSat) allows for increased power capabilities and potential to host multiple or larger payloads. Individual ADCS hardware components were either commercially purchased or built in-house and include an IMU, external magnetometer, 4-wheel reaction wheel assembly, and three torque coils. The ADCS software developed as part of this research includes the QUEST attitude determination algorithm, B-dot de-tumbling algorithm, and PD control algorithm with momentum dumping capability. To facilitate ADCS testing, an air bearing assembly was designed and set up in AFIT\u27s existing Helmholtz cage. The air bearing provides a near-frictionless environment with 360 deg rotation about one axis and limited (35 deg) rotations about the other two axes. The Helmholtz cage consists of three orthogonal magnetic coil pairs that can create a uniform + or - 2 Gauss magnetic eld within the cage. This comprehensive ADCS testing environment was used to test a ground-based 6U CubeSat complete with ADCS, CDH, and EPS components. The custom-built torque coils demonstrated torquing abilities on the spacecraft and yield a 0.66 A-sq m magnetic moment. In addition, single-axis attitude control was achieved using the reaction wheel assembly. Recommendations for further developments and testing are included to achieve the desired 3-axis control

Real-time implementation of some attitude estimation algorithms on a quadrotor UAV / by Siddhant Nayak.

The recent developments in research pertaining to the field of Unmanned Aerial Vehicles (UAVs) is motivated by its technical challenges as well as its practical implications in areas where human presence is inefficient, redundant or dangerous. The absence of human interference requires more robust and precise control techniques. However, most modern attitude control techniques require the knowledge of the current orientation of the body. There is no sensor available that explicitly measures the attitude of a rigid body and hence, for small scale UAVs. it must be estimated using inertial vector measurements from low-cost and low-weight Micro-Electro-Mechanical System (MEMS) sensors like gyroscopes, accelerometers and magnetometers. The predominant attitude representation formulations of a rigid body in three-dimensional space are recapitulated to elucidate the dynamical model of a quadrotor UAV. Low-cost MEMS are prone to significant noise effects from temperature change, vibrations, on-board magnetic fields generated by motors and currents. To improve the accuracy of the measurements sensor calibration techniques are explored. Primitive attitude estimation techniques like TRIAD, Davenports q-method, QUEST.FOAM, SVD method, etc. (which were aimed to be static optimization solutions to Wahbas Problem) were reviewed. These algorithms were extended to incorporate filtering techniques like Kahnan-type, to handle the measurement noise, and complementary filtering, where sensor measurements are fused to reconstruct the orientation of a rigid body. Tlie latest nonlinear observers are also discussed for implementation purposes. Practical implementation and performance comparison of various attitude estimation algorithms has been conducted on a small-scale quadrotor UAV, consisting of an inertial measurement unit (3-axis gyroscope, accelerometer and magnetometer), microcontroller, brushless motors, electronic speed controllers, on-board power supply and necessary frame constructs

Hybrid Projectile Body Angle Estimation for Selectable Range Increase

A Hybrid Projectile (HP) is a tube launched munition that transforms into a gliding UAV, and is currently being researched at West Virginia University. A simple launch timer was first envisioned to control the transformation point in order to achieve maximum distance. However, this timer would need to be reprogrammed for any distance less than maximum range due to the nominal time to deployment varying with launch angle. A method was sought for automatic wing deployment that would not require reprogramming the round. A body angle estimation system was used to estimate the pitch of the HP relative to the Earth to determine when the HP is properly oriented for the designed glide slope angle. It was also necessary to filter out noise from a simulated inertial measurement unit (IMU), GPS receiver, and magnetometer. An Extended Kalman Filter (EKF) was chosen to estimate the Euler angles, position and velocity of the HP while an algorithm determined when to deploy the wings. A parametric study was done to verify the optimum deployment condition using a Simulink aerodynamic model. Because range is directly related to launch angle, various launch angles were simulated in the model. By fixing the glide slope angle to -10° as a deployment condition for all launch angles, the range differed only by a maximum of 6.1% from the maximum possible range. Based on these findings, the body angle deployment condition provides the most flexible option to maintain maximum distance without the need of reprogramming. Position and velocity estimates were also determined from the EKF using the GPS measurements. Simulations showed that the EKF estimates exhibited low root mean squared error values, corresponding to less than 3% of the total position values. Because the HP was in flight for less than a minute in this experiment, the drift encountered was acceptable

Keeping a Good Attitude: A Quaternion-Based Orientation Filter for IMUs and MARGs

Orientation estimation using low cost sensors is an important task for Micro Aerial Vehicles (MAVs) in order to obtain a good feedback for the attitude controller. The challenges come from the low accuracy and noisy data of the MicroElectroMechanical System (MEMS) technology, which is the basis of modern, miniaturized inertial sensors. In this article, we describe a novel approach to obtain an estimation of the orientation in quaternion form from the observations of gravity and magnetic field. Our approach provides a quaternion estimation as the algebraic solution of a system from inertial/magnetic observations. We separate the problems of finding the “tilt” quaternion and the heading quaternion in two sub-parts of our system. This procedure is the key for avoiding the impact of the magnetic disturbances on the roll and pitch components of the orientation when the sensor is surrounded by unwanted magnetic flux. We demonstrate the validity of our method first analytically and then empirically using simulated data. We propose a novel complementary filter for MAVs that fuses together gyroscope data with accelerometer and magnetic field readings. The correction part of the filter is based on the method described above and works for both IMU (Inertial Measurement Unit) and MARG (Magnetic, Angular Rate, and Gravity) sensors. We evaluate the effectiveness of the filter and show that it significantly outperforms other common methods, using publicly available datasets with ground-truth data recorded during a real flight experiment of a micro quadrotor helicopter

UAV perception for safe flight under physical interaction

The control of autonomous flying vehicles with navigation purposes is a challenging task. Complexity arises mainly due to the non-linearity and uncertainty inherently present in the flight mechanics and aircraft-air interactions. Recently, interest has grown for equipping unmanned vehicles with the capacity to interact with their environment, other vehicles or humans. This will enable interesting applications such as autonomous load carrying, aerial refueling or parcel delivering. Having measured the interaction wrenches ease the control problem which can be configured to reject disturbances or to take profit of them to fulfill mission objectives. This thesis will contribute to this area by providing perception solutions which use limited and low cost sensors that enable state and disturbance estimation for possible, but not restricted to, interaction scenarios. This thesis contain three parts. The first part, introduces basic concepts related to the navigation state, aircraft dynamics, and sensor models. In addition, the platform under study is presented and mathematical models associated to it are calibrated. The second part is devoted to the observability analysis and the design of state observers. Linear and non-linear observability analysis techniques are used to unveil that the state of quadrotors equipped with GPS, magnetometers an IMU sensors cannot be uniquely identified in some specific flight configurations. Results of this section are relevant because the conflicting flight configurations contain hover, a flight maneuverer central in many unmanned aerial missions of VtoL vehicles. For many possible singular configurations, insightful descriptions and interpretations of the solution space known as indistinguishable region is provided. Findings are verified in simulation scenarios where it can be seen how a filter fails to recover the true state of an aircraft when imposing the hover flight condition. We discuss then the design of Extended Kalman Filters for state estimation that considers the available sensors. Issues that are typically not reported in the literature, such as when to update or propagate in the estimator algorithm or which coordinate frame should be used to represent each state variable are discussed. This leads to the formulation of four potentially equivalent but different discrete event-based filters for which precise algorithmic expressions are given. We compare the results of the four filters in simulation under known favorable conditions for observability. In order to diminish the effect of flying in the conflicting observability configurations, we provide an alternative filter based on the Schmidt Kalman Filter (SKF). The proposed filter shares the structure of the EKF, behaves better in the instants that the EKF fails and provides similar results in the remaining conditions. The last part of the thesis deals with the estimation of external disturbances. Disturbance estimation results are based on the derivation of a linear model for the aircraft dynamics which then extended with a high order disturbance model to enable the estimation of fast varying disturbances. Two external disturbance estimators from the literature are reviewed and adapted to the new model. Also, two Kalman observers that exploit the linearity of the derived model are presented. A simulation comparison is provided demonstrating that the KF disturbance estimators outperform the other. In addition, this part presents a design methodology of generic quadratic bounded observers for linear systems with ellipsoidal bounded uncertainty. The derived observers maximize a user tunable compromise between the estimation convergence speed and the final volume containing the estimation error. An observer for disturbances acting on a flying platform is derived considering the high order disturbance model above mentioned. Finally, an analysis of the estimation performance with respect to the design parameters is presented.Esta tesis, contribuye en este área formulando soluciones de percepción que permiten la estimación del estado y perturbaciones externas en condiciones normales de vuelos así como casos de interacción para UAVs equipados con sensores limitados y de bajo coste. La tesis se estructura en tres partes. La primera de ellas introduce los conceptos básicos relacionados con el estado de navegación, la dinámica de la aeronave y modelos de sensores. Además, se presenta la plataforma de estudio así como los modelos matemáticos asociados a ella y su calibración. La segunda parte está destinada al análisis de observabilidad y el diseño de observadores de estado. Los resultados de esta sección son importantes porque dentro de las condiciones de vuelo conflictivas se encuentra el vuelo a punto fijo, una maniobra de vuelo central en muchas misiones de vehículos VToL. Se analizan estas condiciones críticas de vuelo y para ellas se deriva y describe el espacio de soluciones posible conocido como región indistinguible. Los resultados son verificados en simulación dónde se puede apreciar como un estimador de estado falla al intentar realizar su tarea cuando la aeronave está en vuelo a punto fijo. Seguidamente se presenta el diseño de filtros extendidos de Kalman (EKF) que proveen estimaciones del estado con la información limitada de los sensores disponibles. Se discuten conceptos que habitualmente no se presentan en la literatura como cuando actualizar o propagar en el algoritmo de estimación o que sistema de referencia se debe utilizar para representar adecuadamente las variables de estado. Esto lleva a la formulación algorítmica de cuatro filtros discretos basados en eventos, diferentes, pero en esencia equivalentes. Se derivan rutinas de inicialización para los filtros y se comparan los resultados en simulación bajo condiciones favorables de estimación. Con la idea de disminuir el efecto de volar en configuraciones de observabilidad conflictivas, se deriva un filtro alternativo basado en el filtro de Schmidt Kalman (SKF). El filtro propuesto comparte estructura con el EKF, tiene un mejor comportamiento allí dónde le EKF falla y una respuesta similar en el resto de condiciones de vuelo. La última parte de la tesis trata con la estimación de perturbaciones externas. Para ello se deriva un modelo lineal que relaciona fuerzas y momentos con velocidades junto a un modelo de alto orden para las perturbaciones. Se estudia su aplicación a dos modelos para la estimación de perturbaciones ya presentes en la literatura. Además, se proponen dos nuevos filtros de Kalman que se aprovechan de la linealidad del modelo. Se presenta una comparativa basada en la simulación de escenarios ideales así como realistas que demuestra que los filtros KF superan al resto. Esta misma parte de la tesis presenta el diseño genérico de estimadores "quadratic bounded" para sistemas dinámicos lineales cuya incertidumbre se encuentra acotada dentro de elipsoides. Estos estimadores maximizan un compromiso, ajustable por el usuario que contempla la velocidad de convergencia así como el volumen de la solución final que contiene el error de estimación. Se deriva un observador de perturbaciones para plataformas aéreas basado en el modelo de alto orden arriba mencionado. Finalmente, se presenta un análisis del desempeño de estimación en función de los parámetros de diseño del filtro