Nick T. Koussoulas

Differential Petri nets: representing continuous systems in a discrete-event world

Differential Petri nets are a new extension of Petri nets. Through the introduction of the differential place, the differential transition, and suitable evolution rules, it is possible to model concurrently discrete-event processes and continuous-time dynamic processes, represented by systems of linear ordinary differential equations. This model can contribute to the performance analysis and design of industrial supervisory control systems and of hybrid control systems in general.

On the Suppression of Off-tracking in Multi-articulated Vehicles through a Movable Junction Technique

The motion of a multi-articulated robotic vehicle as well as of a train-like vehicle is characterized by the deviation of the path of each intermediate vehicle from that of the leading one (off-tracking phenomenon). In this paper, we propose the use of an innovative movable junction, which allows the kingpin to slide along the rear axis of the pulling vehicle, a technique that proved to be efficient in reducing or completely eliminating off-tracking. New kinematic equations are derived and a nonlinear controller is analytically developed, based on the steady-state off-tracking behavior of the n-trailer system. Simulations and a comparison study for various cases without/with this innovative “sliding kingpin” junction technique showed that its use together with an analytically derived controller can make possible the elimination of off-tracking.

Modeling and stability analysis of state-switched hybrid systems via Differential Petri Nets

Abstract State-switched systems are a large class of hybrid systems with numerous applications. In this work, the representation of state-switched systems in a Differential Petri Net (DPN) formalism becomes possible through a novel transformation of the fundamental equation of the DPN model into a form compatible with state-switching. Furthermore, we use the approach of the switching hyperplanes to provide means for the stability analysis of state-switched systems in a DPN framework. We also investigate stability issues of the resulting DPNs and synthesize an algorithm that can determine the stability of the state-switched DPN. Stability conditions are also expressed as Linear Matrix Inequalities (LMI) so that they can be easily determined using commercial software.

Symbolic computation for mobile robot path planning

Abstract Motion planning for mobile robots is an arduous task. Among the various methods that have been proposed for the solution of this problem in its open loop version is the Lafferriere–Sussmann method, which is based on differential geometry and employs piecewise constant inputs. This paper gives a succinct description of the method and of a freely available software tool, called the Lie Algebraic Motion Planner—LAMP and written in Mathematica™, which automates motion planning based on this technique.

CONTROLLER DESIGN FOR OFF-TRACKING ELIMINATION IN MULTI-ARTICULATED VEHICLES

Abstract The motion of a multi-body autonomous robot as well as of a train-like multi-articulated transportation vehicle is characterized by the deviation of the path of each intermediate vehicle from that of the leading one (off-tracking). In this paper, we make use of an innovative junction technique, which allows the kingpin to slide along the axis of the leading vehicle, something that proved to be very effective in reducing off-tracking. We propose two controllers for the elimination of the off-tracking phenomenon, in both robotic and transportation multi-articulated vehicles; the one is heuristically derived while the other one is based on steady-state off-tracking when an n-trailer vehicle moves on a circular trajectory. Simulation results for various cases, without and with the sliding kingpin system, showed that significant off-tracking reduction or even elimination can be achieved.

Motion Planning for Drift-Free Nonholonomic Systems under a Discrete Levels Control Constraint

We solve the Motion Planning Problem for nonholonomic systems without drift when their inputs are restricted to take values in a prescribed discrete levels set of finite cardinality. In particular, we propose algorithms that produce the proper sequence of input levels as well as the corresponding switching times providing exact steering when the system is nilpotent or feedback nilpotentizable. For a general drift-free system, i.e. for a drift-free system that is neither nilpotent nor feedback nilpotentizable another algorithm provides approximate steering within a permissible error. Finally, we apply the proposed algorithms in motion planning for a car-like mobile robot.

SPECTRAL MOMENTS AND THE ANALYSIS OF CHAOTIC SYSTEMS

The simplicity of structure of chaotic systems, combined with the richness of their output, inspires their use in modeling efforts. On the other hand, the difficulty of their analysis warrants approximation methods, especially since the absence, by definition, of well-defined limit sets prohibits, in general, a meaningful linearization. In this work we present some results, which can support a methodology founded on spectral analysis for approximating chaotic systems via stochastic linear systems. The main contribution is the use of spectral moments for identifying the location of embedded limit cycles and the spectrum-based validation of approximations.

Steering of Drift-Free Nonholonomic Systems Under a Discrete Levels Control Constraint

We solve the Motion Planning Problem for nonholonomic systems without drift under a discrete levels constraint, i.e. when it is driven by input that can assume only discrete levels. In particular, we propose an algorithm that steers a drift-free system from a given initial point to a given final point within a finite time interval and we prove that the proposed algorithm provides an exact steering when the system is nilpotentizable. For a general system without drift, i.e., for a drift-free system that is neither nilpotent nor feedback nilpotentizable, the discrete levels control can be computed by an iterative algorithm. Finally, we explore the details of the proposed methods through a specific example.

Computer integrated monitoring, fault identification and control for a bottling line

Todays bottling lines are complex production systems encountered in many kinds of food industries. Without an efficient monitoring system, such lines can prove to be inflexible and hard to manage. This paper presents the main issues which emerged during the conversion of a typical bottling line to a flexible and reconfigurable system, capable of implementing on-line decisions. Real-time monitoring, computer integrated structure, industrial networking, fault identification and modeling of fault propagation are the major themes covered.

Modelling and control of the sliding kingpin anti-jackknife device

Jackknifing is a major cause of disasters in traffic accidents involving articulated trucks. In this work, we examine a tractor/semi-trailer combination that is equipped with a device which allows the kingpin junction to slide along the rear tractor axle. While braking, the articulated vehicle behaves much like an inverted pendulum moving on the horizontal plane. Control of the sliding kingpin motion allows us to stabilise the semi-trailer by compensating for its every deviation away from the nominal position. A simple proportional-derivative (PD) control law proved adequate for a wide variation of road conditions for straight line braking.