Fault Tolerant Control of Nonholonomic Mobile Robot Formations

Author(s):  
T. Dierks ◽  
B. T. Thumati ◽  
S. Jagannathan

In this chapter, a fault tolerant kinematic/torque control law is developed using backstepping for leader-follower based formation control in order to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. First, nominal control laws are derived for the leader and follower robots under the assumption of normal operation (no faults), and the stability of the individual robots and the formation is verified using Lyapunov methods. Subsequently, in the presence of state faults such as actuator fault, flat-tire etc., which could be incipient or abrupt in nature, an online fault detection and accommodation (FDA) scheme is derived to mitigate the effects of a fault by modifying the nominal controller. In other words, an additional term is introduced to the existing control law to minimize the effects of the fault, and this additional term is a function of the unknown fault dynamics which are recovered using the online learning capabilities of a neural network. Further, mathematical stability results are derived using Lyapunov theory, and both the FDA scheme and the formation errors are guaranteed to render asymptotic stability in the presence of faults. Numerical results are provided to verify the theoretical conjectures.

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lina Jin ◽  
Shuanghe Yu ◽  
Dongxu Ren

This paper deals with the circular formation control problem of multiagent systems for achieving any preset phase distribution. The control problem is decomposed into two parts: the first is to drive all the agents to a circle which either needs a target or not and the other is to arrange them in positions distributed on the circle according to the preset relative phases. The first part is solved by designing a circular motion control law to push the agents to approach a rotating transformed trajectory, and the other is settled using a phase-distributed protocol to decide the agents’ positioning on the circle, where the ring topology is adopted such that each agent can only sense the relative positions of its neighboring two agents that are immediately in front of or behind it. The stability of the closed-loop system is analyzed, and the performance of the proposed controller is verified through simulations.


2014 ◽  
Vol 635-637 ◽  
pp. 1199-1202 ◽  
Author(s):  
Zheng Gao Hu ◽  
Guo Rong Zhao ◽  
Da Wang Zhou

For the chattering problem in the traditional sliding mode observer-based fault estimation, a second order sliding mode observer based on the Super-twisting algorithm was proposed. In order to avoid the cumbersome process of proving the stability of the Super-twisting algorithm, a Lyapunov function was adopted. An active fault tolerant control law was designed based on the fault estimation. Finally, simulation show the effectiveness of the proposed approach.


2021 ◽  
Vol 54 (4) ◽  
pp. 641-647
Author(s):  
Mukul Kumar Gupta ◽  
Roushan Kumar ◽  
Varnita Verma ◽  
Abhinav Sharma

In this paper the stability and tracking control for robot manipulator subjected to known parameters is proposed using robust control technique. The modelling of robot manipulator is obtained using Euler- Lagrange technique. Three link manipulators have been taken for the study of robust control techniques. Lyapunov based approach is used for stability analysis of triple link robot manipulator. The Ultimate upper bound parameter (UUBP) is estimated by the worst-case uncertainties subject to bounded conditions. The proposed robust control is also compared with computer torque control to show the superiority of the proposed control law.


Author(s):  
Xiao Lin Ai ◽  
Jian Qiao Yu ◽  
Yong Bo Chen ◽  
Fang Zheng Chen ◽  
Yuan Chuan Shen

This paper investigates the formation control problem of multiple unmanned aerial vehicles (UAVs) with limited communication in a known and realistic obstacle-laden environment. In order to deal with the limited communication constraints, the leader–follower strategy and the virtual leader strategy are integrated into an optimal control framework to formulate this formation control problem. This combination formation framework can be achieved by integrating a redefined directed graph and a proposed information vector. In more practical applications, an obstacle/collision avoidance strategy is achieved by constructing a non-quadratic cost function innovatively using a virtual flow field approach. The proposed optimal control laws, which derive from the local information rather than the global information, are proved to guarantee the stability of the close-loop system by an inverse optimal control approach. The simulation results demonstrate the effectiveness of the formation flight of multiple UAVs with limited communication in an obstacle-laden environment.


2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaowu Yang ◽  
Xiaoping Fan

This study considers the problem of formation control for second-order multiagent systems. We propose a distributed nonlinear formation controller where the control input of each follower can be expressed as a product of a nonlinear term that relies on the distance errors under the leader–follower structure. In the leader–follower structure, a small number of agents are assumed to be the leaders, and they are responsible for steering a group of agents to the specific destination, while the rest of the agents are called followers. The stability of the proposed control laws is demonstrated by utilizing the Lyapunov function candidate. To solve the obstacle avoidance problem, the artificial potential approach is employed, and the agents can avoid each possible obstacle successfully without getting stuck in any local minimum point. The control problem of multiagent systems in the presence of unknown constant disturbances is also considered. To attenuate such disturbances, the integral term is introduced, and the static error is eliminated through the proposed PI controller, which makes the system stable; the adaptive controller is designed to reduce the effect of time-varying disturbances. Finally, numerical simulation results are presented to support the obtained theoretical results.


Author(s):  
Bing Han ◽  
Ju Jiang ◽  
Chaojun Yu

This article develops a distributed adaptive fault-tolerant formation control scheme for the multiple unmanned aerial vehicles to counteract actuator faults and intermittent communication interrupt, where the issues on control input saturation and mismatched uncertainties are also addressed. The discontinuous communication protocol technique is exploited to achieve the stability of the formation system, if the conditions of dwell time and the rate of communication are satisfied. On the basis of the local information of neighboring unmanned aerial vehicles, a novel distributed adaptive mechanism is designed to estimate the bounds of actuator faults and uncertainties, where the input saturation is explicitly taken into consideration. The stability of the whole formation system under the designed fault-tolerant formation control strategy is analyzed using the Lyapunov approach. Finally, simulation results are presented to illustrate the effectiveness of the proposed scheme.


Author(s):  
Emmanuel Sin ◽  
He Yin ◽  
Murat Arcak

Abstract We present a distributed control law to assemble a cluster of satellites into an equally-spaced, planar constellation in a desired circular orbit about a planet. We assume each satellite only uses local information, transmitted through communication links with neighboring satellites. The same control law is used to maintain relative angular positions in the presence of disturbance forces. The stability of the constellation in the desired orbit is proved using a compositional approach. We first show the existence and uniqueness of an equilibrium of the interconnected system. We then certify each satellite and communication link is equilibrium-independent passive with respective storage functions. By leveraging the skew symmetric coupling structure of the constellation and the equilibrium-independent passivity property of each subsystem, we show that the equilibrium of the interconnected system is stable with a Lyapunov function composed of the individual subsystem storage functions. We further prove that the angular velocity of each satellite converges to the desired value necessary to maintain circular, areostationary orbit. Finally, we present simulation results to demonstrate the efficacy of the proposed control law in acquisition and station-keeping of an equally-spaced satellite constellation in areostationary orbit despite the presence of unmodeled disturbance forces.


2008 ◽  
Vol 130 (5) ◽  
Author(s):  
S. M. Shahruz

In this note, a robustness issue of control laws designed by the input-shaping methodology is brought to the fore. A control law designed by this methodology consists of a sequence of step inputs that are applied at designated time instants by a switching mechanism. It is shown that the stability of systems controlled by such control laws may not be robust in the presence of errors in the switching time instants.


2019 ◽  
Vol 07 (01) ◽  
pp. 47-54 ◽  
Author(s):  
Jianan Wang ◽  
Zhengyang Zhou ◽  
Chunyan Wang ◽  
Jiayuan Shan

The formation control problem in multi-quadrotor systems is studied in this paper. Each quadrotor has limited access to its neighbors’ information due to communication constraint. First, the dynamics model of the quadrotor is linearized using Newton–Euler method. The distributed formation control law is then designed and the stability analysis is provided. An experimental platform is built with three Parrot Bebop drones and an indoor motion capture system. Numerical and experimental results are provided to show the effectiveness of the proposed algorithms.


2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zool H. Ismail ◽  
Ahmad ’A. Faudzi ◽  
Matthew W. Dunnigan

This paper presents a new control approach for an underwater vehicle with a kinematically redundant thruster system. This control scheme is derived based on a fault-tolerant decomposition for thruster force allocation and a region control scheme for the tracking objective. Given a redundant thruster system, that is, six or more pairs of thrusters are used, the proposed redundancy resolution and region control scheme determine the number of thruster faults, as well as providing the reference thruster forces in order to keep the underwater vehicle within the desired region. The stability of the presented control law is proven in the sense of a Lyapunov function. Numerical simulations are performed with an omnidirectional underwater vehicle and the results of the proposed scheme illustrate the effectiveness in terms of optimizing the thruster forces.


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