Robert E. Mahony

Nonlinear Complementary Filters on the Special Orthogonal Group

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor

This article provides a tutorial introduction to modeling, estimation, and control for multirotor aerial vehicles that includes the common four-rotor or quadrotor case.

Control of a quadrotor helicopter using visual feedback

We present control methods for an autonomous four-rotor helicopter, called a quadrotor, using visual feedback as the primary sensor. The vision system uses aground camera to estimate the pose (position and orientation) of the helicopter. Two methods of control are studied - one using a series of mode-based, feedback linearizing controllers, and the other using a backstepping-like control law. Various simulations of the model demonstrate the implementation of feedback linearization and the backstepping controllers. Finally,. we present initial flight experiments. where the helicopter is restricted to vertical and yaw motions.

Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in Rn. In these formulas, p-planes are represented as the column space of n×p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications – computing an invariant subspace of a matrix and the mean of subspaces – are worked out.

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

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.

Dynamic modelling and configuration stabilization for an X4-flyer

Abstract A model for the dynamics of a four rotor vertical take-off and landing (VTOL) vehicle known as an X4-flyer is proposed. The model incorporates the airframe and motor dynamics as well as aerodynamic and gyroscopic effects due to the rotors for quasi-stationary flight conditions. A novel control strategy is proposed for configuration stabilization of quasi-stationary flight conditions. The approach taken involves separating the rigid body (airframe) dynamics from the motor dynamics, developing separate control Lyapunov functions for the coupled systems and then bounding the perturbation error due to the interaction to obtain strong practical stability of the complete system.

Landing a VTOL Unmanned Aerial Vehicle on a Moving Platform Using Optical Flow

This paper presents a nonlinear controller for a vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV) that exploits a measurement optical flow to enable hover and landing control on a moving platform, such as, for example, the deck of a sea-going vessel. The VTOL vehicle is assumed to be equipped with a minimum sensor suite [i.e., a camera and an inertial measurement unit (IMU)], manoeuvring over a textured flat target plane. Two different tasks are considered in this paper. The first concerns the stabilization of the vehicle relative to the moving platform that maintains a constant offset from a moving reference. The second concerns regulation of automatic vertical landing onto a moving platform. Rigorous analysis of system stability is provided, and simulations are presented. Experimental results are provided for a quadrotor UAV to demonstrate the performance of the proposed control strategy.

Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints

The problem of stabilization for a class of feedback linearizable systems with multiple state constraints is addressed. The design procedure is constructive, and yields a continuous final control law which guarantees that all specified states remain within certain bounds for all time. The achieved bounds on the states are independent of the initial conditions. The procedure entails shaping the control Lyapunov function, and propagating hard-bounds imposed on the pertinent stabilising functions and associated error signals through the steps of the backstepping control design framework.

Complementary filter design on the special orthogonal group SO(3)

This paper considers the problem of obtaining high quality attitude extraction and gyros bias estimation from typical low cost intertial measurement units for applications in control of unmanned aerial vehiccles. Two different non-linear complementary filters are proposed: Direct complementary filter and Passive non-linear complementary filter. Both filters evolve explicity on the special orthogonal group SO(3) and can be expressed in quaternion form for easy implementation. An extension to the passive ocmplementary filter is proposed to provide adaptive gyro bias estimation.

Image-Based Visual Servo Control of the Translation Kinematics of a Quadrotor Aerial Vehicle

In this paper, we investigate a range of image-based visual servo control algorithms for regulation of the position of a quadrotor aerial vehicle. The most promising control algorithms have been successfully implemented on an autonomous aerial vehicle and demonstrate excellent performance.