Research cracks time-optimal control for flexible structures
First closed-form solution for flexible system control reduces maneuver time calculations to a single scalar equation.
Manuel Keppler's new research presents the first closed-form solution for time-optimal control of flexible structures, solving a decades-old challenge in control theory. Published on arXiv, the paper derives an analytical solution for rest-to-rest maneuvers in systems coupling a double integrator to a harmonic oscillator. This model applies to two-mass-spring systems, single-bending-mode flexible structures, and linearized overhead cranes.
The solution introduces a Pythagorean identity T² = T_r² + 2T_s² that decomposes optimal maneuver time into rigid-body minimum time (T_r) and synchronization time (T_s ≤ π). The 'cost of flexibility' is scale-dependent: small maneuvers incur a penalty where one oscillator costs as much as two additional integrators, while large maneuvers see flexibility asymptotically free. The work proves that adding flexibility never shortens maneuvers, but softening an already flexible structure can—contradicting conventional wisdom that stiffer systems always perform better.
- First closed-form solution for time-optimal control of flexible structures using Pythagorean identity T² = T_r² + 2T_s²
- Flexibility cost scales as T ∝ L^(1/4) for small maneuvers, equivalent to adding two integrators per oscillator mode
- Proves stiffer systems don't always perform better; softening flexible structures can reduce maneuver time
Why It Matters
Enables precise control of flexible robotic arms, cranes, and aerospace systems with closed-form optimization instead of numerical methods.