In order to let multiple robot manipulators cooperatively complete a sequence of tasks in a shared workspace under task execution uncertainty, this letter proposes a multi-robot task allocation framework for constantly assigning tasks to robots, while the interference among concurrent robot motions is account for. An online sequential task assignment method is presented, which decouples the time-extended problem into a sequence of synchronous and asynchronous instantaneous assignment sub-problems. This renders the approach capable of reacting to task execution uncertainties in real-time. A one-step-ahead simulation method is employed to reduce the idle time of robots and improve task completion efficiency. Each instantaneous assignment sub-problem is modeled as an optimal assignment problem with variable utility and solved by a branch-and-bound algorithm, with which multi-robot motion coordination is integrated. Experimental results conducted with three Franka-Emika Panda arms show that these can cooperatively complete all tasks without collision and little waiting time. Simulations with larger multi-robot systems show that the approach scales linearly with the number of robots.