Nikolaj Nordkvist

An Almost Global Tracking Control Scheme for Maneuverable Autonomous Vehicles and its Discretization

This technical note treats the challenging control problem of tracking a desired continuous trajectory for a maneuverable autonomous vehicle in the presence of gravity, buoyancy and fluid dynamic forces and moments. A realistic dynamics model that applies to maneuverable vehicles moving in 3-D Euclidean space is used for obtaining this control scheme. While applications of this control scheme include autonomous aerial and underwater vehicles, we focus on an autonomous underwater vehicle (AUV) application because of its richer, more nonlinearly coupled, dynamics. The desired trajectory and trajectory tracking errors are globally characterized in the nonlinear state space. Almost global asymptotic stability to the desired trajectory in the nonlinear state space is demonstrated both analytically and through numerical simulations.

Attitude State Estimation with Multirate Measurements for Almost Global Attitude Feedback Tracking

A state estimation scheme that does not depend on the statistical distribution of bounded measurement noise is presented. This scheme is used to provide state estimates for feedback in an attitude tracking control scheme that exhibits almost global asymptotically stable tracking of a desired attitude trajectory with perfect state measurements. The control and estimation schemes use the global, unique representation of rigid body attitude provided by rotation matrices. Attitude and angular velocity state estimate updates are obtained from discrete multi-rate measurements using a deterministic filtering scheme. Propagation of discrete state estimates is carried out with a Lie group variational integrator, which preserves the orthogonality of rotation matrices during numerical propagation without reprojection. This integrator is also used to numerically simulate the feedback system. The performance of this attitude tracking control scheme is then compared with that of a recently reported quaternion observer-based continuous feedback attitude tracking scheme. This quaternion-based attitude tracking scheme is shown to exhibit unstable, unwinding behavior. Numerical

Attitude feedback tracking with optimal attitude state estimation

This paper presents an estimator-based attitude tracking control scheme that uses feedback of attitude and angular velocity estimates constructed by an optimal state estimation scheme. The tracking control scheme gives almost global convergence to a desired attitude and angular velocity profile with perfect state feedback. The estimation scheme consists of measurement, filtering and state propagation stages, and the measurements are assumed to have deterministic error bounds. These error bounds are ellipsoidal and are referred to as uncertainty ellipsoids. Each measurement is followed by a filtering stage, which obtains the minimum-volume ellipsoid that contains the intersection of uncertainty ellipsoids corresponding to the estimated states and the measured states. The state estimates are propagated between measurements using a variational integrator that discretizes the equations of motion. This estimator-based tracking control scheme is applied to the model of a satellite in circular Earth orbit. Numerical simulation results with realistic error bounds on attitude and angular velocity measurements show the good performance of this estimator-based control scheme.

A Robust Estimator for Almost Global Attitude Feedback Tracking

This article presents a robust and almost global feedback attitude tracking control scheme in conjunction with a robust deterministic estimator that constructs state estimates for feedback. These control and the estimation schemes use the natural and globally unique representation of rigid body attitude provided by rotation matrices. Attitude and angular velocity state estimates are constructed from discrete (possibly multi-rate) measurements and a deterministic filtering scheme. Computational implementation of this estimator-based tracking scheme is carried out with a Lie group variational integrator, which preserves the rotation matrix structure without need for reprojection. Numerical simulation results obtained using this integrator show the robust and almost global tracking properties of this scheme. We also compare the performance of this attitude tracking control scheme with a quaternion observer-based feedback attitude tracking control scheme that has appeared in recent literature. Numerical simulation results are obtained for tracking an oscillating angular velocity spin maneuver with both the attitude tracking schemes for a satellite in circular Earth orbit. These results demonstrate the advantages of our scheme in attitude tracking of continuous rotational motions.

Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups

We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation analysis and the design of inversion primitives and composition methods. We illustrate the algorithms on an underactuated planar rigid body and on a satellite with two thrusters.

Robust Tracking Control of Autonomous Underwater Vehicles in the Presence of Disturbance Inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.