  Real-world scenarios are characterized by timing uncertainties, e.g., delays,
and disturbances. Algorithms with temporal robustness are crucial in
guaranteeing the successful execution of tasks and missions in such scenarios.
We study time-robust path planning for synthesizing robots' trajectories that
adhere to spatial-temporal specifications expressed in Signal Temporal Logic
(STL). In contrast to prior approaches that rely on {discretize}d trajectories
with fixed time steps, we leverage Piece-Wise Linear (PWL) signals for the
synthesis. PWL signals represent a trajectory through a sequence of
time-stamped waypoints. This allows us to encode the STL formula into a
Mixed-Integer Linear Program (MILP) with fewer variables. This reduction is
more pronounced for specifications with a long planning horizon. To that end,
we define time-robustness for PWL signals. Subsequently, we propose
quantitative semantics for PWL signals according to the recursive syntax of STL
and prove their soundness. We then propose an encoding strategy to transform
our semantics into a MILP. Our simulations showcase the soundness and the
performance of our algorithm.
