We describe a model to estimate motion from monocular visual and inertial measurements. We analyze the model and characterize the conditions under which its state is observable, and its parameters are identifiable. These include the unknown gravity vector, and the unknown transformation between the camera coordinate frame and the inertial unit. We show that it is possible to estimate both state and parameters as part of an on-line procedure, but only provided that the motion sequence is â??rich enoughâ??, a condition that we characterize explicitly. We then describe an efficient implementation of a filter to estimate the state and parameters of this model, including gravity and camera-to-inertial calibration. It runs in real-time on an embedded platform. We report experiments of continuous operation, without failures, re-initialization, or re-calibration, on paths of length up to 30 km. We also describe an integrated approach to â??loop-closureâ??, that is the recognition of previously seen locations and the topological re-adjustment of the traveled path. It represents visual features relative to the global orientation reference provided by the gravity vector estimated by the filter, and relative to the scale provided by their known position within the map; these features are organized into â??locationsâ?? defined by visibility constraints, represented in a topological graph, where loop-closure can be performed without the need to re-compute past trajectories or perform bundle adjustment. The software infrastructure as well as the embedded platform is described in detail in a previous technical report.

Visual-inertial navigation, mapping and localization: A scalable real-time causal approach

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.

/pdf/keeping-a-good-attitude-a-quaternion-based-orientation-2uoi13loy2.pdf

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

Time-varying formation control for unmanned aerial vehicles with switching interaction topologies

The present invention provides methods and apparatus for unmanned aerial vehicles (UAVs) with improved reliability. According to one aspect of the invention, interference experienced by onboard sensors from onboard electrical components is reduced. According to another aspect of the invention, user-configuration or assembly of electrical components is minimized to reduce user errors.

Unmanned aerial vehicle and operations thereof

Real-time orientation estimation using low-cost inertial sensors is essential for all the applications where size and power consumption are critical constraints. Such applications include robotics, human motion analysis, and mobile devices. This paper presents a linear Kalman filter for magnetic angular rate and gravity sensors that processes angular rate, acceleration, and magnetic field data to obtain an estimation of the orientation in quaternion representation. Acceleration and magnetic field observations are preprocessed through a novel external algorithm, which computes the quaternion orientation as the composition of two algebraic quaternions. The decoupled nature of the two quaternions makes the roll and pitch components of the orientation immune to magnetic disturbances. The external algorithm reduces the complexity of the filter, making the measurement equations linear. Real-time implementation and the test results of the Kalman filter are presented and compared against a typical quaternion-based extended Kalman filter and a constant gain filter based on the gradient-descent algorithm.

A Linear Kalman Filter for MARG Orientation Estimation Using the Algebraic Quaternion Algorithm

This paper considers the question of using a nonlinear complementary filter for attitude estimation of fixed-wing unmanned aerial vehicle (UAV) given only measurements from a low-cost inertial measurement unit. A nonlinear complementary filter is proposed that combines accelerometer output for low frequency attitude estimation with integrated gyrometer output for high frequency estimation. The raw accelerometer output includes a component corresponding to airframe acceleration, occurring primarily when the aircraft turns, as well as the gravitational acceleration that is required for the filter. The airframe acceleration is estimated using a simple centripetal force model (based on additional airspeed measurements), augmented by a first order dynamic model for angle-of-attack, and used to obtain estimates of the gravitational direction independent of the airplane manoeuvres. Experimental results are provided on a real-world data set and the performance of the filter is evaluated against the output from a full GPS/INS that was available for the data set.

/pdf/a-complementary-filter-for-attitude-estimation-of-a-fixed-on3b6oh9oc.pdf

A complementary filter for attitude estimation of a fixed-wing UAV

In this paper we propose a simple non-linear observer for attitude estimation based only on output from a typical inertial measurement unit (IMU) and dynamic pressure sensor embarked on a low-cost unmanned aerial vehicle. In particular, we aim to provide a good quality attitude estimate in the absence of global positioning system (GPS) ground truth and with potential low-frequency bias and high-frequency noise in the IMU sensor measurements. In addition, the case where the IMU only provides gyrometer and accelerometer outputs is considered; that is, there is no magnetometer output or it cannot be used due to local magnetic disturbances such as are common on a vehicle with electric motors. The proposed observer uses a simple centripetal force model (based on gyrometer and dynamic pressure measurements), augmented by a first-order dynamic model for angle of attack, to estimate non-inertial components of the acceleration. This estimate is used to correct the accelerometer output to provide a low-frequency es...

A non-linear observer for attitude estimation of a fixed-wing unmanned aerial vehicle without GPS measurements:

This paper presents methods which enable the Rao-Blackwellised (R-B) particle filtering technique to be applicable for the airborne simultaneous localisation and mapping problem. Although R-B filter has been successfully applied to mobile/ground vehicles, its extension to flying vehicles has been impractical due to the high dimensionality involved in inertial navigation system (INS). To overcome this problem, the full INS state is further partitioned into an external state (vehicle pose) and an internal state (navigation and sensor calibration), with a particle filter being applied only to the external state. The computational complexity is further reduced by developing a hybrid R-B Inertial-SLAM. Simulation results will be presented with simulated flight data, showing reliable performances during loop-closures.

https://www.araa.asn.au/acra/acra2007/papers/paper161final.pdf

Mark Euston

Papers

A complementary filter for attitude estimation of a fixed-wing UAV

A non-linear observer for attitude estimation of a fixed-wing unmanned aerial vehicle without GPS measurements:

Rao-Blackwellised Inertial-SLAM with Partitioned Vehicle Subspace