Multi-agent systems under temporal logic tasks have great potential due to their ability to deal with complex tasks. The control of these systems, however, poses many challenges and the majority of existing approaches result in large computational burdens. We instead propose computationally efficient and robust feedback control strategies for a class of systems that are, in a sense, feedback equivalent to single integrator systems, but where the dynamics are partially unknown for the control design. A bottom-up scenario is considered in which each agent is subject to a local task from a limited signal temporal logic fragment. Notably, the satisfaction of a local task may also depend on the behavior of other agents. We provide local continuous-time feedback control laws that, under some sufficient conditions, guarantee satisfaction of the local tasks. Otherwise, a local detection & repair scheme is proposed in combination with the previously derived feedback control laws to deal with infeasibilities, such as when local tasks are conflicting. The efficacy of the proposed method is demonstrated in simulations.