Learning to Execute Timed-Temporal-Logic Navigation Tasks under Input Constraints in Obstacle-Cluttered Environments

This study focuses on addressing the problem of motion planning within workspaces cluttered with obstacles while considering temporal and input constraints. These specifications can encapsulate intricate high-level objectives involving both temporal and spatial constraints. The existing literature lacks the ability to fulfill time specifications while simultaneously managing input-saturation constraints. The proposed approach introduces a hybrid three-component control algorithm designed to learn the safe execution of a high-level specification expressed as a timed temporal logic formula across predefined regions of interest in the workspace. The first component encompasses a motion controller enabling secure navigation within the minimum allowable time interval dictated by input constraints, facilitating the abstraction of the robot's motion as a timed transition system between regions of interest. The second component utilizes formal verification and convex optimization techniques to derive an optimal high-level timed plan over the mentioned transition system, ensuring adherence to the agent's specification. However, the necessary navigation times and associated costs among regions are initially unknown. Consequently, the algorithm's third component iteratively adjusts the transition system and computes new plans as the agent navigates, acquiring updated information about required time intervals and associated navigation costs. The effectiveness of the proposed scheme is demonstrated through both simulation and experimental studies.