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This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive vector fields (RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the distances and velocities among the agents is designed to scale the RVFs adequately. It is shown that when the agents are at risk of collision, the distances among them are always greater than the safety distance. Numerical simulations and a comparison with a repulsive potential function (RPF) illustrate the agents’ performance.

This paper deals with the formation control problem without collisions for second-order multi-agent systems. We propose a control strategy which consists of a bounded attractive component to ensure convergence to a specific geometrical pattern and a complementary repulsive component to guarantee collision-free rearrangement. For convergence purposes, it is assumed that the communication graph contains at least a directed spanning tree. The avoidance complementary component is formed by applying repulsive vector fields with unstable focus structure. Using the well-known input-to-state stability property a control law for second-order agents is derived in a constructive manner starting from the first-order case. We consider that every agent is able to detect the presence of any other agent in the surrounding area and also can measure and share both position and velocity with his predefined set of neighbours. The resulting control law ensures the convergence to the desired geometrical pattern without collisions during the transient behaviour, as well as bounded velocities and accelerations. Numerical simulations are provided to show the performance and effectiveness of the proposed strategy.

SUMMARYIn this paper, a general solution to the formation control problem without collisions for first-order multi-agent systems is proposed. The case of an arbitrary number of mobile agents on a plane with saturated input velocity is analysed. Besides, conditions on the communication graph among agents are relaxed to the only requirement of containing a directed spanning tree. This general approach is an extended result from the simpler case of combinations of cyclic pursuit communication graphs. The proposed solution to this problem is designed in two steps. First, the asymptotic convergence in the absence of collisions is ensured. After this, the non-collision problem is faced by analysing the most general possible geometrical scenario which can lead to collision among agents. Discontinuous vector fields with unstable counterclockwise focus behaviour are applied by every agent in order to repel each other. Numerical simulations illustrate the performance of the proposed scheme.

Two trajectory tracking control strategies based on the leader–followers scheme for a group of differential-drive mobile robots are presented where the output to control is the mid-point of the whe...

This paper deals with the general formation control problem for first order multi-agent systems. We investigate the behaviour of an arbitrary number of mobile agents moving on a plane with constrained input velocity when they are required to reach a specific spatial pattern. A general communication graph among agents is considered, relaxing conditions to the only requirement of containing a directed spanning tree. The solution to this problem is provided attending two issues. First, the asymptotic convergence to the desired formation pattern is ensured. Then a non-collision analysis is presented regarding the most general geometrical scenario which can lead to a collision among agents. This later issue is solved by using repulsive vector fields with unstable focus behaviour. Numerical simulations as well as experimental results are provided in order to illustrate the effectiveness of the proposed control law.

This paper studies the formation tracking problem for a multi-agent system composed by a set of quadrotor UAVs. Parrot AR.Drone 2.0 quadrotors are used as agents of the system. The AR.Drone 2.0 features an internal controller to stabilize the angular dynamics. This controller is modelled and identified through the least squares method. The proposed control strategy is designed using a time-varying version of the backstepping technique for each agent. For the implementation of the control law, it is assumed that each agent measures only the leader and its own positions, while the leader also knows the desired trajectory the system must follow. Linear and angular velocities of the agents are estimated using suitable Luenberger observers. The proposed control strategy allows the leader agent to converge asymptotically to a predetermined flight trajectory while the follower agents converge asymptotically to their own trajectories defined by the leader position and a constant formation vector. The theoretical results are validated through real-time experiments.

In this paper we propose a non-linear control law to achieve trajectory tracking in the 3D space for a commercial AR.Drone 2.0 quadrotor. The proposed control law is based on a non-linear time varying version of the Backstepping technique that takes into account the dynamics of the internal orientation controller of the AR.Drone. The stability of the control law is ensured by the design of recursive Lyapunov functions and its performance is tested by numeric simulations on MATLAb Simulink environment.

This paper studies the 3D trajectory tracking for the quadrotor commercial prototype AR.Drone 2.0 of the French company Parrot. The proposed control strategy is designed using a time-varying version of the backstepping technique. For the implementation of the control law, it is assumed that only the position and orientation of the AR.Drone are known; linear and angular velocities of the AR.Drone are estimated using suitable Luenberger observers. The proposed control strategy allows an AR.Drone 2.0 to converge asymptotically to a predetermined flight trajectory. The theoretical results are validated through real-time experiments.

This paper studies the collision avoidance problem in the time-varying formation tracking control for multi-agent 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 some agents. This control strategy allows a set of mobile agents to track a predetermined trajectory while they achieve a time-varying formation. For the collision avoidance, we add a repulsive vector field of the unstable focus type to the time-varying formation tracking control law. A leader-followers scheme is employed, using formation graphs 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.

In this paper we propose a nonlinear control law to achieve trajectory tracking in the 3D space for a commercial Bebop 2 quadrotor. The proposed control law is based on a nonlinear time varying version of the Backstepping technique, which includes an integral gain for disturbance rejection and that takes into account the dynamics of the internal controller for the orientation of the quadrotor. The stability of the control law is ensured by the design of recursive Lyapunov functions and its performance is tested by real-time experiments.

This paper proposes a heterogeneous multi-agent robot system, composed of differential-drive robots and omnidirectional mobile robots to emulate the parking task from a kinematic point of view. For this aim, a control strategy, based on the feedback linearization techniques, is proposed, obtaining asymptotic convergence to the desired trajectory. Numerical simulations illustrate a comparison between the behavior of the heterogeneous system and a standard n-trailer system while performing the parking task.

For finite dimensional linear system the root-locus method is well established however for the case of delayed systems the method has some problems due to the transcendental term involved. This work intends to illustrate the problems that arises when a root-locus diagram is performed as well as to develop a Matlab function that provides the root-locus diagram for delayed low order systems. In this way, some comments about the problems that should be tackled to obtain a generalization of the computational method for delayed systems with realmpoles andnzeros

This paper addresses the formation control problem without collisions for multiagent systems. A general solution is proposed for the case of any number of agents moving on a plane subject to communication graph composed of cyclic paths. The control law is designed attending separately the convergence to the desired formation and the noncollision problems. First, a normalized version of the directed cyclic pursuit algorithm is proposed. After this, the algorithm is generalized to a more general class of topologies, including all the balanced formation graphs. Once the finite-time convergence problem is solved we focus on the noncollision complementary requirement adding a repulsive vector field to the previous control law. The repulsive vector fields display an unstable focus structure suitably scaled and centered at the position of the rest of agents in a certain radius. The proposed control law ensures that the agents reach the desired geometric pattern in finite time and that they stay at a distance greater than or equal to some prescribed lower bound for all times. Moreover, the closed-loop system does not exhibit undesired equilibria. Numerical simulations and real-time experiments illustrate the good performance of the proposed solution.

International audience; Two nonlinear systems having the same number of inputs, but not the same number of state variables, are considered. The problem of the existence of two invertible state feedback laws and a surjective mapping from the higher dimensional state space of one system into the lower dimensional state space of the second system is stated, such that the rst system dynamics reduces exactly to the second system dynamics. This problem generalizes the linear feedback equivalence problem of two systems and is fully solved in the special case of feedback linearizable systems.

This paper proposes the emulation of a physical standard or generalized n?trailer through the decentralized control of a multi-agent system composed of several differentially driven mobile robots. The key point is to solve a time-varying version of the well known formation tracking or marching problem. The problem is solved both in discrete- and continuous-time cases. Four different control laws are proposed which require different variables to be available for feedback or feedforward, depending on the specifications of the experimental platform. The performance of the proposed control laws is illustrated through real-time experiments. It is shown that the discrete-time control law exhibits a performance comparable to that of the continuous-time control law with a sampling period 20 times larger than the one used in the continuous-time experiment.