Formation Reconfiguration Problem Research Articles

Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.

Fuel-optimal satellite formation reconfiguration method with best passive safety parameters

This paper investigates the problem of satellite formation reconfiguration from the best passive safety parameters while ensuring the minimum fuel cost and desired formation configuration. Based on the relative eccentricity and inclination vectors, a hybrid method is proposed that combines the analytical solution and the genetic algorithm optimization method. It transforms the fuel-optimal conditions into the constraints of optimization model, which theoretically ensures the optimal fuel cost. The proposed hybrid approach is applicable to satellite formation reconfiguration problems with variable relative eccentricity and inclination vectors and passive safety concerns. Compared with the optimal three-impulse strategy and the analytical method in two different reconfiguration scenarios, the proposed method is proven to be more general and has advantages in passive safety performance.

Reconfiguration for UAV Formation: A Novel Method Based on Modified Artificial Bee Colony Algorithm

The flight formation of unmanned aerial vehicles (UAVs) needs to be reconfigured whenever necessary to cope with complex environments and varying tasks. However, the continuity, nonlinearity and high dimensionality of the UAV formation control parameters bring significant challenges to the efficiency and safety of UAV formation reconfiguration. To this end, this paper proposes a reconfiguration strategy of the UAV formation based on a modified Artificial Bee Colony (ABC) algorithm, which ensures superior efficiency and safety level simultaneously. Specifically, we first formulate the formation reconfiguration problem minimizing the time consumed for reconfiguration under the constraints of safety and connection. Then the continuous optimization problem is discretized by using the control parameterization and time discretization (CPTD) method. Finally, we use a modified ABC algorithm to find the solution of formation reconfiguration. Extensive performance evaluations are conducted to verify the superiority of the proposed method. It is concluded that the proposed algorithm achieves a better performance than the existing approaches in literature in solving the problem of 3-D formation reconfiguration.

Resilient Formation Reconfiguration for Leader–Follower Multi-UAVs

Among existing studies on formation reconfiguration for multiple unmanned aerial vehicles (multi-UAVs), the majority are conducted on the assumption that the swarm scale is stationary. In fact, because of emergencies, such as communication malfunctions, physical destruction, and mission alteration, the scale of the multi-UAVs can fluctuate. In these cases, the achievements of formation reconfiguration for fixed-scale multi-UAVs are no longer applicable. As such, in this article, the formation reconfiguration problem of leader–follower multi-UAVs is investigated with a variable swarm scale taken into consideration. First, a streamlined topological structure is designed on the basis of the parity of the vertex numbers. Then, three formation reconfiguration strategies corresponding to the scenarios covering leader disengagement, follower detachment, and new member additions are developed with the aim of reducing the frequency of connection changes. Moreover, in terms of the leader election link of the leader disengagement scenario, a knowledge-based performance assessment model for UAVs is constructed with the help of the hierarchical belief rule base (BRB). Finally, the proposed formation reconfiguration strategies for leader disengagement, new member addition, and follower disengagement are demonstrated through simulations. The connection retention rate (CRR) for swarm communication topology under the three formation reconfiguration strategies can reach 67%, 90%, and 100%, respectively.

Collision-Free Distributed Control for Multiple Quadrotors in Cluttered Environments With Static and Dynamic Obstacles

To ensure robust flight of multiple quadrotors in unknown environments, this letter proposes a distributed cooperative control algorithm with a separation-merge mechanism to solve the problem of safe flight and formation reconfiguration. The separation-merge framework integrates the obstacle avoidance mechanism, inter-robot collision avoidance mechanism, and formation reconfiguration mechanism, and couples them all to the control layer. Obstacle detection mechanism and velocity adjustment mechanism are designed based on the obstacle avoidance behavior of the pigeons. And a rotational potential energy is introduced to solve the case of local minima and oscillations where the rotation angle can be changed in real-time according to the relative position. Inspired by spring damping system, a collision avoidance mechanism is designed with the help of Hooke's law with damping. A formation reconfiguration mechanism is designed based on consensus theory, which enables multiple quadrotors to quickly return to the prescribed formation after obstacle avoidance. The proposed method is integrated into a multi-quadrotor system and its effectiveness is verified in the visualization simulator and outdoor experiments.

Formation Control Algorithm of Multi-UAVs Based on Alliance

Among the key technologies of Multi-Unmanned Aerial Vehicle (UAV) leader–follower formation control, formation reconfiguration technology is an important element to ensure that multiple UAVs can successfully complete their missions in a complex operating environment. This paper investigates the problem of formation reconfiguration due to battlefield mission requirements. Firstly, in response to the mission requirements, the article proposes the Ant Colony Pheromone Partitioning Algorithm to subgroup the formation. Secondly, the paper establishes the alliance for the obtained subgroups. For the problem of no leader within the alliance formed after grouping or reconfiguring, the Information Concentration Competition Mechanism is introduced to flexibly select information leaders. For the problem of the stability of alliance structure problem, the control law of the Improved Artificial Potential Field method is designed, which can effectively form a stable formation to avoid collision of UAVs in the alliance. Thirdly, the Lyapunov approach is employed for convergence analysis. Finally, the simulation results of multi-UAV formation control show that the partitioning algorithm and the competition mechanism proposed can form a stable alliance as well as deal with the no-leader in it, and the improved artificial potential field designed can effectively avoid collision of the alliance and also prove the highly efficient performance of the algorithm in this paper.

The fuel consumption analysis for satellite formation reconfiguration based on three-impulsive approach

Currently micro/nano satellites have become the protagonists in most formation flying missions, and there is an urgent demand to propose a reliable approach for quick fuel estimation of multiple-impulsive scheme on-board to achieve formation reconfiguration problems. This paper presents an optimal control approach based on multiple impulses for satellite formation in-plane reconfiguration issue in near circular orbit. Based on initial small deviation in the cylindrical coordinates system, a relative orbit motion expression is investigated, and a time-varying propagate system without perturbation is presented in this paper, which is suitable to calculate the solution of relative orbital maneuver by multiple impulses. The formation reconfiguration problem of this relative orbit motion is considered, and orbital motion equations with initial deviations are presented for relative orbital transfer calculation. Through different combinations of method from normal four-impulsive solution, the optimal three-impulsive method for relative orbital transfer in plane is obtained by analysis solution based on graphical and numerical way. In the end of paper, the effectivity and optimality of method is validated, and fuel consumption is analyzed through simulations of assumptive different formation reconfiguration missions.

Formation Reconfiguration for Fixed-Wing UAVs

This study proposes a coordinated path following approach to solve the formation reconfiguration problem in a guided manner. A novel coordinated path following control law is proposed, which steers a fleet of UAVs towards their closest projection points on their respective paths by controlling the angular velocity of each UAV, and achieves coordinated formation reconfiguration by synchronizing the UAVs’ closest projection points via controlling the linear velocity. Each UAV only uses its neighbors’ destination arc distances for coordination, which as a result saves communication bandwidth. The UAVs’ velocity constraints are also satisfied, with the linear velocity converging to the cruise speed under the proposed control law, which is helpful to prolong the flight time. The hardware-in-the-loop simulation, as well as the field experiments with seven to ten fixed-wing UAVs, are performed to validate the effectiveness of the proposed method.

A Formation Reconfiguration Algorithm for Multi‐UAVs Based on Distributed Cooperative Coevolutionary with an Adaptive Grouping Strategy

The Formation reconfiguration problem plays a crucial role in the implementation of complex tasks for multiple unmanned aerial vehicles, which attracted increasing attention in the past decade. Taking into consideration the control parameters and time discretization of the multi-UAVs in the 3 Dimensional (3-D) space, the formation reconfiguration problem can be formulated as a large-scale combinatorial optimization problem with complex constraints and tight couplings between variables. The problem results in the reduction in efficiency and effectiveness using classic bio-inspired algorithms. In this paper, a formation reconfiguration method based on cooperative coevolutionary algorithm is proposed along with a new decomposition strategy to improve the optimization capability and prevent premature convergence. In the proposed approach, variables of multi-UAV are divided into several sub-groups based on an adaptive grouping strategy. The proposed strategy groups the variables in order to better deal with the tight coupling among them, taking into account the variables' variance and multi-UAVs characteristics of the formation reconfiguration problem. Therefore, each subgroup can adopt the Self-adaptive differential evolution strategy with neighborhood search (SaNSDE) with the aim to optimize the UAV's control inputs using multithreaded programming. SaNSDE contributes to calculating the results in a fully distributed and paralleled manner. Optimal solution is then obtained through cooperation and coordination with all subcomponents. Simulation results based on extreme scenarios adopted by previous researches demonstrate that the proposed algorithm outperformed the existing approaches including Particle swarm optimization (PSO), Differential evolution (DE), and the cooperative coevolution algorithms with different well-known grouping strategies.

Distributed RISE control for spacecraft formation reconfiguration with collision avoidance

In this paper, we investigate the distributed formation reconfiguration problem of multiple spacecraft with collision avoidance in the presence of external disturbances. Artificial potential function (APF) based virtual velocity controllers for the spacecraft are firstly constructed, which overcome the local minima problem through introducing auxiliary inputs weighted by bump functions. Then, based on the robust integral of the sign of the error (RISE) control methodology, a distributed continuous asymptotic tracking control protocol is proposed, accomplishing both formation reconfiguration and the collision avoidance among spacecraft and with obstacles. Furthermore, using tools from graph theory, Lyapunov analysis and backstepping technique, we show the stability and collision avoidance performance of the closed-loop multiple spacecraft system. Numerical simulations for a spacecraft formation are finally provided to validate the effectiveness of the proposed algorithm.

Spacecraft formation flying reconfiguration with extended and impulsive maneuvers

This paper presents the control solutions to the spacecraft formation reconfiguration problem when impulsive or extended maneuvers are considered, and the reference orbit is circular. The proposed approach for the derivation of the control solutions is based on the inversion of the linearized equations of relative motion parameterized using the mean relative orbit elements. The use of mean relative orbit elements eases the inclusion of perturbing accelerations, such as the Earth’s oblateness effects, and offers an immediate insight into the relative motion geometry. Several maneuvering schemes of practical operational relevance are considered and the performance of the derived impulsive and piecewise continuous control solutions are investigated through the numerical propagation of the nonlinear relative dynamics. Finally, the benefits of the new extended maneuvers strategies are assessed through a comparison with the corresponding impulsive one.

Trajectory Following and Improved Differential Evolution Solution for Rapid Forming of UAV Formation

In this paper we proposed the circle trajectory assembly algorithm to control the multi-UAVs circular assembly formation. CTFAP solution provides rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance. Proposed Distributed model prediction control framework improves the optimization ability and reduces the computation consumption with the better convergence ability of the UAV formation. Firstly, a circular trajectory following algorithm with an adaptive parameter is proposed to complete the rapid formation of UAVs on a circular orbit and solve the problem of large scattering distance during formation forming. Then, in the stage of formation reconfiguration, with distributed model prediction control framework (DMPC), the proposed method gets the prediction information of DMPC to optimize the population of classical differential evolution (DE) algorithm and improve the iterative optimization ability of DE algorithm. Experiments show that the proposed differential evolution algorithm greatly improves the efficiency of solving the formation reconfiguration problem under the DMPC framework and overcomes the disadvantages of random population of classical DE. For the proposed rapid forming method, assembly range is reduced by 41% compared with direct linearly formation assembly, and the formation forming time is reduced by approximately 21%. Compared with other optimization algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and DE, the proposed differential evolution algorithm reduces instruction response time of single-drones by 16%–30%.

Reconfiguration of Three-Craft Coulomb Formation Based on Patched-Conic-Section Trajectories

This paper investigates the nonequilibrium fixed-shape three-craft Coulomb formation reconfiguration problem. Being aware that using the feedback-control approach might result in the chattering of the charges due to the nonequilibrium nature of the system dynamics, this paper proposes a trajectory planning approach to accomplish the reconfiguration. Entire maneuver trajectories are divided into multiple phases. During each phase, only two of the three craft are charged. In this way, the relative trajectory of the charged spacecraft during a certain phase is a conic section. Entire trajectories are composed of patched conics and/or straight lines. The procedures determining the three-phase maneuver strategy are developed, including a preadjusting phase and two transition phases. Numerical simulations demonstrate the effectiveness of the algorithm and the elegance of the charge histories.

Cooperative UAVs Formation Reconfiguration in an Obstacle-Loaded Environment via Model Predictive Control

Recently, Unmanned Aerial Vehicles (UAVs) have attracted a great deal of attention in academic, civilian and military communities as prospective solutions to a wide variety of applications. The use of cooperative UAVs has received growing interest in the last decade and this provides an opportunity for new operational paradigms. In this paper, the problem of formation reconfiguration for a group of N cooperative UAVs in an obstacle-loaded environment is solved using decentralized Learning Based Model Predictive Control (LBMPC). The formation of the multiple cooperative UAVs respects the general rules of flocking known as Reynold’s rules. Each UAV is required to avoid collision with nearby flockmates, attempts to match the velocity of other team members and attempts to stay close to other team members respecting the desired formation. When static obstacles appear, the UAVs are required to steer around the obstacle or pass through avoiding collision with the obstacles or with each other. A state transformation algorithm is applied to linearize the UAV dynamics generating a linear system allowing the implementation in real life. Our main contribution in this paper lays in solving the formation reconfiguration problem for a group of cooperative UAVs forming a desired formation using decentralized LBMPC in the presence of obstacles.

Gaussian pigeon-inspired optimization approach to orbital spacecraft formation reconfiguration

With the rapid development of space technology, orbital spacecraft formation has received great attention from international and domestic academics and industry. Compared with a single monolithic, the orbital spacecraft formation system has many advantages. This paper presents an improved pigeon-inspired optimization (PIO) algorithm for solving the optimal formation reconfiguration problems of multiple orbital spacecraft. Considering that the uniform distribution random searching system in PIO has its own weakness, a modified PIO model adopting Gaussian strategy is presented and the detailed process is also given. Comparative experiments with basic PIO and particle swarm optimization (PSO) are conducted, and the results have verified the feasibility and effectiveness of the proposed Gaussian PIO (GPIO) in solving orbital spacecraft formation reconfiguration problems.

Research on the Path Optimization of Satellite Formation Reconfiguration Based on Gauss Pseudospectral Method

Aim to the path programme problem of satellite formation reconfiguration under low thrust, optimization is simulated based on Gauss Pseudospectral Method (GPM). The simulation result demonstrates that the GPM can effectively solve the the path optimization problem.

Spacecraft fuel-optimal and balancing maneuvers for a class of formation reconfiguration problems

This paper presents fuel optimal and balancing methodologies for reconfiguring multiple spacecraft in formation subject to a Newtonian gravity field. For a kind of continuous-thrust propulsion system, a fuel-optimal control problem is formulated to minimize the integral squared control subject to the linearized Hill or Clohessy–Wiltshire dynamics of relative motion with respect to a circular reference orbit. Palmer’s analytical solution for general reconfiguration is adapted to maneuvers between projected circular orbits, resulting in the optimal fuel consumption index as a function of configuration parameters such as orbit radius, phase angle, and transfer time. Parametric analyses reveal unique characteristics of individual fuel optimality and gross fuel consumption: for an arbitrary selection of initial/terminal orbit radii, (i) there exist special transfer times such that individual fuel consumption is optimally uniform for all phase angles, and (ii) the total fuel expenditure for a group of three or more spacecraft is invariant for the relatively same configuration with respect to the departure phase. These results serve to effectively design fuel balancing strategies for formation reconfiguration of multiple spacecraft.

Optimal Pulse Strategies for Relative Orbit Transfer Along a Circular Orbit

This paper is concernedwith a fuel-optimal relative orbit transfer problem forHill–Clohessy–Wiltshire equations. The input is of the pulse type and the performance index is the total velocity change required for a transfer. For the in-plane motion, the existence of optimal three-pulse strategies is shown and the minimum total velocity change is explicitly given under the condition that the difference of orbit size is relatively larger than that of drift velocity. For the out-of-plane motion, the existence of optimal single-pulse strategies is shown. The orbit transfer problem covers formation reconfiguration problem as a special case. Midpoints of the optimal pulses coincide with those points at which the velocity along the radial direction is zero. Using this information and null controllability with vanishing energy of the Hill–Clohessy–Wiltshire equations, suboptimal feedback controllers are designed. Simulation results with optimal open-loop strategies and feedback controls are given for two formation reconfiguration problems.

Differential evolution-based receding horizon control design for multi-UAVs formation reconfiguration

Formation reconfiguration is one of the most complicated problems on multiple uninhabited aerial vehicles (multi-UAVs) co-ordinated control. Based on the differential evolution (DE) algorithm, a novel type of control method using receding horizon control (RHC) is proposed aiming at driving multi-UAVs to form a new flying formation. The global control problem of multi-UAVs formation reconfiguration is transformed into several online local optimization problems within a series of receding horizons, while the DE algorithm is adopted to optimize the control sequences for each UAV. The working process of the RHC controller is presented in detail. Finally, two simulation experiments are performed, and simulation results show the feasibility and effectiveness of our proposed control approach.

Optimal Formation Reconfiguration of Multiple Spacecraft with Docking and Undocking Capability

Optimal control problems associated with formation reconfiguration of multiple spacecraft with docking and undocking capability are considered. The basic approach is to decompose the optimal formation reconfiguration problem into several simple optimal control problems. Explicit solutions of the minimum-fuel and minimum-energy control problems for reconfiguration of simple formation patterns formed by simultaneous docking of multiple spacecraft are obtained. Simulation results are given to demonstrate the effectiveness of the proposed approach.