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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.

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 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.