Distance-based Formation Control Research Articles

Optimal time-invariant distributed formation tracking for second-order multi-agent systems

This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton’s method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies.

Distributed Adaptive Path-Following Control for Distance-Based Formation of Fixed-Wing UAVs under Input Saturation

This paper investigates the distance-based formation and cooperative path-following control problems for multiple fixed-wing unmanned aerial vehicles (UAVs). In this study, we design the distance-based formation control structure to achieve the virtual leader and followers pre-defined rigid formation pattern, ensuring simultaneously relative localization. A path-following control strategy based on adaptive dynamic surface and neural network control technology is proposed to approximate the uncertain disturbances of the environment and unmodeled dynamics. And the longitudinal and lateral subsystems’ adaptive fault-tolerant controllers are designed, respectively, to achieve the fault-tolerant control of UAVs’ formation in three-dimensional environments. Furthermore, the adaptive sliding mode controller with an auxiliary controller is designed to realize the UAVs path following with limited input saturation. Finally, simulation examples are given to clarify and verify the effectiveness of the theoretical results.

Directed Distance-Based Formation Control of Nonlinear Heterogeneous Agents in 3-D Space

This paper studies distance-based formation control of a set of nonlinear multi-agent systems over directed graphs. We propose a distributed, distance-based formation control scheme for a set of heterogeneous, nonlinear agents over a particular class of minimally, structurally persistent, directed graphs in a 3-D space, namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">directed trilateral Laman</i> graphs. The responsibility of controlling each directed edge is assigned to only one of the adjacent agents. The state-dependent Riccati equation is used to design the control method for nonlinear agents. Based on the mathematical induction and stability theory of cascade interconnected systems, we rigorously prove the asymptotic stability of the overall formation. A combination of signed area and volume constraints is used to prevent agents from converging to the flip-ambiguous frameworks in 3-D space. The proposed control law assures collision avoidance between the neighboring pairs of agents. Simulation results are provided to verify the theoretical results.

Avoiding Ambiguous Framework in Distance-based Formation Control Using Virtual Followers

In this study, we develop a shape formation controller based on regular distance-based control law. As distance rigidity theory may not be successful in achieving desired shape when the control system defined under minimally rigid graph. As a matter of fact, the formation may converge to ambiguous framework when the group of mobile robots did not initialize in proper way. This is a well-known issue with distance-based formation control while there are multiple equilibrium points in the dynamics. We introduce a new controller by adding virtual constraints to the system. The performance of control system is exemplified through numerical simulations and the convergence to the desired formation for all initial conditions validated with stability analysis.

Avoiding Ambiguous Framework in Distance-based Formation Control Using Virtual Followers

Avoiding Ambiguous Framework in Distance-based Formation Control Using Virtual Followers

Distance-Based Formation Control for Fixed-Wing UAVs with Input Constraints: A Low Gain Method

Due to the nonlinear and asymmetric input constraints of the fixed-wing UAVs, it is a challenging task to design controllers for the fixed-wing UAV formation control. Distance-based formation control does not require global positions as well as the alignment of coordinates, which brings in great convenience for designing a distributed control law. Motivated by the facts mentioned above, in this paper, the problem of distance-based formation of fixed-wing UAVs with input constraints is studied. A low-gain formation controller, which is a generalized gradient controller of the potential function, is proposed. The desired formation can be achieved by the designed controller under the input constraints of the fixed-wing UAVs with proven stability. Finally, the effectiveness of the proposed method is verified by the numerical simulation and the semi-physical simulation.

Gradient-based bearing-only formation control: An elevation angle approach

This paper proposes an elevation angle rigidity theory in both 2D and 3D spaces, and applies it to solve multi-agent formation control with only inter-agent bearing/direction measurements in agents’ local coordinate frames. Motivated by the sensor technology in measuring elevation angle and angular diameter, we develop elevation angle rigidity by attaching each agent in a multi-agent framework with a rod in 2D and a ball in 3D, respectively. By defining the elevation angle rigidity matrix, conditions for infinitesimal elevation angle rigidity are derived. Compared to previously developed angle rigidity-based and bearing rigidity-based formation control laws, the proposed elevation angle rigidity-based control law can maintain the gradient-based control property. Compared to distance-based formation control laws, less sensor measurements are required. The formation maneuvering with desired translation and rotation is also realized by using only local bearing measurements. Simulation examples illustrate the advantages and effectiveness of the proposed approach.

Neural Network-Based Formation Control With Target Tracking for Second-Order Nonlinear Multiagent Systems

This article proposes a distance-based formation control and target tracking for multiagent systems, where agents are modeled using second-order nonlinear systems in the presence of disturbance. By applying a rigid graph theory, we developed a neural network (NN)-based backstepping controller to address the distance-based formation control problem of nonlinear multiagent systems. To compensate for the unknown nonlinearity in the system dynamics, the radial basis function NN was used where the NN tuning law was derived based on Lyapunov stability theory. We rigorously proved the uniform ultimate boundedness of the formation distance error and NN weights’ norm estimation error. Finally, using simulation results, we demonstrated the proposed method’s performance on the second-order, nonlinear multiagent systems. To provide further evaluation, we compared the proposed distance-based method and existing displacement-based methods.

Spectral Properties of the Normalized Rigidity Matrix for Triangular Formations

This work establishes properties of the normalized rigidity matrix in two- and three-dimensional spaces. The upper bound of the normalized rigidity matrix singular values is derived for minimally and infinitesimally rigid frameworks in two- and three-dimensional spaces. We prove that the transformation of a framework does not affect the normalized rigidity matrix properties. The largest minimum singular value of the normalized rigidity matrix for a rigid framework of three agents in two-dimensional space is given as well as necessary and sufficient conditions to reach that value. These results can be used in stability analysis and control design of a distance-based formation control. The numerical simulation for multi-agent systems in two-dimensional space illustrates the theoretical results. Moreover, a real-time simulation is provided to demonstrate the spectral properties of the normalized rigidity matrix.

Forced Variational Integrators for the Formation Control of Multiagent Systems

Formation control of autonomous agents can be seen as a physical system of individuals interacting with local potentials, and whose evolution can be described by a Lagrangian function. In this article, we construct and implement forced variational integrators for the formation control of autonomous agents modeled by double integrators. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions. We find error estimations for the rate of the energy dissipated along with the agents' motion to achieve desired formations. Consequently, this permits to providing sufficient conditions on the time step for the convergence of discrete formation control systems such as the consensus problem in discrete systems. We present practical applications such as the rapid estimation of regions of attraction to desired shapes in distance-based formation control.

Distance‐based formation control for multi‐lane autonomous vehicle platoons

This paper investigates the formation control of connected autonomous vehicle (CAV) platoons moving in multi lanes using distance-based formation control techniques based on rigid graphs and V2V communication. A hierarchical architecture is proposed to decompose the cooperative control into velocity planning and vehicle dynamic control. A new velocity planning method is first developed via a distributed distance-based formation controller so that each vehicle can keep platoon and change lane. Then, for the vehicle dynamics with nonlinearities and bounded disturbances, an adaptive controller is designed for regulating driving/braking torque to achieve the longitudinal velocity output of the velocity planner. The steering controller is designed to adjust the yaw angle of each vehicle to track and change lanes. Furthermore, stability analysis is conducted based on the Lyapunov theory. Finally, the applications of the proposed control designs to various of automated highway system (AHS) scenarios including lane-change, curve lane and platoon overtaking, are simulated and numerically analysed to validate the effectiveness of theoretical results.

Distance-Based Formation Control With Goal Assignment for Global Asymptotic Stability of Multi-Robot Systems

This letter presents a distance-based formation control with the goal assignment for multiple nonholonomic mobile robots. One of the most challenging issues in the distance-based formation control is the convergence to undesirable formations caused by the gradient-based control law. Even though the target formation is globally rigid, only the local stability is guaranteed. In order to overcome this restriction, we present a novel goal assignment algorithm switching the goal positions of two agents in the target formation. This assignment algorithm helps to avoid the convergence to undesirable formations and thus the global asymptotic convergence can be achieved. To show the effectiveness of the proposed distance-based formation controller with the goal assignment algorithm, simulation and experimental results are provided.

Noether Symmetries and Decay Laws in Formation Control of Multi-agent Systems

Abstract Distance-based formation control of agents with double integrator dynamics can be seen as a stabilization system whose evolution can be described by a time-dependent Lagrangian function. In this paper, a Noether theorem for this class of systems is obtained, giving rise to an intrinsic geometric understanding of the exponential decay for the constants of the motion of the agents, in particular, linear and angular momentum. An interesting family of geometric integrators, called variational integrators, is defined by using discretizations of the Hamilton’s principle of critical action. The variational integrators preserve some geometric features such as the momentum map, and the decay of the system’s energy presents a good behavior. We derive variational integrators for time-dependent Lagrangian systems that can be employed in the context of distance-based formation control algorithms. In particular, we provide an accurate numerical integrator preserving the exponential decay of the constants of motion.

Distance-based Leader-Follower Formation Control of Mobile Robots Using Relative Target Positions

Distance-based Leader-Follower Formation Control of Mobile Robots Using Relative Target Positions

Multi-Agent Formation Tracking for Autonomous Surface Vehicles

In this article, the problem of collaborative tracking of an underwater target using autonomous surface vehicles (ASVs) is studied. Distance-based formation control with a collision-avoidance potential function is employed as a solution. A formation control protocol is devised and applied to the formation tracking problem. With the protocol, the vehicles form a desired formation around a moving target in order to continuously estimate its position, while the centroid of the formation tracks the target. Almost global stability is proved for the case with three tracking agents. A fully operational platform with four ASVs was built to implement the derived algorithms. One of the vehicles was used to simulate a target and the rest to form a triangular formation around it. Power usage of a naval vessel is highly affected by water resistance forces which increases significantly with the velocity. This was accounted for by adding an additional term to the formation tracking protocol, thereby increasing the overall system endurance. Experimental results are presented.

Distributed Robust Adaptive Gradient Controller in Distance-Based Formation Control With Exogenous Disturbance

In this article, we present a distributed robust adaptive gradient controller for distance-based formation systems with exogenous disturbances. Based on the proposed controller, we consider two undirected formation topologies: Minimally infinitesimally rigid formation and nonminimally infinitesimally rigid formation. For both formation systems, we show that the distributed robust adaptive gradient controller guarantees a local stability of formation systems with exogenous disturbances. Furthermore, an upper-boundedness set of squared-distance error is obtained based on Lyapunov stability analysis for minimally infinitesimally rigid formation systems. We verify the validity of the theoretical results through numerical simulations.

Distance-Based Formation Control for Quadrotors with Collision Avoidance via Lyapunov Barrier Functions

In this paper, group formation control with collision avoidance is investigated for heterogeneous multiquadrotor vehicles. Specifically, the distance-based formation and tracking control problem are addressed in the framework of leader-follower architecture. In this scheme, the leader is assigned the task of intercepting a target whose velocity is unknown, while the follower quadrotors are arranged to set up a predefined rigid formation pattern, ensuring simultaneously interagent collision avoidance and relative localization. The adopted strategy for the control design consists in decoupling the quadrotor dynamics in a cascaded structure to handle its underactuated property. Furthermore, by imposing constraints on the orientation angles, the follower will never be overturned. Rigorous stability analysis is presented to prove the stability of the entire closed-loop system. Numerical simulation results are presented to validate the proposed control strategy.

Distance-Based Formation Control With Bounded Disturbances

In this letter, we study distance-based formation control of single- and double-integrator modeled agents with unknown bounded disturbances. We propose distributed control laws to simultaneously achieve the desired formation shape and eliminate the effects of disturbances. The stability of the systems under the proposed control laws is analyzed based on Lyapunov stability theory of nonsmooth systems and Barbalat's lemma. Further, sufficient conditions are given to ensure the system to approach the set of desired formation. Finally, simulation results are provided to support the analysis.

Prescribed performance distance-based formation control of Multi-Agent Systems

This paper presents a novel control protocol for robust distance-based formation control with prescribed performance in which agents are subjected to unknown external disturbances. Connectivity maintenance and collision avoidance among neighboring agents are also handled by the appropriate design of certain performance bounds that constrain the inter-agent distance errors. As an extension to the proposed scheme, distance-based formation centroid maneuvering is also studied for disturbance-free agents, in which the formation centroid tracks a desired time-varying velocity. The proposed control laws are decentralized, in the sense that each agent employs local relative information regarding its neighbors to calculate its control signal. Therefore, the control scheme is implementable on the agents’ local coordinate frames. Using rigid graph theory, input-to-state stability, and Lyapunov based analysis, the results are established for minimally and infinitesimally rigid formations in 2-D or 3-D space. Furthermore, it is argued that the proposed approach increases formation robustness against shape distortions and can prevent formation convergence to incorrect shapes under the effect of external disturbances, which is likely to happen in conventional distance-based formation control methods. Finally, extensive simulation studies clarify and verify the proposed approach.

A Data-Driven Method Based on Quadratic Programming for Distance-Based Formation Control of Euler–Lagrange Systems

Distance-based formation control of second-order autonomous agents can be seen as a physical system of particles linked by springs, whose evolution may be described by a Lagrangian function. In this letter we present a method based on quadratic programming to approximate the unknown Lagrangian function associated with the distance-based formation control of second-order agents from a set of sample data.