Desired Formation Configuration Research Articles

Fault‐tolerant formation control of non‐linear multi‐vehicle systems with application to quadrotors

This study is concerned with the fault-tolerant (FT) formation control problem with a guaranteed H ∞ performance for non-linear multi-vehicle systems subject to actuator faults. The authors consider a practical situation: the information transferred between adjacent vehicles is disturbed and each vehicle is interfered by stochastic disturbance and measurement noise. For each vehicle, a decentralised state observer and an adaptive fault estimator are designed based on which a novel cooperative FT control (FTC) protocol is proposed to drive all the vehicles to the desired formation configuration. Taking the system noise into consideration, the error dynamics are modelled by I t o ^ stochastic differential equations, whose properties are used for designing and analysing the Lyapunov function in the framework of I t o ^ calculus. It is proved that the formation error system is mean-square asymptotically stable with a prescribed attenuation level in an H ∞ sense by the proposed FTC scheme. The observer, estimator and controller gains can be obtained by solving algebraic Riccati inequalities. Finally, the theoretical results are illustrated by simulations and real experiments.

Neural network formation control of a team of tractor–trailer systems

SUMMARYThis paper addresses the formation tracking control of a group of tractor–trailer systems in the presence of model uncertainties. A virtual leader–follower formation technique is used to design a controller in order to force a team of tractor–trailer systems to construct a desired formation configuration. Since tractor–trailer systems have a nonlinear multi-input multi-output model with strong couplings, multi-layer neural networks are employed to overcome unknown nonlinearities and uncertain parameters by using on-line weight tuning algorithms. Neural network approximation errors and external disturbances are also compensated with adaptive robust signals. The dynamic surface control approach has been used to reduce the complexity of the proposed controller effectively. Lyapunov’s direct method proves that all signals in the closed-loop formation control system are bounded and tracking errors converge to a neighborhood of the origin whose size is adjustable. Finally, simulation results will be provided to illustrate the efficiency of the proposed controller.

Decentralised consensus-based formation tracking of multiple differential drive robots

ABSTRACTThis article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper.

Time Shift Governor for Coordinated Control of Two Spacecraft Formations

A parameter governor-based controller is applied to control a pair of satellites to an unforced periodic relative orbit in Hill’s frame with the desired phasing thereby achieving and maintaining a two satellite formation while satisfying the imposed constraints. To accomplish this, the controller adjusts commanded time shifts to each satellite along the target trajectory. We refer to such a parameter governor as the time shift governor. Theoretical guarantees are presented for the convergence to the desired formation configuration for the case when the set of possible time shifts is finite. Simulation results are presented to illustrate the proposed approach.

Distance-based Formation Control Using Angular Information Between Robots

Distance-based formation of groups of mobile robots provides an alternative focus for motion coordination strategies respect to the standard consensus-based formation strategies. However, the setup formulation introduces non rigidity problems, multiple formation patterns that verify the distance constraints or local minima appeared when collision avoidance strategies are added to the control laws. This paper proposes a novel combined distance-based potential functions with attractive-repulsive behavior in order to simplify the navigation problem as well as the use of angular information between robots to reduce the likelihood of unwanted formation patterns. Moreover, this approach eliminates the local minima generated by the control laws to reach the desired formation configuration in the case of three robots. The analysis addresses the case of omnidirectional robots and is extended to the case of unicycle-type robots with numerical simulations and real-time experiments.

Optimal H∞ robust output feedback control for satellite formation in arbitrary elliptical reference orbits

A two degree-of-freedom signal-based optimal H∞ robust output feedback controller is designed for satellite formation in an arbitrary elliptical reference orbit. Based on high-fidelity linearized dynamics of relative motion, uncertainties introduced by non-zero eccentricity and gravitational J2 perturbation are separated to construct a robust control model. Furthermore, a distributed robust control model is derived by modifying the perturbed robust control model of each satellite with the eigenvalues of the Laplacian matrix of the communication graph, which represent uncertainty in the communication topology. A signal-based optimal H∞ robust controller is then designed primarily. Considering that the uncertainties involved in the distributed robust control model have a completely diagonal structure, the corresponding analyses are made through structured singular value theory to reduce the conservativeness. Based on simulation results, further designs including increasing the degrees of freedom of the controller, modifying the performance and control weighted functions, adding a post high-pass filter according to the dynamic characteristics, and reducing the control model are made to improve the control performance. Nonlinear simulations demonstrate that the resultant optimal H∞ robust output feedback controller satisfies the robust performance requirements under uncertainties caused by non-zero eccentricity, J2 perturbation, and varying communication topology, and that 5m accuracy in terms of stable desired formation configuration can be achieved by the presented optimal H∞ robust controller. In addition to considering the widely discussed uncertainties caused by the orbit of each satellite in a formation, the optimal H∞ robust output feedback control model presented in the current work considers the uncertainties caused by varying communication topology in the satellite formation that works in a cooperative way. Other new improvements include adopting a new method to more accurately describe and analyze the effects of the higher-order J2 perturbation, combining all the uncertainties into a diagonal structure, and utilizing a structured singular value to synthesize and analyze the controller.

Quadcopter formation flight control combining MPC and robust feedback linearization

This paper presents an integrated and practical control strategy to solve the leader–follower quadcopter formation flight control problem. To be specific, this control strategy is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight. The proposed control scheme uses a hierarchical approach consisting of model predictive controller (MPC) in the upper layer with a robust feedback linearization controller in the bottom layer. The MPC controller generates the optimized collision-free state reference trajectory which satisfies all relevant constraints and robust to the input disturbances, while the robust feedback linearization controller tracks the optimal state reference and suppresses any tracking errors during the MPC update interval. In the top-layer MPC, two modifications, i.e. the control input hold and variable prediction horizon, are made and combined to allow for the practical online formation flight implementation. Furthermore, the existing MPC obstacle avoidance scheme has been extended to account for small non-apriorily known obstacles. The whole system is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time. Formation flight experiments are set up in Vicon motion-capture environment and the flight results demonstrate the effectiveness of the proposed formation flight architecture.

Distributed Bearing-Only Quadrilateral Formation Control

AbstractA distributed control law for quadrilateral (four-agent) formation control with bearing-only measurements and relative pair-wise inter-agent angle constraints is introduced. A strong convergence result is established with ensures the desired formation configuration is globally asymptotically stable. In addition, it is shown that the distributed control law is generally robust to a single agent motion failure. Illustrative examples are provided to demonstrate the claims.

Distributed Role Assignment in Multi-Robot Formation

In this paper, we study the problem of distributed role assignment for multiple mobile robots. This problem arises when a mobile robot in the team must decide what role to take on in a desired formation configuration. In some applications, in which the center and orientation of a desired formation are not predetermined, the rotation and translation of the formation can be computed by using average consensus protocols. A conflict arises when the same role is assigned to more than one robot. This problem is resolved by using a negotiation strategy, while each assigned robot is traveling to the target position. Furthermore, dynamic consensus is used to measure the degree of task completion in this work. Once the consensus reaches a preset threshold, implying that robots should abandon the current task and start the next one. We verify our proposed framework through simulations on a team of nonholonomic mobile robots performing distributed formation switching.

Nonlinear Optimization of Low-Thrust Trajectory for Satellite Formation: Legendre Pseudospectral Approach

In this paper, we focus on the design of a fuel-optimal maneuver strategy to reconfigure satellite formation using a low-thrust propulsion system. We cast it as an optimization problem with a desired final satellite formation configuration subject to collision avoidance constraints on the paths of the chief and all deputy satellites. The satellite terminal orbit states corresponding to this desired formation configuration are ensured by imposing an energy-matching condition and final geometry configuration constraints in the problem formulation. In addition, we adopt our recently developed relative satellite kinematics model to accurately describe relative satellite orbit geometry in the presence of J 2 effects. The resulting nonlinear optimal control problem is converted into a nonlinear programming problem by the application of the Legendre pseudospectral method and is then solved by using a sparse nonlinear optimization software named TOMLAB/SNOPT. Simulation results demonstrate the efficiency of our proposed method in designing fuel-optimal maneuvers for a wide class of satellite formation problems.

A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems

In this paper, a feedback control strategy that achieves convergence of a multi-agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle-type kinematics. When inter-agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible. It is shown that under certain assumptions, formation infeasibility forces the agents’ velocity vectors to a common value at steady state. This provides a connection between formation infeasibility and flocking behavior for the multi-agent system. We finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility.

Formation Control of Marine Surface Craft: A Lagrangian Approach

This paper presents a method for formation control of marine surface craft inspired by Lagrangian mechanics. The desired formation configuration and response of the marine surface craft are given as a set of constraint functions. The functions are treated according to constraints in analytical mechanics. Thus, constraint forces arise and feedback from the constraint functions keeps the formation assembled. Since the constraint functions are designed for a desired effect, the forces can be interpreted as control laws. Examples of constraint functions that maintain a formation are presented. Furthermore, the same approach has been applied with no major modification to position control purposes for a single vessel. An extension to underactuated vessels is given. Simulations with nonlinear models of tugboats illustrate the proposed method versatility and its robustness with respect to environmental disturbances and time delays