Hard-constraint trajectory planners often rely on commercial solvers and demand substantial computational resources. Existing soft-constraint methods achieve faster computation, but either (1) decouple spatial and temporal optimization or (2) restrict the search space. To overcome these limitations, we introduce MIGHTY, a Hermite spline-based planner that performs spatiotemporal optimization while fully leveraging the continuous search space of a spline. In simulation, MIGHTY achieves a 9.3% reduction in computation time and a 13.1% reduction in travel time over state-of-the-art baselines, with a 100% success rate. In hardware, MIGHTY completes multiple high-speed flights up to 6.7 m/s in a cluttered static environment and long-duration flights with dynamically added obstacles.
