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Development and testing of multi-robot systems employing wireless signal-based sensing requires access to suitable hardware, such as channel monitoring WiFi transceivers, which can pose significant limitations. The WiFi Sensor for Robotics (WSR) toolbox, introduced by Jadhav et al. in 2022, provides a novel solution by using WiFi Channel State Information (CSI) to compute relative bearing between robots. The toolbox leverages the amplitude and phase of WiFi signals and creates virtual antenna arrays by exploiting the motion of mobile robots, eliminating the need for physical antenna arrays. However, the WSR toolbox's reliance on an obsoleting WiFi transceiver hardware has limited its operability and accessibility, hindering broader application and development of relevant tools. We present an open-source simulation framework that replicates the WSR toolbox's capabilities using Gazebo and Matlab. By simulating WiFi-CSI data collection, our framework emulates the behavior of mobile robots equipped with the WSR toolbox, enabling precise bearing estimation without physical hardware. We validate the framework through experiments with both simulated and real Turtlebot3 robots, showing a close match between the obtained CSI data and the resulting bearing estimates. This work provides a virtual environment for developing and testing WiFi-CSI-based multi-robot localization without relying on physical hardware. All code and experimental setup information are publicly available at https://github.com/BrendanxP/CSI-Simulation-Framework, Comment: 6+1 pages (text + references), 6 figures

In this paper, we restructure the Neural Interconnection and Damping Assignment - Passivity Based Control (Neural IDA-PBC) design methodology, and we formally analyze its closed-loop properties. Neural IDA-PBC redefines the IDA-PBC design approach as an optimization problem by building on the framework of Physics Informed Neural Networks (PINNs). However, the closed-loop stability and robustness properties under Neural IDA-PBC remain unexplored. To address the issue, we study the behavior of classical IDA-PBC under approximations. Our theoretical analysis allows deriving conditions for practical and asymptotic stability of the desired equilibrium point. Moreover, it extends the Neural IDA-PBC applicability to port-Hamiltonian systems where the matching conditions cannot be solved exactly. Our renewed optimization-based design introduces three significant aspects: i) it involves a novel optimization objective including stability and robustness constraints issued from our theoretical analysis; ii) it employs separate Neural Networks (NNs), which can be structured to reduce the search space to relevant functions; iii) it does not require knowledge about the port-Hamiltonian formulation of the system's model. Our methodology is validated with simulations on three standard benchmarks: a double pendulum, a nonlinear mass-spring-damper and a cartpole. Notably, classical IDA-PBC designs cannot be analytically derived for the latter., Comment: Preprint

We study the properties of remnant function, which is a function of output remnant versus amplitude of the input signal, of Preisach hysteresis operators. The remnant behavior (or the leftover memory when the input reaches zero) enables an energy-optimal application of piezoactuator systems where the applied electrical field can be removed when the desired strain/displacement has been attained. We show that when the underlying weight of Preisach operators is positive, the resulting remnant curve is monotonically increasing and accordingly a Newton and secant update laws for the iterative remnant control are proposed that allows faster convergence to the desired remnant value than the existing iterative remnant control algorithm in literature as validated by numerical simulation., Comment: Accepted/inpress for LCSS

This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each other exponentially. This concept exhibits a more expansive nature when contrasted with another generalized contraction framework known as partial contraction. The first result establishes a connection between the output contraction of a time-varying system and the output exponential stability of its variational system. Subsequently, we derive a sufficient condition for achieving output contraction in time-varying systems by applying the output contraction Lyapunov criterion. Finally, we apply the results to analyze the output exponential stability of nonlinear time-invariant systems.

This paper studies the contraction property of time-varying differential-algebraic equation (DAE) systems by embedding them to higher-dimension ordinary differential equation (ODE) systems. The first result pertains to the equivalence of the contraction of a DAE system and the uniform global exponential stability (UGES) of its variational DAE system. Such equivalence inherits the well-known property of contracting ODE systems on a specific manifold. Subsequently, we construct an auxiliary ODE system from a DAE system whose trajectories encapsulate those of the corresponding variational DAE system. Using the auxiliary ODE system, a sufficient condition for contraction of the time-varying DAE system is established by using matrix measure which allows us to estimate an lower bound on the parameters of the auxiliary system. Finally, we apply the results to analyze the stability of time-invariant DAE systems, and to design observers for time-varying ODE systems.

Unlike the case with identical neighboring agents whose actions are mirrored, the problem of distributed formation control design with heterogeneous sensing is not straightforward. In this paper, we consider the problem of distributed formation control where each agent can only control distances or bearings with its neighbors. We firstly develop a rigidity theory with heterogeneous sensing to ensure that the desired shape is well-posed. Secondly, we propose an iterative method that allows us to scale up the number of agents with heterogeneous sensing. Finally, numerical simulations show the effectiveness of our method., Comment: 11 pages, 7 figures

The presence of faulty or underactuated manipulators can disrupt the end-effector formation keeping of a team of manipulators. Based on two-link planar manipulators, we investigate this end-effector formation keeping problem for mixed fully- and under-actuated manipulators with flexible joints. In this case, the underactuated manipulators can comprise of active-passive (AP) manipulators, passive-active (PA) manipulators, or a combination thereof. We propose distributed control laws for the different types of manipulators to achieve and maintain the desired formation shape of the end-effectors. It is achieved by assigning virtual springs to the end-effectors for the fully-actuated ones and to the virtual end-effectors for the under-actuated ones. We study further the set of all desired and reachable shapes for the networked manipulators' end-effectors. Finally, we validate our analysis via numerical simulations., Comment: 14 pages, 11 figures

This paper addresses the problem of end-effector formation control for a mixed group of two-link manipulators moving in a horizontal plane that comprises of fully-actuated manipulators and underactuated manipulators with only the second joint being actuated (referred to as the passive-active (PA) manipulators). The problem is solved by extending the distributed end-effector formation controller for the fully-actuated manipulator to the PA manipulator moving in a horizontal plane by using its integrability. This paper presents stability analysis of the closed-loop systems under a given necessary condition, and we prove that the manipulators' end-effector converge to the desired formation shape. The proposed method is validated by simulations.

Currently, the general aim of flocking and formation control laws for multi-agent systems is to form and maintain a rigid configuration, such as, the alpha-lattices in flocking control methods, where the desired distance between each pair of connected agents is fixed. This introduces a scalability issue for large-scale deployment of agents due to unrealizable geometrical constraints and the constant need of centralized orchestrator to ensure the formation graph rigidity. This paper presents a flexible distributed flocking cohesion algorithm for nonholonomic multi-agent systems. The desired geometry configuration between each pair of agents is adaptive and flexible. The distributed flocking goal is achieved using limited information exchange (i.e., the local field gradient) between connected neighbor agents and it does not rely on any other motion variables measurements, such as (relative) position, velocity, or acceleration. Additionally, the flexible flocking scheme with safety is considered so that the agents with limited sensing capability are able to maintain the connectedness of communication topology at all time and avoid inter-agent collisions. The stability analysis of the proposed methods is presented along with numerical simulation results to show their effectiveness., Comment: 9 pages, 2 figures

This letter studies the problem of cooperative nearest-neighbor control of multi-agent systems where each agent can only realize a finite set of control points. Under the assumption that the underlying graph representing the communication network between agents is connected and the interior of the convex hull of all finite actions of each agent contains the zero element, consensus or distance-based formation problems can practically be stabilized by means of nearest-neighbor control approach combined with the well-known consensus control or distributed formation control laws, respectively. Furthermore, we provide the convergence bound for each corresponding error vector which can be computed based on the information of individual agent's finite control points. Finally, we show Monte Carlo numerical simulations that confirm our analysis.

Navigation and exploration within unknown environments are typical examples in which simultaneous localization and mapping (SLAM) algorithms are applied. When mobile agents deploy only range sensors without bearing information, the agents must estimate the bearing using the online distance measurement for the localization and mapping purposes. In this paper, we propose a scalable dynamic bearing estimator to obtain the relative bearing of the static landmarks in the local coordinate frame of a moving agent in real-time. Using contraction theory, we provide convergence analysis of the proposed range-only bearing estimator and present upper and lower-bound for the estimator gain. Numerical simulations demonstrate the effectiveness of the proposed method.

We present a distributed source-seeking and flocking control method for networked multi-agent systems with non-holonomic constraints. Based solely on identical on-board sensor systems, which measure the source local field, the group objective is attained by appointing a leader agent to seek the source while the remaining follower agents form a cohesive flocking with their neighbors using a distributed flocking control law in a connectivity-preserved undirected network. To guarantee the safe separation and group motion for all agents and to solve the conflicts with the "cohesion" flocking rule of Reynolds, the distributed control algorithm is solved individually through quadratic-programming optimization problem with constraints, which guarantees the inter-agent collision avoidance and connectivity preservation. Stability analysis of the closed-loop system is presented and the efficacy of the methods is shown in simulation results., Comment: 16 pages, 10 figures

We present a data-driven dissipative verification method for LTI systems based on using multiple input-output data. We assume that the supply-rate functions have a quadratic difference form corresponding to the general dissipativity notion known in the behavioural framework. We validate our approach in a practical example using a two-degree-of-freedom planar manipulator from Quanser, with which we demonstrate the applicability of multiple datasets over one-shot of data recently proposed in the literature.

In this work, we propose a collision-free source-seeking control framework for unicycle robots traversing an unknown cluttered environment. In this framework, obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming and the source seeking control relies solely on the use of on-board sensors that measure the signal strength of the source. To tackle the mixed relative degree of the CBF, we proposed three different CBFs, namely the zeroing control barrier functions (ZCBF), exponential control barrier functions (ECBF), and reciprocal control barrier functions (RCBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We provide rigorous analysis of the three different methods and show the efficacy of the approaches in simulations using Matlab, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS., Comment: 15 pages, 11 figures

The aim of this work is to assess the influence of different degrees of adaptability of the power take-off (PTO) system on the power absorption of dense wave energy converter (WEC) arrays. The adaptability is included in simulations through a transmission ratio that scales the force actuating the PTO relative to the force generated by the motion of a floater. A numerical model is used in which hydrodynamic interactions between floaters and nonlinearities in the PTO are considered. The lower computational cost of this numerical model makes it possible to study the power extraction of a dense WEC array in irregular waves to easily create power matrices and other performance metrics. The methodology is applied to the case study of the Ocean Grazer WEC to showcase the potential performance improvements achieved through the inclusion of a transmission ratio. The analysis shows that including a high degree of adaptability and choosing WEC array configurations and PTO designs specific to potential deployment locations early in the design process can lead to an increase in extracted power., Comment: this version is the published article; the results with adaptability per time window are updated, thus, also the following results based on those values

Recent developments in communication technologies, such as 5G, together with innovative computing paradigms, such as edge computing, provide further possibilities for the implementation of real-time networked control systems. However, privacy and cyber-security concerns arise when sharing private data between sensors, agents and a third-party computing facility. In this paper, a secure version of the distributed formation control is presented, analyzed and simulated, where gradient-based formation control law is implemented in the edge, with sensor and actuator information being secured by fully homomorphic encryption method based on learning with error (FHE-LWE) combined with a proposed mixed uniform-logarithmic quantizer (MULQ). The novel quantizer is shown to be suitable for realizing secure control systems with FHE-LWE where the critical real-time information can be quantized into a prescribed bounded space of plaintext while satisfying a sector bound condition whose lower and upper-bound can be made sufficiently close to an identity. An absolute stability analysis is presented, that shows the asymptotic stability of the closed-loop secure control system.

We propose a Kron-based model-order reduction method for mass-action kinetics chemical reaction networks (CRN) with constant inflow and proportional outflow. The reduced-order models preserve the CRN structure and we establish that the resulting reduced-order models have the same DC-gain or zero-moment as that of the full-order ones. Subsequently, we present the spectrum interlacing property of the Kron-reduced open CRN and propose the use of Gramians-based approach for single-species single-substrate chemical network to get the upper-bound of approximation error and to use it in determining a good set of nodes to be removed systematically. Finally, we evaluate the applicability and efficacy of our results in two well-known biochemical kinetic models: the activated sludge model (ASM) 1 and McKeithan's T-cell receptor model., Comment: Submitted to IEEE Transactions on Automatic Control

In this work we exploit the universal approximation property of Neural Networks (NNs) to design interconnection and damping assignment (IDA) passivity-based control (PBC) schemes for fully-actuated mechanical systems in the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC method into a supervised learning problem that solves the partial differential matching equations, and fulfills equilibrium assignment and Lyapunov stability conditions. A main consequence of this, is that the output of the learning algorithm has a clear control-theoretic interpretation in terms of passivity and Lyapunov stability. The proposed control design methodology is validated for mechanical systems of one and two degrees-of-freedom via numerical simulations., Comment: Accepted in 4th Annual Learning for Dynamics and Control (L4DC) Conference

We present three classes of distributed formation controllers for achieving and maintaining the 2D/3D formation shape of manipulator end-effectors to cope with different scenarios due to availability of modeling parameters. We firstly present a distributed formation controller for manipulators whose system parameters are perfectly known. The formation control objective is achieved by assigning virtual springs between end-effectors and by adding damping terms at joints, which provides a clear physical interpretation of the proposed solution. Subsequently, we extend it to the case where manipulator kinematic and system parameters are not exactly known. An extra integrator and an adaptive estimator are introduced for gravitational compensation and stabilization, respectively. Simulation results with planar manipulators and with seven degree-of-freedom humanoid manipulator arms are presented to illustrate the effectiveness of the proposed approach., Comment: arXiv admin note: text overlap with arXiv:2103.14595

We present the design and experimental validation of source seeking control algorithms for a unicycle mobile robot that is equipped with novel 3D-printed flexible graphene-based piezoresistive airflow sensors. Based solely on a local gradient measurement from the airflow sensors, we propose and analyze a projected gradient ascent algorithm to solve the source seeking problem. In the case of partial sensor failure, we propose a combination of Extremum-Seeking Control with our projected gradient ascent algorithm. For both control laws, we prove the asymptotic convergence of the robot to the source. Numerical simulations were performed to validate the algorithms and experimental validations are presented to demonstrate the efficacy of the proposed methods., Comment: Published in IEEE Transactions on Robotics

This paper considers the use of fully homomorphic encryption for the realisation of distributed formation control of multi-agent systems via edge computer. In our proposed framework, the distributed control computation in the edge computer uses only the encrypted data without the need for a reset mechanism that is commonly required to avoid error accumulation. Simulation results show that, despite the use of encrypted data on the controller and errors introduced by the quantization process prior to the encryption, the formation is able to converge to the desired shape. The proposed architecture offers insight on the mechanism for realising distributed control computation in an edge/cloud computer while preserving the privacy of local information coming from each agent., Comment: 8 pages, 6 figures, conference

Based on a one-shot input-output set of data from an LTI system, we present a verification method of dissipativity property based on a general quadratic supply-rate function. We show the applicability of our approach for identifying suitable general quadratic supply-rate function in two numerical examples, one regarding the estimation of $\mathcal{L}_2$-gains and one where we verify the dissipativity of a mass-spring-damper system., Comment: v1 published paper at ECC 2021; v2 (ArXiv) corrections on Theorem 1 and Example 1 and minor notation typos

This paper addresses the problem of end-effector formation control for manipulators that are subjected to external disturbances: input disturbance torques and disturbance forces at each end-effector. The disturbances are assumed to be non-vanishing and are superposition of finite number of sinusoidal and step signals. The formation control objective is achieved by assigning virtual springs between end-effectors, by adding damping terms at joints, and by incorporating internal model-based dynamic compensators to counteract the effect of the disturbances; all of which presents a clear physical interpretation of the proposed approach. Simulation results are presented to illustrate the effectiveness of the proposed approach.

This paper focuses on securing a triangular shape (up to translation) for a team of three mobile robots that uses heterogeneous sensing mechanism. Based on the available local information, each robot employs the popular gradient-based control law to attain the assigned individual task(s). In the current work, robots are assigned either distance and signed area task(s) or bearing task(s). We provide a sufficient condition on the gain ratio $R_{\text{Ad}}$ between the signed area and the distance control term such that the desired formation shape, an isosceles triangle, is reached from all feasible starting positions. Numerical simulations are provided to support the theoretical analyses., Comment: 13 pages, submitted for journal publication

This paper focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses heterogeneous sensing mechanism. Depending on the convenience and reliability of the local information, each robot utilizes the popular gradient-based control law which, in this paper, is either the distance-based or the bearing-only formation control. For the two and three robot case, we show that the use of heterogeneous gradient-based control laws can give rise to an undesired invariant set where a distorted formation shape is moving at a constant velocity. The (in)stability of such an invariant set is dependent on the specified distance and bearing constraints. For the two robot case, we prove almost global stability of the desired equilibrium set while for the three robot case, we guarantee local asymptotic stability for the correct formation shape. We also derive conditions for the three robot case in which the undesired invariant set is locally attractive. Numerical simulations are presented for illustrating the theoretical results in the three robot case., Comment: 15 pages

In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior angle measurements of the neighboring robots' disk, which can be obtained from low-cost vision sensors, we propose a gradient-based distributed control law and show the exponential convergence property of the associated error system. By construction, the proposed control law has the appealing property of ensuring collision avoidance between neighboring robots. We also present simulation results for {a team} of four circular mobile robots forming a rectangular shape., Comment: 6 pages, submitted to the 59th IEEE Conf. Dec. Control and IEEE Control Systems Letters

In this work we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework. The proposed design method, called virtual contraction based control (v-CBC), combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system exhibits properties such as structure preservation, differential passivity and the existence of (incrementally) passive maps., Comment: 10 pages, 4 figures, journal paper

In this paper, we present the design and implementation of a robust motion formation distributed control algorithm for a team of mobile robots. The primary task for the team is to form a geometric shape, which can be freely translated and rotated at the same time. This approach makes the robots to behave as a cohesive whole, which can be useful in tasks such as collaborative transportation. The robustness of the algorithm relies on the fact that each robot employs only local measurements from a laser sensor which does not need to be off-line calibrated. Furthermore, robots do not need to exchange any information with each other. Being free of sensor calibration and not requiring a communication channel helps the scaling of the overall system to a large number of robots. In addition, since the robots do not need any off-board localization system, but require only relative positions with respect to their neighbors, it can be aimed to have a full autonomous team that operates in environments where such localization systems are not available. The computational cost of the algorithm is inexpensive and the resources from a standard microcontroller will suffice. This fact makes the usage of our approach appealing as a support for other more demanding algorithms, e.g., processing images from onboard cameras. We validate the performance of the algorithm with a team of four mobile robots equipped with low-cost commercially available laser scanners., Comment: 6 pages. ICARCV 2018

In this paper we present three distributed control laws for the coordination of networked Euler-Lagrange (EL) systems. We first reformulate the passivity-based control design method in \cite{Arcak} by considering that each edge is associated with an \emph{artificial spring system} instead of the usual diffusive coupling among the communicating agents. With this configuration, the networked EL system possesses a "symmetric" feedback structure which together with the strict passivity of both agents' and edges' dynamics lead to a strictly passive network dynamics. Subsequently we present the networked version of two different passivity-based tracking controllers %local controllers that are particular cases of our method and the one in \cite{Arcak}. Numerical simulation is presented to show the performance of the proposed methods., Comment: Submitted to Necsys2018, 7 pages, 1 figure

In this work we propose a family of trajectory tracking controllers for marine craft in the port-Hamiltonian (pH) framework using virtual differential passivity based control (v-dPBC). Two pH models of marine craft are considered, one in a body frame and another in an inertial frame. The structure and workless forces of pH models are exploited to design two virtual control systems which are related to the original marine craft's pH models. These virtual systems are rendered differentially passive with an imposed steady-state trajectory, both by means of a control scheme. Finally, the original marine craft pH models in closed-loop with above controllers solve the trajectory tracking problem. The performance of the closedloop system is evaluated on numerical simulations., Comment: Submitted to CDC 2018

Based on recent advances in contraction methods in systems and control, in this paper we present the virtual differential passivity based control (v-dPBC) technique. This is a constructive design method that combines the concept of virtual systems and of differential passivity. We apply the method to the tracking control problem of flexible joints robots (FJRs) which are formulated in the port-Hamiltonian (pH) framework. Simulations on a single flexible joint link are presented for showing the performance of a controller obtained with this approach., Comment: 8 pages, 2 figures, submitted to Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control 2018

This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations., Comment: 6 pages. Accepted in the 2007 IFAC World Congress

In this paper, we propose a new robustness notion that is applicable for certifying systems' safety with respect to external disturbance signals. The proposed input-to-state safety (ISSf) notion allows us to certify systems' safety in the presence of the disturbances which is analogous to the notion of input-to-state stability (ISS) for analyzing systems' stability., Comment: 9 pages, pre-print submitted to Automatica

In this paper, we propose a novel trajectory tracking controller for fully-actuated mechanical port-Hamiltonian (pH) systems, which is based on recent advances in contraction-based control theory. Our proposed controller renders a desired sliding manifold (where the reference trajectory lies) attractive by making the corresponding error system partially contracting. Finally, we present numerical simulation results where a SCARA robot is commanded by our proposed tracking control law., Comment: 7 pages, 3 figures

Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by introducing distributed parameters to the prescribed inter-distances we are able to manipulate the steady-state motion of the formation. This manipulation is in the form of inducing simultaneously the combination of constant translational and angular velocities and a controlled scaling of the rigid formation. While the computation of the distributed parameters for the translational and angular velocities is based on the well-known graph rigidity theory, the parameters responsible for the scaling are based on some recent findings in bearing rigidity theory. We carry out the stability analysis of the modified gradient system and simulations in order to validate the main result., Comment: 6 pages In proceedings 55th Conference on Decision and Control, year 2016

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated., Comment: 10 pages

Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a Control Matrix Function inequality. Based on this result, we provide the construction of such synchronizer via backstepping approaches. In some particular cases, we show how global exponential synchronization may be obtained.

Recently it has been reported that range-measurement inconsistency, or equivalently mismatches in prescribed inter-agent distances, may prevent the popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape, and even worse from standing still at any location. In this paper, instead of treating mismatches as the source of ill performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation or their combination while guaranteeing asymptotically no distortion in the formation shape occurs. Such motion control results are then applied to (a) the alignment of formations orientations and (b) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller., Comment: 14 pages

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation., Comment: 14 pages, conditionally accepted in Automatic Control, IEEE Transactions on

We investigate how the following properties are related to each other: i)-A manifold is "transversally" exponentially stable; ii)-The "transverse" linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.