GR(1)-Guided Deep Reinforcement Learning for Multi-Task Motion Planning under a Stochastic Environment

Motion planning has been used in robotics research to make movement decisions under certain movement constraints. Deep Reinforcement Learning (DRL) approaches have been applied to the cases of motion planning with continuous state representations. However, current DRL approaches suffer from reward sparsity and overestimation issues. It is also challenging to train the agents to deal with complex task specifications under deep neural network approximations. This paper considers one of the fragments of Linear Temporal Logic (LTL), Generalized Reactivity of rank 1 (GR(1)), as a high-level reactive temporal logic to guide robots in learning efficient movement strategies under a stochastic environment. We first use the synthesized strategy of GR(1) to construct a potential-based reward machine, to which we save the experiences per state. We integrate GR(1) with DQN, double DQN and dueling double DQN. We also observe that the synthesized strategies of GR(1) could be in the form of directed cyclic graphs. We develop a topological-sort-based reward-shaping approach to calculate the potential values of the reward machine, based on which we use the dueling architecture on the double deep Q-network with the experiences to train the agents. Experiments on multi-task learning show that the proposed approach outperforms the state-of-art algorithms in learning rate and optimal rewards. In addition, compared with the value-iteration-based reward-shaping approaches, our topological-sort-based reward-shaping approach has a higher accumulated reward compared with the cases where the synthesized strategies are in the form of directed cyclic graphs.