Multi-robot systems (MRS) can accomplish more complex tasks with two or more robots and have produced a broad set of applications. The presence of a human operator in an MRS can guarantee the safety of the task performing, but the human operators can be subject to heavier stress and cognitive workload in collaboration with the MRS than the single robot. It is significant for the MRS to have the provable correct task and motion planning solution for a complex task. That can reduce the human workload during supervising the task and improve the reliability of human-MRS collaboration. This dissertation relies on formal verification to provide the provable-correct solution for the robotic system. One of the challenges in task and motion planning under temporal logic task specifications is developing computationally efficient MRS frameworks. The dissertation first presents an automaton-based task and motion planning framework for MRS to satisfy finite words of linear temporal logic (LTL) task specifications in parallel and concurrently. Furthermore, the dissertation develops a computational trust model to improve the human-MRS collaboration for a motion task. Notably, the current works commonly underemphasize the environmental attributes when investigating the impacting factors of human trust in robots. Our computational trust model builds a linear state-space (LSS) equation to capture the influence of environment attributes on human trust in an MRS. A Bayesian optimization based experimental design (BOED) is proposed to sequentially learn the human-MRS trust model parameters in a data-efficient way. Finally, the dissertation shapes a reward function for the human-MRS collaborated complex task by referring to the above LTL task specification and computational trust model. A Bayesian active reinforcement learning (RL) algorithm is used to concurrently learn the shaped reward function and explore the most trustworthy task and motion planning solution
