Certified Zonotopic Reachability Analysis for Trajectory Tracking on Lie Groups
Certified Zonotopic Reachability Analysis for Trajectory Tracking on Lie Groups
This research paper introduces a certified zonotopic reachability analysis method for trajectory tracking on Lie groups, addressing safety certification under unknown disturbances. The authors propose propagating linear error dynamics with zonotopes while enclosing nonlinear effects in closed form, achieving tighter bounds than existing ellipsoid methods. Validated through simulations of planar aircraft and multirotors, as well as real flights of a quadrotor, the method ensures all reachable tracking errors are contained within the computed tubes, even under larger disturbances where traditional ellipsoid approaches fail.
The authors present a method for certifying safety in autonomous vehicle trajectory tracking by propagating error bounds using zonotopes on Lie groups, demonstrating tighter and valid bounds compared to ellipsoid methods in both simulation and real-world quadrotor flights.
Source: arXiv Robotics — research abstracts · Read original article ↗
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Hybrid coordinates make these terms matched, so that our controller cancels every nonlinear term that does not contain the disturbance. Our tubes give tighter bounds than the ellipsoid method in simulations of a planar aircraft and a fully actuated multirotor and in real flights of a quadrotor, where the tube contains every measured attitude error. Under larger disturbances and the same feedback gain, the ellipsoid
Open source S5
arXiv:2611.12767v1 Announce Type: cross Abstract: Autonomous vehicles track planned trajectories close to obstacles. Unknown disturbances make them deviate from these trajectories. With a bound on the tracking error that disturbances can cause, a planned trajectory can be certified as safe before execution. Existing set-based methods bound the tracking error by one invariant ellipsoid for the whole trajectory or by i
Open source S2
Source：arXiv Robotics — research abstracts · arxiv.org