Zdenek Hurak

Combined line-of-sight inertial stabilization and visual tracking: application to an airborne camera platform

The paper describes a novel pointing & tracking feedback algorithm for an inertially stabilized double gimbal airborne camera system equipped with a computer vision system. The key idea is to enhance the intuitive decoupled controller structure its optical axis. The resulting controller can also compensate for the apparent translation between the camera and the observed object, but then the velocity of this mutual translational motion must be measured or estimated. The proposed algorithm turns out to be more insensitive to longer sampling periods of the computer vision system.

Delay compensation in a dual-rate cascade visual servomechanism

The paper presents a simple technique for a compensation of a one-sampling-period delay in the outer (position) loop in a cascade visual servomechanism with the inner feedback loop taking care of a velocity. The result presented in the paper is mainly relevant for visual servoing applications, since the velocity sensors such as tachometers or gyros usually achieve much higher sampling rate compared to computer vision systems playing the role of position sensors. The technique is based on the concept of a modified Smith compensator wherein the undelayed output of a mathematical model is replaced by a measured value of a signal from the inner loop. Casting this intuitive solution as a special instance of a theoretical methodology not only gives an insight but also suggests a generalization based on a multirate estimation theory, which might offer yet some more improvement.

PDdE-based analysis of vehicular platoons with spatio-temporal decoupling

Abstract The paper provides exact analytical solutions of wave-like PDdE-based (partial differential-difference equation) models of several popular vehicular platooning problems with bidirectional distributed control. Efficient evaluation of eigenvalues, eigenfunctions and wave velocities is proposed for a finite vehicular platoon without an approximation by a continuum model. Thanks to the decoupling of spatial and temporal dynamics, closed-loop stability can be analyzed by looking at a characteristic polynomial using a root-locus-like graphical technique. Although the paper only contains discussions for static state feedback controllers (using measurements of inter-vehicular distances and relative velocities), extensiona to higher-order (dynamic) controllers is straighforward and will be included in the extended version of the paper.

Minimum Distance to the Range of a Banded Lower Triangular Toeplitz Operator in l 1 and Application in l 1 -Optimal Control

The subject of the paper is the best approximation in

Harmonic instability of asymmetric bidirectional control of a vehicular platoon

\ell^1

Vibration rejection for inertially stabilized double gimbal platform using acceleration feedforward

of a given infinite sequence by sequences in the range of a given banded lower-triangular Toeplitz operator. Necessary and sufficient conditions for the existence of a minimizing solution are established and a numerical algorithm for finding such a solution is designed and theoretically founded. It is also shown that an optimal error sequence is only finitely nonzero. The relevancy of the problem in systems theory is outlined and numerical examples are presented.

AN ALGEBRAIC APPROACH TO THE CONTROL OF SPATIALLY DISTRIBUTED SYSTEMS — THE 2-D SYSTEMS CASE WITH A PHYSICAL APPLICATION

This paper deals with harmonic instability of asymmetric control of vehicular platoons. The considered platoons are composed of identical linear models of arbitrary order but there must be at least two integrators in the open loop. Each vehicle only responds to the movement of its immediate neighbors-the predecessor and the follower-and these two couplings are nonidentical. We show that for arbitrary asymmetry of intervehicular coupling, there is an exponential growth of the peak in the platoons magnitude frequency responses as the number of vehicles grows-a phenomenon called harmonic instability in the literature. Whereas it has been already shown for some particular cases that the beneficial effects of having the Laplacian eigenvalues lower-bounded by a nonzero constant come at the cost of harmonic instability, here we generalize this result to any linear controllers.

Vehicular platooning experiments with racing slot cars

The paper documents a computational design and an experimental verification of a vibration rejection scheme for an inertially stabilized platform mounted on a mobile base. The mechanical configuration of the platform is that of a standard double gimbal, which realizes a mass stabilization of the line of sight of an optoelectronic payload such as a camera an/or laser ranger finder. Nonideal static balancing of the payload gives rise to projection of the carrier vibrations onto a disturbing torque acting on the payload around the joint axes. This disturbance can be left for the existing inertial angular rate feedback to attenuate but a better solution can be devised. The cause of this disturbing torque — the linear acceleration of the carrier — can be measured, filtered and fed forward to the two direct drive motors. Experiments prove that significant vibration rejection is achieved with this feedforward compensation scheme.

Vehicular platooning experiments with LEGO MINDSTORMS NXT

Abstract In this paper we develop new results on control systems design for spatially distributed linear systems using an n -D systems approach. The basic ideas are explained using as an example heat conduction in a rod where the measurements and control action applied are based on an array of sensors and heaters. The first part of the analysis given shows how the process dynamics for this case can be approximately described by a 2-D transfer function, i.e. a fraction of two bivariate polynomials. This is followed by stability analysis and tests. Finally, a Youla-Kucera parametrization of all stabilizing controllers is used to develop a simple design procedure for H 2 -optimal control laws.

Control design for image tracking with an inertially stabilized airborne camera platform

The paper reports on an affordable platform for indoor experimental verification of algorithms for distributed control of platoons of vehicles. The platform is based on commercially available racing slot cars (by Carrera) equipped with an on-board 32-bit microcontroller-based control system. The assembled PCB board was provided by Freescale Semiconductor, Rožnov pod Radhoštěm, Czech Republic, within their Freescale Race Challenge 2012 competition of individual autonomous slot cars organized for student teams in Czech and Slovak republics. The documentation is freely available online. Some extra components such as an infrared range sensor and a wireless communication module have been added to the original system. The capabilities and potentials of the proposed platform are demonstrated on platooning experiments using two of the most popular platoon control schemes: predecessor following and leader following. Some technical parameters of the platform as well as design experience are shared in the report. It is hoped to encourage other teams to build a similar setup and possibly expose their new distributed control algorithms to an experimental competition.