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This paper explores continuous-time control synthesis for target-drivennavigation to satisfy complex high-level tasks expressed as linear temporallogic (LTL). We propose a model-free framework using deep reinforcementlearning (DRL) where the underlying dynamic system is unknown (an opaque box).Unlike prior work, this paper considers scenarios where the given LTLspecification might be infeasible and therefore cannot be accomplishedglobally. Instead of modifying the given LTL formula, we provide a generalDRL-based approach to satisfy it with minimal violation. To do this, wetransform a previously multi-objective DRL problem, which requires simultaneousautomata satisfaction and minimum violation cost, into a single objective. Byguiding the DRL agent with a sampling-based path planning algorithm for thepotentially infeasible LTL task, the proposed approach mitigates the myopictendencies of DRL, which are often an issue when learning general LTL tasksthat can have long or infinite horizons. This is achieved by decomposing aninfeasible LTL formula into several reach-avoid sub-tasks with shorterhorizons, which can be trained in a modular DRL architecture. Furthermore, weovercome the challenge of the exploration process for DRL in complex andcluttered environments by using path planners to design rewards that are densein the configuration space. The benefits of the presented approach aredemonstrated through testing on various complex nonlinear systems and comparedwith state-of-the-art baselines. The Video demonstration can be foundhere:https://youtu.be/jBhx6Nv224E.

Learning Minimally-Violating Continuous Control for Infeasible Linear Temporal Logic Specifications