Trajectory planning method optimizes drone flight paths without needing models
Trajectory Bundle Method in SE(3) for Black-Box Fixed-Wing Aircraft Trajectory Optimization
Robotics
Summary
Planning safe and doable flight paths for flying robots is hard when you don't know exactly how they move. The authors created a way to plan paths that respect 3D rotations and positions, using special math tools that don't need detailed models or derivatives. They tested this method on a drone flying through a tricky space and found it could plan smooth, collision-free maneuvers. This approach helps plan complex moves even when the robot’s dynamics are unknown or hard to model.
What this means in practice
- •For drone navigation engineers: Plan acrobatic flight paths for drones without needing exact aerodynamic models or derivatives.
- •For robotics software developers: Develop motion planning tools that handle complex robot rotations and translations using black-box models.
Authors
Matthew D. Osburn, Cameron K. Peterson, John L. Salmon
Abstract
Dynamically feasible trajectory optimization for rigid-body systems is naturally formulated on the special Euclidean group SE(3) but is challenging when dynamics are available only as black-box computations without derivatives. This paper formulates the Trajectory Bundle Method (TBM) for motion planning implicitly on SE(3). Bundles are constructed in the Lie algebra and propagated through nonlinear rigid-body dynamics using exponential and logarithmic maps, enabling derivative-free planning of non-Euclidean trajectories. We show that Euclidean TBM interpolation error is bounded quadratically by bundle diameter and extend this result to SE(3), where the bound additionally depends on a local Lipschitz constant of the Log map. Numerical experiments corroborate these bounds. Finally, we demonstrate SE(3) TBM by optimizing an acrobatic, collision-free fixed-wing maneuver through a rotated aperture without explicit models or derivatives of the vehicle dynamics, aerodynamics, or collision model.