Motion Coordination of Mechanical Systems: Leader-Follower Synchronization of Euler-Lagrange Systems using Output Feedback Control

Abstract

his thesis proposes two motion synchronization approaches to coordinate the motion of a follower to a leader within the Euler-Lagrange system framework. The information requirements from the leader are that of position and orientation only, i.e. the mathematical model with its parameters and the velocity and acceleration of the leader are considered unknown and unmeasured.

The follower is responsible for the control action necessary to coordinate the systems, and the leader system is free to manoeuvre independently of the follower. There is no off-line synchronization of the systems through predefined paths or trajectories. %The parameters of the dynamic model of the leader are unknown, and its unmeasured system states (velocity and acceleration) must be estimated in order to be utilized in the coordination controller of the follower.

The concept of motion control of multiple objects is discussed in terms of the different forms of synchronization; cooperation (where all objects contribute equally) and coordination (where one object governs the motion of the others). Motivating examples and literature provide the motivation for the definition of two motion coordination problems. The output reference state feedback synchronization problem is defined by utilizing only output feedback from the desired motion reference, while assuming state feedback for the follower in the coordination control law. Furthermore, to increase the usefulness of the proposed control schemes and to provide robustness towards loss or poor quality of velocity measurements, the requirements of state information for the follower are alleviated in the definition of the output reference output feedback synchronization problem utilizing only output information of both the leader and the follower in the synchronization design. Furthermore, the necessary tools of stability are presented to prove that the proposed coordination schemes are uniformly ultimately bounded or practically asymptotically stable closed-loop systems.

In order to solve the output reference state feedback and the output reference output feedback synchronization problems, an observer-controller scheme is proposed that estimates the unknown states of the leader indirectly through a nonlinear model-based error observer. The observer-controller approach makes the follower system a physical observer of the leader system through the coupled observer and controller error-dynamics. A second nonlinear model-based observer is introduced for the follower to remove the state feedback assumption. The observer-controller scheme is proven to be uniformly globally ultimately bounded when utilizing state feedback of the follower in the coordination control law, and to be uniformly semiglobally ultimately bounded when utilizing only output feedback of the follower in the coordination control law. The observer-controller approach to motion coordination is studied through simulations and experiments, and a back-to-back comparison between ideal simulations and practical experiments is presented to allow for a discussion on the performance of the scheme under modelling errors, measurement noise and external disturbances. The observer-controller scheme is demonstrated to be suitable for practical applications.

Furthermore, a virtual vehicle scheme is proposed to solve the output reference state/ output feedback synchronization problems through a cascaded approach. The virtual vehicle approach is based on a two-level control structure to decouple the estimation and coordination error dynamics in the stability analysis and the tuning process. The virtual vehicle scheme estimates the unknown states of the leader through a virtual kinematic vehicle stabilized to the output of the leader system. A stable first-order velocity filter is introduced for the follower to remove the state feedback assumption. The virtual vehicle scheme is proven to be uniformly globally practically asymptotically stable when utilizing state feedback of the follower in the coordination control law, and to be uniformly semiglobally practically asymptotically stable when utilizing only output feedback of the follower in the coordination control law. Application of the virtual vehicle scheme to both vehicle coordination and robot manipulator coordination is presented, and the virtual vehicle approach to motion coordination is studied through simulations and experiments. The virtual vehicle scheme is demonstrated to be suitable for practical applications. In addition, an extension to a dynamic synchronization scheme is proposed to impose a smooth behaviour on the follower during a change of relative position.

The proposed coordination schemes are compared in terms of estimation principle, performance and robustness. Simulation studies compare the performance of the proposed schemes in terms of gain tuning and bounds on the closed-loop errors, and in terms of impact from external disturbances, modelling errors and measurement noise. The two coordination schemes are distinguished by concept rather than by performance, and both of the proposed schemes are believed to be suitable for practical implementation in coordination applications.