Localization Based Coordinated Control of Multi-Agent Systems Using Bearing Measurements


Student thesis: Doctoral Thesis

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Awarding Institution
  • Gang Gary FENG (Supervisor)
  • Lu LIU (Co-supervisor)
  • Xinping Guan (External person) (External Supervisor)
Award date3 Sep 2020


In recent years, coordinated control of multi-agent systems has attracted intensive attention because of its wide applications in environmental monitoring, resource exploration, military operations and other fields. In practice, multi-agent systems are often unable to observe much information under non-ideal circumstances, and their sensing abilities are often very limited. All of those factors would make coordinated control of multi-agent systems much more challenging.

This thesis mainly studies how to design distributed coordinated control strategies based on bearing measurements to achieve control tasks in the absence of global position information. Our key idea is to design the bearing-based localization algorithms to estimate the relative position information, and then to design distributed control laws based on the obtained estimate. Sufficient conditions are established to show when and how the localization algorithms are integrated with the coordinated control methods, such that the stability of the overall systems are guaranteed. The main results of this thesis are summarized as follows.

(1) The target entrapping problem of a single-integrator modeled agent using bearing-only measurements is studied. Existing works need to either estimate the position of the target with the knowledge of the agent, or maintain an exact circular motion around the target. An estimator-controller framework for the agent is proposed to entrap the static target, where the estimator is designed to estimate the relative position with bearing measurements by exploiting the orthogonality property, and the controller is then designed based on the obtained estimate to achieve the desired relative position. Within this framework, the agent entraps the target without any prior position information in an arbitrarily shaped orbit. Sufficient conditions on the desired orbiting shapes which support the agent for successful localization and entrapment simultaneously are characterized. It is proved that the estimation and tracking errors both converge to zero as time goes to infinity. Extensions to a moving target and multiple agents are also discussed and analyzed respectively.

(2) The shape-preserving formation control problem of single integrator multi-agent systems using bearing measurements is studied. The above estimator-controller framework is adopted for the concerned formation control problem. The relative position estimator is designed by exploiting orthogonality to cope with the high non-linearity of bearing measurements, and the controller is then designed with the estimated relative positions for the agents to achieve a time-varying formation with a preserved shape. With rigorous theoretical analysis, the asymptotic stability of the closed-loop system is guaranteed.

(3) The distributed entrapping control problem of double integrator multi-agent systems using bearing measurements is studied. A time-varying entrapping formation with a prescribed shape, which is elastic and rotational with respect to the target is adopted. Such a formation allows agents to move even in restricted areas while still entrapping the target as a whole. To achieve the entrapping formation based on bearing measurements, a leader-follower structure is adopted, and a design framework integrating formation shape observers, relative position estimators and distributed controllers is proposed. The rigorous stability analysis of the overall system is also given. It is shown that the convergence of the integrated system is guaranteed if its bearing observability is satisfied. Since the desired formation is determined by the trajectories of the leaders, the sufficient conditions on the trajectories of the leaders are characterized, such that the bearing observability of the integrated system is always satisfied. The estimation errors and the formation tracking errors converge to zero asymptotically.

(4)The leader-follower formation control problem of nonholonomic agents using local bearing measurements is studied. The above estimator-controller framework is extended for a pair of agents in local coordinate systems, where an estimator is first developed to estimate the relative position in its local coordinate system with bearing measurements, to avoid directly using positions or relative positions in the global reference frame. A control law is then designed for the follower to follow the leader based on the estimated relative position in its local coordinate system. It is shown that the estimation error converges to zero, if some conditions on the relative angular velocity between the leader and the follower are satisfied. It is also shown that the stability of the closed-loop system involving both the estimator and the controller is guaranteed if some mild conditions on the trajectory of the leader are satisfied. Extension to the case of multiple followers is also considered.

(5) The path optimization problem of mobile sensor networks for angle-of-arrival (AOA) target localization is studied. The localization scheme adopts the consensus-based extended information filter. A new idea of equipping sensors with information-driven mobility to improve the estimation accuracy with respect to a stationary target is proposed. A gradient descent method is used for mobile sensors, which are subject to geometric constraints, to choose the next optimal waypoints. The corresponding optimization problem is solved in a distributed manner, by selecting a proper cost function for each mobile sensor. Sufficient conditions are given to ensure the estimation error convergence. Moreover, it is shown that the mobility of sensors does decrease the estimation error bounds compared with static sensor networks, which is beneficial for the localization performance.

    Research areas

  • Bearing-based localization, Formation control, Distributed control, Stability analysis, Co-design of the estimator and the controller