Time-Optimal solutions of Parallel Navigation and Finsler geodesics
M. Rafie-Rad
TL;DR
This paper presents a geometric framework for solving time-optimal control problems in parallel navigation, leveraging Finsler geometry and Pontryagin's maximum principle to characterize optimal trajectories with feedback advantages.
Contribution
It introduces a novel geometric approach using Finsler geodesics and control theory to determine time-optimal paths in parallel navigation systems.
Findings
Derived a non-linear control system for parallel navigation
Characterized time-optimal trajectories via geometric formulation
Highlighted feedback advantages of the approach
Abstract
A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The time-optimal trajectories of the Parallel navigation are characterized through a geometric formulation. It is notable that the approach has the advantages using feedback.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Control and Dynamics of Mobile Robots