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In this paper, we propose a model-free reinforcement learning method tosynthesize control policies for motion planning problems with continuous statesand actions. The robot is modelled as a labeled discrete-time Markov decisionprocess (MDP) with continuous state and action spaces. Linear temporal logics(LTL) are used to specify high-level tasks. We then train deep neural networksto approximate the value function and policy using an actor-criticreinforcement learning method. The LTL specification is converted into anannotated limit-deterministic B\"uchi automaton (LDBA) for continuously shapingthe reward so that dense rewards are available during training. A na\"ive wayof solving a motion planning problem with LTL specifications usingreinforcement learning is to sample a trajectory and then assign a high rewardfor training if the trajectory satisfies the entire LTL formula. However, thesampling complexity needed to find such a trajectory is too high when we have acomplex LTL formula for continuous state and action spaces. As a result, it isvery unlikely that we get enough reward for training if all sample trajectoriesstart from the initial state in the automata. In this paper, we propose amethod that samples not only an initial state from the state space, but also anarbitrary state in the automata at the beginning of each training episode. Wetest our algorithm in simulation using a car-like robot and find out that ourmethod can learn policies for different working configurations and LTLspecifications successfully.

Continuous Motion Planning with Temporal Logic Specifications using Deep Neural Networks