  Motion planning of autonomous agents in partially known environments with
incomplete information is a challenging problem, particularly for complex
tasks. This paper proposes a model-free reinforcement learning approach to
address this problem. We formulate motion planning as a probabilistic-labeled
partially observable Markov decision process (PL-POMDP) problem and use linear
temporal logic (LTL) to express the complex task. The LTL formula is then
converted to a limit-deterministic generalized B\"uchi automaton (LDGBA). The
problem is redefined as finding an optimal policy on the product of PL-POMDP
with LDGBA based on model-checking techniques to satisfy the complex task. We
implement deep Q learning with long short-term memory (LSTM) to process the
observation history and task recognition. Our contributions include the
proposed method, the utilization of LTL and LDGBA, and the LSTM-enhanced deep Q
learning. We demonstrate the applicability of the proposed method by conducting
simulations in various environments, including grid worlds, a virtual office,
and a multi-agent warehouse. The simulation results demonstrate that our
proposed method effectively addresses environment, action, and observation
uncertainties. This indicates its potential for real-world applications,
including the control of unmanned aerial vehicles (UAVs).
