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The trajectory tracking problem for a group of unicycle-type robots is addressed and solved by means of a partial state feedback strategy based on the leader-followers scheme using an observer to estimate the orientation angle of each mobile robot. The control law is based on an extended kinematic model where the output function to be controlled is the mid-point of the wheels axis of each robot. This choice leads to an ill defined control law when the robot is at rest. To avoid such a singularity, a complementary control law is enabled when the linear velocity of each robot is close to zero. It is shown that the combination of a classical dynamic full information controller with an exponentially convergent vehicle attitude observer yields an asymptotically stable closed-loop system. Real-time experiments show the performance of the proposed control scheme.

This papers focuses on a time-varying version of the containment problem for multi-agent systems. This problem consists in that a subgroup of agents, called leaders, achieve trajectory tracking while they carry out a time-varying formation. At the same time, another subgroup of agents, called followers, converge to the convex hull formed by the leaders. We propose a decentralized control strategy, that is, agents have no global knowledge of the goal to achieve, knowing only the position and velocity of some agents. To represent the interactions between agents formation graphs are used. The results are presented for front points of unicycle-type mobile robots. The theoretical results are verified by numerical simulation and also are validated experimentally.

The trajectory tracking problem for a wheeled mobile robot is addressed and solved by means of a partial state feedback strategy based on measurements from an indoor vision based absolute positioning system. The Cartesian coordinates provided by the localization system are fed to the proposed observer in order to estimate the orientation of the vehicle. It is shown that the combination of a classical dynamic full information controller with an asymptotically convergent vehicle attitude observer, designed using the immersion and invariance technique, yields a locally asymptotically stable closed-loop system. Real time experiments show the performance of the proposed control scheme.

This paper presents the design and analysis of three trajectory tracking control strategies for groups of unicycle-type robots using the leader-followers scheme. The leader converges asymptotically to a predefined trajectory path while the follower robots achieve a desired formation pattern at same time. The control laws are based on a dynamical extension of the kinematic model of unicycles considering the midpoint of the wheels axis of the robots as output function. When the linear velocity of unicycles is close to zero, a complementary control law is enabled momentarily to avoid singularities. It is demonstrated that in the switched closed-loop system, the orientation angles converge to the same value. Finally, some numerical simulations and real-time experiments show the performance of the control strategies.

A synthesis approach is proposed for discrete-event coordination architectures applied to a class of automated manufacturing systems (AMS) in which a clear separation is established between equipment control activities and product manufacturing procedures. Manufacturing procedures are modeled by regular languages constructed with a class of control commands named imperative. Equipment controllers are synthesized as a standard discrete-event supervisors dealing only with operational and safety issues of equipment groupings. The control of equipment modules is carried out following the imperative control commands sequences. Conditions are established to guarantee that the manufacturing procedure of a given product can be achieved using the synthesized supervisors in a particular AMS. Therefore, equipment controllers are not needed to be modified to consider the manufacturing of different products, whilst the construction of achievable manufacturing procedures becomes an ''ad hoc'' simple process using a reduced set of procedural blocks. The approach is illustrated with an experimental AMS.

This paper addresses the trajectory tracking problem for a remotely controlled quad-rotor vertical take off and landing aircraft (VTOL), under the restriction that only the inertial coordinates are available for measurement. The problem is solved in two steps: first, a discrete-time local exponential observer is designed which allows estimating the roll and pitching angles as well as all the velocities of the VTOL; Second, a discrete-time dynamic linearizing controller is proposed and the VTOL actual states variables are replaced by their corresponding estimates. It is shown that a kind of separation principle holds, in the sense that exponential convergence to the prescribed trajectory is preserved. Real-time experiments show that the proposed observer-controller scheme exhibits good performance.

Resumen: En este trabajo se presenta una estrategia de control en tiempo discreto para el seguimiento de trayectorias de un robot móvil tipo (2,0) controlado remotamente. La estrategia de control se desarrolló mediante un enfoque de modos deslizantes, considerando el modelo discreto exacto del vehículo en el cual se incluyen los efectos del retardo de transporte causado por la propagación de las señales sobre una red de comunicación. El esquema de control garantiza el seguimiento de trayectorias predeterminadas obteniéndose convergencia asintótica de los errores de seguimiento. La estrategia propuesta es evaluada mediante una serie de resultados por simulación. Palabras clave: Robot móvil, retardos de transporte, control en tiempo discreto, modos deslizantes

This paper proposes the emulation of the socalled kingpin mechanism in order to reduce the off-tracking effects exhibited by the standard and generalized n-trailer systems. In turn, both systems are emulated by a group of differential-drive mobile robots trough time-varying relative position vectors using the leader-follower scheme. A control law is proposed which involves the position of the virtual sliding kingpin mechanism. It is shown that when the virtual kingpin mechanism is used in the control law, the off-tracking effects are significantly reduced compared to when this virtual mechanism is not used. Numerical simulations and real-time experiments show the performance of the proposed control law.

A drillstring mechanism used for oil or gas drilling behaves as a torsional pendulum. The lowest part of the drillstring exhibits self-excited vibrations induced by nonlinear friction at the rock-crushing tool. Since these vibrations can lead to premature degradation of highly expensive mechanical and electronic components, a control strategy is necessary to attenuate or even eliminate their adverse effects. A multi-loop control design is proposed, which is composed by an inner and an outer loop. The aim of the inner-loop is to add enough damping to suppress stick-slip vibrations, while the objective of the outer-loop is to achieve the desired drillstring velocity.

A multi-steered general n-trailer is considered in this work. A global path-tracking control strategy for the n-trailer is proposed. Three nonlinear control laws are used to solve the problem by means of a commutation scheme. This commutation scheme allows to avoid the singularities inherent to a feedback linearization scheme. Simulation results show that the proposed scheme has good performance.

This paper develops the kinematic model of a class of multi steered general n -trailer system. The proposed kinematic model includes as particular cases the general and standard n -trailer systems commonly found in the literature. It is shown that the system is completely linearizable by dynamic state feedback and the explicit design of this dynamic compensator is also presented.

This paper addresses the asymptotic output tracking problem for the model of an overhead crane. It is shown that the model is linearizable by dynamic state feedback when the full state is available for measurement. In the more realistic situation when the angle that the rope forms with respect to the vertical axis cannot be measured, two different nonlinear observers are used in order to estimate the actual value. These are: a numerical observer and a high gain observer. Numerical experiments serve to compare the performance of the proposed schemes.

This article studies a time-varying version of the so-called containment problem with collision avoidance for multiagent systems. The proposed control strategy is decentralized, since agents have no global knowledge of the goal to achieve, knowing only the position and velocity of a subset of agents. This control strategy allows a subset of mobile agents (called leaders) to track a prescribed trajectory while they achieve a time-varying formation. Simultaneously, another subset of mobile agents (called followers) converge exponentially to the region bounded by the leaders. For the collision avoidance, we added a repulsive vector field of the unstable focus type to the time-varying containment control law. Formation graphs are used to represent interactions between agents. The results are presented for the front points of differential-drive mobile robots. The theoretical results are verified by numerical simulation. Additionally, an experimental case study is presented.

This paper presents an overview of recent results on the use of a group of differential-drive mobile robots to emulate the motion of different types of mechanical structures. The type of mechanical structure is emulated by choosing suitable relative position vectors between the mobile robots. A control law is proposed to achieve such relative positions. It is shown that despite of the simplicity of the control law it is possible to emulate the mechanical structures changing only the corresponding relative position vectors and their time derivative. Numerical simulations and real-time experiments show the performance of the control law.

In this paper we study some structural properties of nonlinear systems with delays. A specially adapted mathematical setting is developed and used to characterize the equivalence to the so-called triangular form. We claim that this result opens several research lines in the study of the considered class of systems.

In analogy with the continuous-time case, a general notion of controlled invariance with respect to quasi-static-state feedback is introduced for discrete-time nonlinear systems which incorporates the earlier definition of controlled invariance with respect to regular static-state feedback. This new notion is used to derive a geometric solution to the dynamic disturbance decoupling problem. The proposed solution is a natural generalization of the geometric solution to the static disturbance decoupling problem.

The problem of local asymptotic continuous feedback stabilization of single-input nonlinear systems is considered here. The aim is to explicitly construct a continuous asymptotically stabilizing feedback for a class of nonlinear systems that is known to be continuous feedback asymptotically stabilizable, but for which the known results do not provide an effective method to compute the stabilizer. Computer simulations are included to show practical applicability of our approach.

The goal of this paper is to show that if a system is locally feedback linearizable and satisfies a suitable transversality condition, then it is practically stabilizable by discontinuous state feedback. In this case, an explicit construction of the stabilizer is given.

Within a linear algebraic framework, we present a new characterization of the class of nonlinear systems which are equivalent to a prime system. We then introduce a class of generalized output transformations that can be thought of as a generalization to the nonlinear setting of a unimodular transformation in the output space. Our main result gives necessary and sufficient conditions for equivalence to a prime system under a certain group of transformations that includes generalized output transformations.

This paper studies a time-varying version of the so-called containment problem for multi-agent systems. The proposed control strategy is decentralized and allows a subset of mobile agents (called leaders) to track a predetermined trajectory while they achieve a time-varying formation. Simultaneously, another subset of mobile agents (called followers) converge exponentially to the area bounded by the leaders. The results are presented for the front points of unicycle-type robots. The theoretical results are verified by numerical simulation.

This paper proposes a control law to emulate the behavior of a standard n-trailer using a multi-agent robot system conformed by a group of unicycle-type robots. A sliding kingpin technique is used in order to reduce or completely eliminate the off-tracking (oversteer phenomenon) that the trailers of this kind of systems exhibit when they are following trajectories with a certain radius of curvature. Numerical simulations show the performance of the control law and a comparison is made between the control law with and without the sliding kingpin technique.

This paper presents three trajectory tracking control strategies for unicycle-type robots based on a leader-followers scheme. The leader robot converges asymptotically to a smooth trajectory, while the follower robots form an undirected open-chain configuration at the same time. It is also shown that the orientation angles of all the robots converge to the same value. The control laws are based on a dynamic extension of the kinematic model of each robot. The output function to be controlled is the midpoint of the wheel axis of every robot. This choice leads to an ill-defined control law when the robot is at rest. To avoid such singularities, a complementary control law is enabled momentarily when the linear velocity of the unicycles is close to zero. Finally, numerical simulations and real-time experiments show the performance of the control strategies.

The paper presents a linear algebraic solution of the dynamic disturbance decoupling problem for a submersive discrete-time nonlinear system. The solution is looked for in the class of regular (invertible) dynamic compensators. Necessary and sufficient conditions in terms of certain subspaces, defined by the system, are given both for the cases of measurable and unmeasurable input disturbances. The linear-algebraic solvability conditions are shown to be equivalent to the earlier conditions, formulated in terms of certain functions appearing in the inversion algorithm. The equivalence relies on the fact that the two versions of the inversion algorithm for systems with disturbances produce the basis for the above subspaces. Moreover, we establish that when the disturbance decoupling problem is solvable by adynamic state feedback, then it is solvable by a quasi-static state feedback.

The goal of this paper is to derive necessary and sufficient conditions under which a driftless system is feedback equivalent to a system in extended Goursat form. Our results are formulated using tools from exterior differential systems theory and improve the results previously reported in the literature in two ways. First, an algorithmic procedure is given which allows to decide in a finite number of steps whether these conditions are met. Second, up to integration of a Pfaffian system, we are able to explicitly compute the transformation which brings the system into extended Goursat form.

International audience; We define, in an infinite-dimensional differential geometric framework, the "infinitesimal Brunovsky form" which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by "endogenous dynamic feedback".NB: this paper follows "A differential geometric setting for dynamic equivalence and dynamic linearization", by J.-B. Pomet, published in the same 1995 volume, which is its natural intrduction.This is a corrected version of the reports http://hal.inria.fr/inria-00074360 and http://hal.inria.fr/inria-00074361

This paper presents an experimental comparison between discrete- and continuous-time formation and marching controllers for Multi-Agent Systems. The analysis is applied to the kinematic model of unicycle-type robots where the output function is a point off the robots' wheels axis. The control strategies are based on Artificial Potential Functions. The discrete-time model is obtained using Euler approximation. The comparison is made by matching the sum of the control signals of all the robots. Since there is an algebraic relation between the control signals and the energy applied to the system, if the overall control is equal for both schemes then the errors of the discrete- and continuous-time schemes can be compared.

Formation control is an important issue of motion coordination of Multi-agent Robots Systems. The goal is to coordinate a group of agents to achieve a desired formation pattern. The control strategies are decentralized because every robot does not possess information about the positions and goals of all the other robots. Based on the formation graphs properties and the local potential functions approach, we obtain a formal result about global convergence to the desired pattern for any formation graph. Also, we characterize the topologies of the formation graphs where the centroid of positions remains stationary. Finally, the control approach is extended to the case of unicycle-type robots.

This paper focusses on the design and analysis of a control strategy that allows multi-agent robots systems to track a predetermined trajectory whilst they achieve time-varying formation. The strategies are based on artificial potential functions and the leader-follower scheme. The control laws herein are decentralized since it is assumed that the agents have no knowledge of the goals of the other agents and can sense position and velocity of some agents only. The analysis is applied to the kinematic model of unicycle-type robots, where the output function to control is a point outside the robot's wheels axis. The control law proposed in the paper allows to emulate the standard and generalized n-trailer kinematics.

Multi-agent Robots Systems (MARS) can be defined as sets of autonomous robots coordinated through a communication system to achieve cooperative tasks. During the last 20 years, MARS have found a wide range of applications in terrestrial, spatial and oceanic explorations emerging as a new research area (Cao et al. (1997)). Some advantages can be obtained from the collective behavior of MARS. For instance, the kind of tasks that can be accomplished are inherently more complex than those a single robot can accomplish. Also, the system becomes more flexible and fault-tolerant (Yamaguchi (2003)). The range of applications includes toxic residues cleaning, transportation and manipulation of large objects, alertness and exploration, searching and rescue tasks and simulation of biological entities behaviors (Arai et al. (2002)). The study ofMARS extends the classical problems of single robotswith new issues likemotion coordination, task decomposition and task assignment, network communications, searching and mapping, etc. Therefore, the study of MARS encompass distributed systems, artificial intelligence, game theory, biology, ethology, economics, control theory, etc. Motion coordination is an important research area of MARS, specifically formation control (Chen & Wang (2005)). The main goal is to coordinate a group of mobile agents or robots to achieve a desired formation pattern avoiding inter-agent collisions at the same time. The formation strategies are decentralized because it is assumed that every agent measures the position of a certain subset of agents and, eventually, it detects the position of other agents when a minimal allowed distance is violated and collision danger appears. Thus, the main intention is to achieve desired global behaviors through local interactions (Francis et al. (2004)). Also, the decentralized approaches offer greater autonomy for the robots, less computational load in control implementations and its applicability to large scale groups (Do (2007)). According to Desai (2002); Muhammad & Egerstedt (2004), the possible inter-agent communications and the desired relative position of every agent with respect to the others can be represented by a FormationGraph (FG). The application of different FG’s to the same group of robots produces different dynamics on the team behavior. In the literature, some special FG topologies are chosen and the convergence to the desired formation and non-collision is analyzed for any number of robots. A decentralized formation strategy must comply with two fundamental requirements: Global convergence to the desired formation and inter-agent collision avoidance (Cao et al. (1997)). 6

This paper presents two marching control strategies for unicycles using Artificial Potential Fields. The strategies are based on the leader-followers scheme where the leader agent must follow a prescribed trajectory and the rest of the agents achieves a desired formation at the same time. The agents can detect another agent only (minimum sensing requirements) and it is assumed that a centralized control does not exist. The main goal is to achieve desired global behaviors through local interactions. The results are validated by numerical simulations. Finally, the performance of the proposed strategies is evaluated over an experimental set-up consisting of three unicycle-type robots.

A novel formation control strategy with collision avoidance is presented for the case of two point robots moving in the plane. The control law is based on the design of attractive and repulsive vector fields which guarantee the non-existence of undesired equilibria. The strategy falls in a variable structure control approach which guarantees convergence to the desired formation and non-collision for all initial conditions. The results are extended to the case of formation of unicycles. The performance of the proposed strategy is evaluated over an experimental set-up consisting of two unicycle-type robots.

An analysis of the convergence and non-collision conditions of a formation control strategy for multi-agent robots based on local potential functions is presented. The goal is to coordinate a group of agents, considered as points in plane, to achieve a particular formation. The control law is designed using local attractive forces only where every agent knows the position of another two agents reducing the requirements of the control law implementation. The control law guarantees the convergence to the desired formation but does not avoid inter-agent collisions. A set of necessary and sufficient non- collision conditions based on the explicit solution of the closed- loop system is derived. The conditions allow to conclude from the initial conditions whether or not the agents will collide. The formal proof is presented for the case of three agents. The result is extended to the case of formations of three unicycles.

The problem of trajectory tracking by means of dynamic partial state feedback for the kinematic model of the unicycle mobile robot is addressed and solved. It is shown that the combination of a classical dynamic full information controller with an exponentially stable angular attitude estimator, designed using the immersion and invariance technique, yields a locally asymptotically stable closed-loop system. Numerical simulations complete the paper.

A low cost strategy for indoor real-time stabilization of a remotely controlled flying robot is proposed. The strategy is based on a discrete-time Luenberger observer combined with a low cost and fast positioning system. The positioning system delivers the coordinates, roll and pitch angles of robot. The discrete-time Luenberger observer is used to estimate all the velocities. A local stabilizer is designed as if all states were measurable. It is shown that the observer and the stabilizer satisfy a kind of separation principle, in the sense that local stability of the closed loop system is preserved when the actual states are replaced by their estimates. Real-time experiments show the performance of the proposed scheme.

The goal of this paper is to introduce the notion of exogenous state feedback for discrete-time systems. It is shown that a discrete-time system may be linearizable by exogenous feedback, even if it can not be linearized by endogenous feedback. This property was completely unexpected and constitutes a fundamental difference with respect to the continuous-time case. The theory is illustrated through an example whose structure is similar to the exact discrete-time model of a mobile robot, showing that the above mentioned property concerns not only academic examples, but physical systems as well.

In this work, it is presented a discrete time control strategy for the solution of the path-tracking problem for a wheeled mobile robot of the type (2,0). It is assumed that the mobile robot is remotely controlled over a communication network that induces a transport delay. The exact discrete-time model of the mobile robot including the induced delay is developed. It is presented a discrete-time strategy control based on a sliding mode approach that allows to solve the path-tracking problem. The closed loop stability of the overall system is clearly stated. The proposed control strategy is evaluated by mean of computer simulation.

This paper studies the discrete-time stabilization of a planar vertical take off and landing aircraft (PVTOL). A Luenberger-type observer is proposed and a sufficient condition on the sampling period is obtained such that the error observer convergence rate becomes exponential. The observer requires measurements of the horizontal and vertical coordinates only and estimates the roll angle and the velocities of the PVTOL. A local stabilizer which makes use of the actual state variables is designed. It is shown that the observer and the stabilizer satisfy a separation principle, in the sense that local stability of the closed loop system is preserved when the actual states are replaced by their estimates. Numerical simulations show that the proposed control strategy is robust in the face of measurements corrupted by noise.

The goal of this paper is to show that when differential forms are viewed as elements of a suitable differential vector space, they provide a powerful tool to tackle the feedback linearization problem. Our formalism allows us to give necessary and sufficient conditions for dynamic linearization as well as to recover the early results in feedback linearization (either static or dynamic) in a computationally very convenient way. >

The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas for nonlinear continuous-time systems the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recast through the language of differential forms. This yields a solution which is completely constructive. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. >

The algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete-time nonlinear systems. The accessibility problem for nonlinear discrete-time systems is shown to be easy to tackle by means of standard linear algebraic tools, whereas this is not the case for nonlinear continuous-time systems, in which case the most suitable approach is provided by differential geometry. The feedback linearization problem for discrete-time systems is recasted through the language of differential forms. In the event that a system is not feedback linearizable, the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a Pfaffian system. A discrete-time system may be linearizable by dynamic state feedback, though it is not linearizable by static state feedback. Necessary and sufficient conditions are given for the existence of a so-called linearizing output, which in turn is a sufficient condition for dynamic state feedback linearizability.

The purpose of this paper is to give a discrete-time analogue of the notion of controlled invariance under quasi-static state feedback and to show that it is possible to present a geometric solution of the dynamic disturbance decoupling problem in terms of this new notion.

A design strategy is proposed for a two-layer modular discrete-event coordination controller applied to a class of automated manufacturing systems (AMS). Controllers in each layer are synthesized as discrete-event supervisors dealing only with operational and safety issues of equipment groupings. Manufacturing procedures, modeled by languages constructed with a class of control commands named imperative , drive the execution of the upper layer. The control of equipment modules is carried out at the lower layer following the imperative control commands. Conditions are established to guarantee that the manufacturing sequence of a given product can be achieved using the synthesized supervisors in a particular AMS. The development of a coordination controller for an experimental AMS is employed to illustrate the proposed strategy.

The goal of this paper is three fold. Firstly, an algorithm is developed which allows to design continuous stabilizers for triangular systems. The algorithm is based on new theoretical results on asymptotic feedback stabilization of triangular systems. These results provide an explicit method for the design of the stabilizing feedback and demonstrate the asymptotic stability of the closed loop system for a certain subclass of triangular systems. This subclass includes some of the so-called singular triangular systems, i.e. those having uncontrollable or even nonstabilizable linear approximation. Therefore, unavoidably the proposed feedback is continuous only. Secondly, employing the above algorithm, a bundle of computer algebra programs is implemented, which allows to automatically compute a continuous stabilizer for any given triangular system. Several particular examples are studied to test all these procedures, including the case study of an underactuated weakly coupled mechanical system. Finally, some outlooks are given about the stability proof for the case of general singular triangular systems. Even though the proof is not complete at this stage, some very interesting properties of the closed loop system are put forward, including some properties which are of interest even from dynamical systems' point of view.