English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This article presents a method to automatically generate energy-optimaltrajectories for systems with linear dynamics, linear constraints, and aquadratic cost functional (LQ systems). First, using recent advancements inoptimal control, we derive the optimal motion primitive generator for LQsystems--this yields linear differential equations that describe all dynamicalmotion primitives that the optimal system follows. We also derive theoptimality conditions where the system switches between motion primitives--asystem of equations that are bilinear in the unknown junction time. Finally, wedemonstrate the performance of our approach on an energy-minimizing submersiblerobot with state and control constraints. We compare our approach to anenergy-optimizing Linear Quadratic Regulator (LQR), where we learn the optimalweights of the LQR cost function to minimize energy consumption while ensuringconvergence and constraint satisfaction. Our approach converges to the optimalsolution 6,400% faster than the LQR weight optimization, and that our solutionis 350% more energy efficient. Finally, we disturb the initial state of thesubmersible to show that our approach still finds energy-efficient solutionsfaster than LQR when the unconstrained solution is infeasible.

LQ-OCP: Energy-Optimal Control for LQ Problems