Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the time-varying formation tracking for multiple manipulator systems (MMSs) under fixed and switching directed graphs with a dynamic leader, whose acceleration cannot change too fast. An explicit mathematical formulation of time-varying formation is developed based on the related practical applications. A class of extended inverse dynamics control algorithms combining with distributed sliding-mode estimators are developed to address the aforementioned problem. By invoking finite-time stability arguments, several novel criteria (including sufficient criteria, necessary and sufficient criteria) for global finite-time stability of MMSs are established. Finally, numerical experiments are presented to verify the effectiveness of the theoretical results. (Z.-H Guan).1 required without losing system stability, which products the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. However, to the authors' knowledge, the mathematical formulations of time-varying formation tracking are still not clear, which impedes the development and applications of the relative technologies.On the other hand, networked robotic systems have been broadly studied due to their various advantages, including flexibility, adaptivity, fault tolerance, redundancy, and the possibility to invoke distributed sensing and actuation [21]. Many control algorithms for global asymptotic tracking of networked robotic systems described by Euler-Lagrange systems can be found in the literature. Adaptive control approaches are proposed to address the leader-follower and leaderless coordination problems for multi-manipulator systems based on graph theory [22,23]. Distributed containment control had been developed for global asymptotic stability of Lagrangian networks under directed topologies containing a spanning tree [24]. Some distributed average tracking algorithms had been developed invoking extended PI control and applied to networked Euler-Lagrange systems [25]. The task-space tracking control problems of networked robotic systems under strongly connected graphs without task-space velocity measurements had been investigated [26]. In presence of kinematic and dynamic uncertainties, task-space synchronization had been addressed for multiple manipulators under strong connected graphs by invoking passivity control [27] and adaptive control [28]. All of the aforementioned control algorithms produce global asymptotic tracking of robotic manipulators, which implies that the system trajectories converge to the equilibrium as time goes to infinity. Finite-time stabilization of dynamical systems may give rise to fast transient and high-precision performances besides finite-time convergence to the equilibrium, and a lot of work has been done in the last several years [29]-[31].Motivated b...