MIGHTY: Hermite Spline-based Efficient Trajectory Planning

TL;DR

MIGHTY introduces a Hermite-spline trajectory planner that jointly optimizes spatial waypoints, endpoint derivatives, and segment durations to exploit a continuous search space while preserving local control. The framework provides closed-form gradients for both control-point based and sampled-state costs, with reparameterizations that improve numerical stability. Through extensive simulations and real-world hardware tests, MIGHTY consistently reduces computation time and travel time relative to state-of-the-art baselines while maintaining safety in static and dynamic environments. The results demonstrate that joint spatiotemporal optimization on Hermite splines yields faster, more agile, and robust onboard trajectory planning for high-speed autonomous flight in cluttered spaces.

Abstract

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.

Figures (10)

• Figure 1: Benchmarking environment for a simple corner avoidance scenario. The blue-shaded polygons show the safe flight corridor. MIGHTY's trajectory is colored by speed (warmer colors indicate faster speeds).
• Figure 2: Benchmarking results for MIGHTY and GCOPTER for simple corner avoidance scenario in Fig \ref{['fig:simple_benchmarking_rviz']}. MIGHTY achieves lower computation time, travel time, and path length, while GCOPTER yields lower jerk.
• Figure 3: Complex-scene benchmarking setup. MIGHTY's trajectory is color-mapped by speed (warm=fast), and GCOPTER's trajectory is blue. The blue-shaded polygons show the safe flight corridor. The start is at $(0,0,0.5)\,m$, and 24 goals lie on a grid with $x,y\in[-15,15]\,m$ and $z=2.5m$. Blue-shaded polygons show the safe flight corridor sequence from one run.
• Figure 4: Ablation study comparing MIGHTY with scaled and unscaled variables in the complex benchmarking scenario. The scaled version shows $\approx 2\times$ faster computation time, with lower jerk and slightly shorter path length, while travel time is nearly identical.
• Figure 5: (Top) Static obstacle environment used for benchmarking. (Bottom) Top view of the point cloud and path generated by MIGHTY in the static environment. The warmer colors indicate faster speeds.