Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems

Soon-Jo Chung, Jean-Jacques E. Slotine
2009 IEEE Transactions on robotics  
Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem.
more » ... Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling. I. INTRODUCTION Distributed and decentralized synchronization of large groups of dynamic systems is an area of intensive research. In this article, we study cooperative control and global exponential synchronization of groups of Lagrangian systems, such as mechanical robots. Our results apply both to exact matching of all individual state variables, or, through a translation of the state space, to convergence to specific (perhaps time-varying) formation patterns. Furthermore, we construct complex robot networks where multiple groups of fully synchronized elements coexist. Such concurrent synchronization seems pervasive in biology, and in particular in the brain where multiple rhythms coexist and neurons can exhibit many qualitatively different types of oscillations [34] . The objective of this paper is to establish a unified synchronization framework that can achieve both synchronization of the configuration variables of the robots and stable tracking of a common desired trajectory. Although an uncoupled trajectory tracking control law, in the absence of external disturbances, would achieve synchronization to a common desired trajectory, the presence of various disturbances motivates the mutual synchronization of the system variables. On the other hand, the synchronization to the average of initial conditions is not sufficient for multi-robot or multi-vehicle systems where a desired trajectory is explicitly given. For example, a large swarm of robots can first synchronize their attitudes and positions to form a certain formation pattern, then track the common desired trajectory to accomplish the given mission. In production processes, such as manufacturing and automotive applications, where high flexibility, manipulability, and maneuverability cannot be achieved by a single system [38], there has been widespread interest in cooperative schemes for multiple robot manipulators that track a predefined trajectory. A stellar formation flight interferometer [8], [9] is another example where precision control of relative spacecraft motions is indispensable. The proposed synchronization tracking control law can be implemented for such purposes, where a common desired trajectory can be explicitly given. The proposed strategy can achieve more efficient and robust performance through local interactions, especially in the presence of non-identical external disturbances. Further, we generalize the proposed control law such that multiple dynamic systems can synchronize themselves from arbitrary initial conditions without the need for a common reference trajectory. As a result, other potential applications include oscillation synchronization of robotic locomotion [15], [35], [39], and tele-manipulation of robots [3], [29] . The main contributions of this work can be stated as follows. • Concurrent synchronization that exploits the multiple time scale behaviors from two types of inputs (a reference trajectory and local couplings) permits construction of a complex time-varying network comprised of numerous heterogeneous systems. • In contrast with prior work on consensus and flocking problems using graphs, the proposed strategy primarily deals with dynamic networks consisting of nonlinear time-varying dynamics. • We use contraction analysis [26], [47] as our main nonlinear stability tool, thereby deriving exact and global results with exponential convergence, as opposed to asymptotic convergence of prior work. • The proposed control laws are of a decentralized form requiring only local velocity/position coupling feedback for global exponential convergence, thereby facilitating implementation in real systems. • The theory is generalized and extended to multi-robot systems with non-identical dynamics, linear coupling control, partial state coupling, uni-directional coupling, and adaptive control.
doi:10.1109/tro.2009.2014125 fatcat:ymtlheokgfeyrewcrf7rddjhty