Relative State Error Research Articles

Robustness in formation control of mobile robots using leader-follower method

This paper presents the robustness in formation control of multiple mobile robots using leader-follower method. The uncertainty considered is the measured error which is included in the relative state. The robust stability conditions against the relative state error are derived by Lyapunov’s stability theory (direct method). We also obtain the formation steady-state deviation when formation stability is ensured. The formation control environment is constructed on Simulink. The validity of the stability condition and the steady-state deviation is demonstrated by numerical simulation. It is seen that the L-F method provides a robust control law against the relative state error although large formation steady-state deviation is occurred in some cases.

Novel Reference Trajectory-Based Finite-Time Consensus Protocols for Multiagent Systems With Non-Identical Nonlinear Dynamics

This paper investigates the finite-time consensus for second-order multiagent systems under directed networks, where each agent is described by a non-identical nonlinear system. By using the reference trajectory-based method, two novel protocols are developed for the leader-follower and leaderless cases, respectively. It is noted that the dynamical evolutions of each agent's state and the reference trajectory are coupled, and the information of reference trajectories is not allowed to transmit in the communication channels. By the developed protocols, the relative state errors among agents can converge to the origin (instead of a neighborhood of the origin) within a finite time, though there are unknown parameters in agents' dynamics. The nonlinear terms in agents' dynamics are not required to be bounded by known constants or functions, which invalidates many consensus schemes based on the sliding mode control. Using the graph theory, Lyapunov functional method and finite-time stability theory, sufficient conditions are established for the finite-time consensus of considered multiagent systems. Finally, simulation examples are given to validate the effectivity of the proposed protocols.

Distributed adaptive event‐triggered containment control for multi‐agent systems under a funnel function

AbstractIn this article, the adaptive event‐triggered containment control problem is investigated for a class of uncertain nonlinear multi‐agent systems with an adjustable funnel function. To address the high‐frequency oscillations or overshooting problem of fast learning, a predictor is considered. Different from the existing event‐triggered control results, a novel adaptive event‐triggered condition is designed, which depends on the prediction error instead of relative state error. In order to further improve both the transient and steady‐state performance, a modified funnel control strategy is introduced, and distributed containment errors are converged to an adjustable funnel boundary. The proposed control scheme guarantees that the closed‐loop system is stable and all followers converge to the convex hull constructed by the leaders. Finally, two simulation examples are provided to confirm the effectiveness of the proposed control method.

A Framework of High-precision State Estimation for Approaching, Orbiting, and Touching an Asteroid

High-precision state estimation lies at the core of asteroid exploration. This paper investigates the high-precision state estimation methods in asteroid approaching, orbiting, and touching phases. The system and measurement models are established, and state estimation strategies are designed respectively for each phase. In the approaching phase, the star image is used to directly determine the relative orbit of the spacecraft to the target asteroid. To improve the optical state estimation precision, a deceleration-orientation-deceleration strategy is developed. In the orbiting phase, coupled orbit-attitude estimation is realized based on the terrain features of the asteroid, and the effect of dynamic error on the accuracy of state estimation is analysed. Then, a decoupled orbit-attitude state estimation method is developed to avoid the affection of dynamic error. In the touching phase, lidar measurement is used to determine the relative orbit and attitude of the spacecraft with respect to the landing spot. Based on the triple-stage state estimation framework proposed in this paper, the relative state error of the spacecraft converges from 100km level to 1mm level.

Safe Proximity Operation to Rotating Non-Cooperative Spacecraft with Complex Shape Using Gaussian Mixture Model-Based Fixed-Time Control

This paper studies the safety control problem for rotating spacecraft proximity maneuver in presence of complex shaped obstacles. First, considering the attitude change of the target spacecraft, a dynamic model of close-range relative motion in a body-fixed coordinate system is derived using a novel approach. Then, the Gaussian mixture model (GMM) is utilized to reconstruct the complex shape of the spacecraft, and a novel GMM-based artificial potential function (APF) is proposed to represent the collision avoidance requirement. By combining GMM-based APF with fixed-time stability methodology, a fixed-time control (FTC) is designed for close-range proximity operation to a rotating spacecraft having a complex shape. The presented GMM-FTC scheme can guarantee the convergence of relative state errors, and ensure that no collision occurs. Finally, simulation results are provided to illustrate the feasibility of the proposed control approach.

Aperiodic Sampled-Data-Based Control for Interval Type-2 Fuzzy Systems via Refined Adaptive Event-Triggered Communication Scheme

This article is devoted to event-triggered stabilization for a class of interval type-2 (IT2) fuzzy systems with aperiodic sampling. First, the IT2 Takagi-Sugeno fuzzy model and sampled-data controllers are established subject to mismatched membership functions. Second, considering a nonuniform sampling case, a refined adaptive event-triggered communication scheme is proposed in a hierarchy form to dynamically adjust the direction and rate of the event-triggered threshold parameter by state changing trend and relative state error, respectively. Thus, a complete dual-directional regulating mechanism with sensitivity to state variation is reasonably created to give extra flexibility, which is beneficial for a preferable tradeoff between control performance and network resource. Third, considering the practical behaviors on the sampling interval, a novel integral type of time-dependent Lyapunov function is constructed. Then, the stability criterion and the controller design approach are derived. Finally, the numerical examples are provided to demonstrate the effectiveness and advantages of the proposed methods.

A novel relative navigation algorithm for formation flight

For higher accuracy and better performance, a novel relative navigation framework named full parallel distributed architecture is presented, using inertial navigation system, global positioning system, and data link. Aiming at multiple aircraft, it is designed to enable each plane to serve as a fusion center. Also this structure enhances the collaboration between aircraft by sharing the relative navigation information. It breaks the limitation of the single fusion center method and can adapt to the reconfiguration of formation. A two-stage filtering estimation algorithm based on Kalman filter is developed to determine relative position, attitude, and velocity between the formation aircraft. Each vehicle contains not only a local filter but also a relative state filter, which helps to improve the accuracy of the relative state error model. The relative navigation system is designed as a closed loop system with parallel processing and real-time performance. Simulation results compared with the traditional centralized filtering method indicate that the approach provides better estimates and restrains the error divergency effectively.

Distributed finite‐time formation control for multiple quadrotors via local communications

SummaryThis paper investigates finite‐time formation tracking control problem for multiple quadrotors with external disturbance. The states of the virtual leader are not available to all the followers and the network topology is described by a directed graph. The model of each quadrotor is divided into position subsystem and attitude subsystem. Firstly, novel distributed finite‐time state observers are designed to estimate the relative state errors between followers and the virtual leader. Secondly, the values of these observers are used to design controllers that achieve finite‐time robust coordinated tracking in the position subsystem. Thirdly, the terminal sliding mode disturbance observers and finite‐time attitude tracking controllers are proposed, respectively, in the attitude subsystem to estimate the external disturbance and achieve attitude tracking control. The finite‐time stability analysis of the control algorithms is carried out using the Lyapunov theory and the homogeneous technique. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.

Event-Triggered Control for Consensus Problem in Multi-Agent Systems With Quantized Relative State Measurements and External Disturbance

For decreasing communication load and overcoming network constrains, such as the limited bandwidth and data loss in multi-agent networks, this paper integrates the two control strategies to investigate the bounded consensus problem of multi-agent systems (MASs) with external disturbance on the basis of an undirected graph, namely, the quantized control and the event-triggered control. In the existence of the external disturbance, two types of the high-gain control laws with the uniform quantized relative state measurements for the bounded consensus problem of MASs are first discussed, respectively. Then, in order to save the limited network resources in a multi-agent network, the event-triggered quantized communication protocols are designed based on the first case to obtain the bounded consensus in multi-agent systems. Moreover, it is shown that “Zeno behavior” phenomenon can be excluded under the two event-triggered quantized control mechanisms, and the boundness of the relative state error can be adjusted by selecting the different parameters. Finally, two examples are shown to validate the feasibility and efficiency of our theoretical analysis.

Initial Relative Orbit Determination Analytical Covariance and Performance Analysis for Proximity Operations

This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for close-in proximity operations when the camera offset from the vehicle center of mass allows for range observability. Emphasis is placed on developing closed-form error covariance equations for the initial relative orbit state solution and verification of the analytic covariance equations through systematic nonlinear Monte Carlo simulation of typical rendezvous missions. Closed-form analytic estimates of the relative state error covariance based on angle measurement errors, attitude knowledge errors, and camera center-of-mass offset uncertainties for three or more observations are obtained. A two-body Monte Carlo simulation system is used to evaluate the performance of the closed-form relative state estimation algorithms and associated closed-form covariance equations. The sensitivity of the solution accuracy to spacecraft trajectories, camera offset, camera accuracy, attitude knowledge, and the time interval between measurements is presented and discussed.

Application of a Differential Drag Controller to a Full System Simulation

Differential drag control presents an opportunity to control satellites without the use of a fuel-based propulsion system. The relative state of a pair or formation of satellites can be controlled via relative accelerations provided by a differential drag force. The drag acceleration of each vehicle can be altered by changing the area of the vehicle in the direction of motion. In research to date, differential drag controllers have been considered separately from state estimation systems that will be used for orbit determination. This paper examines an integrated system that combines a state estimator with a differential drag controller. A Kalman filter is used to estimate position and velocity elements with realistic levels of measurement noise, as well as measurement biases and atmospheric density. A differential drag controller based on the Hill-Clohessy-Wiltshire equations is presented that takes estimates from the Kalman filter and determines the appropriate control behavior. Modifications are made to the controller to reduce unnecessary actuations due to relative state error. The integrated system is tested with a nonlinear propagation model including the effects of J 2, dynamic modeling errors, and an altitude-varying atmosphere to determine the controller performance in a realistic mission environment.

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

SUMMARYThis paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication flow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.