Tarek Hamel

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.

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.

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 aerial robotic systems using linear image features

An image-based eye-in-hand visual servo-control design is proposed for underactuated rigid-body dynamics. The dynamic model considered is motivated by recent work on vertical takeoff and landing aerial robotic vehicles. The task considered is that of tracking parallel linear visual features. The proposed design exploits the geometry of the task considered and passivity-like properties of rigid-body dynamics to derive a control Lyapunov function using backstepping techniques.

Landing of a Quadrotor on a Moving Target Using Dynamic Image-Based Visual Servo Control

This paper addresses the landing problem of a vertical take-off and landing vehicle, exemplified by a quadrotor, on a moving platform using image-based visual servo control. Observable features on a flat and textured target plane are exploited to derive a suitable control law. The target plane may be moving with bounded linear acceleration in any direction. For control purposes, the image of the centroid for a collection of landmarks is used as position measurement, whereas the translational optical flow is used as velocity measurement. The proposed control law guarantees convergence to the desired landing spot on the target plane, without estimating any parameter related to the unknown height, which is also guaranteed to remain strictly positive. Moreover, convergence is guaranteed even in the presence of bounded and possibly time-varying disturbances, resulting, for example, from the motion of the target plane, measurement errors, or wind-induced force disturbances. To improve performance, an estimator for unknown constant force disturbances is also included in the control law. Simulation and experimental results are provided to illustrate and assess the performance of the proposed controller.

Attitude control of rigid body dynamics from biased IMU measurements

Commercially viable aerial robotic vehicles require low-cost attitude stabilisation systems that are robust to noise and sensor bias. A typical attitude stabilisation system consists of MEMs accelerometers, gyroscopes linked to separate attitude estimator and attitude controller algorithms. This paper proposes a non-linear attitude stabiliser for low-cost aerial robotic vehicles that combines attitude and bias estimation with control. The attitude control algorithm is based on a non-linear control Lyapunov function analysis derived directly in terms of the rigid-body attitude dynamics and measurement signals.

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

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 estimate of the gravitational direction. This inertial direction, along with the gyrometer output, is then used to drive a fully non-linear attitude observer posed on the orthogonal group of rotation matrices SO(3). The observer is augmented with an integral state that ensures compensation of gyrometer bias. The resulting observer is simple to implement and fully non-linear. 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/inertial navigation system (INS) that was available for the data set.

Adaptive depth estimation in image based visual servo control of dynamic systems.

This paper considers the question of designing a fully image based visual servo control for a dynamic system. The work is motivated by the ongoing development of image based visual servo control of small aerial robotic vehicles. The observed targets considered are coloured blobs on a flat surface to which the normal direction is known. The theoretical framework is directly applicable to the case of markings on a horizontal floor or landing field. The image features used are a first order spherical moment for position and an image flow measurement for velocity. A fully non-linear adaptive control design is provided that ensures global stability of the closed-loop system.

State estimation for invariant systems on Lie groups with delayed output measurements

This paper proposes a state estimation methodology for invariant systems on Lie groups where outputs of the system are measured with delay. The proposed method is based on cascading an observer and a predictor. The observer uses delayed measurements and provides estimates of delayed states. The predictor uses those estimates together with the current inputs of the system to compensate for the delay and to provide a prediction of the current state of the system. We consider three classes of left-invariant, right-invariant, and mixed-invariant systems and propose predictors tailored to each class. The key contribution of the paper is to exploit the underlying symmetries of systems to design novel predictors that are computationally simple and generic, in the sense that they can be combined with any stable observer or filter. We provide a rigorous stability analysis demonstrating that the prediction of the current state converges to the current system trajectory if the observer state converges to the delayed system trajectory. The good performance of the proposed approach is demonstrated using a sophisticated Software-In-The-Loop simulator indicating the robustness of the observer-predictor methodology even when large measurement delays are present.

Adding an integrator for output regulation of systems with matrix Lie-group states

This paper considers the problem of tracking reference trajectories for systems defined on matrix Lie Groups. Both the reference system (exosystem) and controlled system have states on the same matrix Lie group, with the exosystem having constant velocity. The measurements are associated with a group action on a homogeneous space of the state space and can be thought of as measured partial relative state information. We look for a controller depending only on the relative state errors and the local state of the controlled system, that is a control that is independent of the exogenous variables. The proposed design embeds an integral estimate of the unknown exosystem velocity as a dynamic state in the controller. The approach is motivated by a range of robotics applications posed on classical Lie-groups SO(3), SE(3), SL(3), although we develop a general result for kinematic systems on arbitrary matrix Lie-groups. In the specific case of SO(3), namely systems defined on the Lie-group of orthogonal rotations, we go further by presenting an `error feedback controller for systems modeled by kinematics and dynamics equations.