Dependent Reachable Sets for the Constant Bearing Pursuit Strategy

TL;DR

This paper characterizes the geometry of reachable sets for agents using the constant bearing pursuit strategy, providing theoretical bounds and empirical validation through simulations.

Contribution

It introduces the concept of dependent reachable sets and derives geometric bounds for them in the context of constant bearing pursuit.

Findings

Derived geometric bounds for dependent reachable sets.

Formulated and analyzed an original optimization problem.

Validated the shape of the reachable set through simulations.

Abstract

This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable set}, is characterized using the constant bearing pursuit strategy as a case study. Key theoretical results are presented that provide geometric bounds for the associated dependent reachable set. Simulation results are presented to empirically establish the shape of the dependent reachable set. In the process, an original optimization problem is formulated and analyzed for the constant bearing pursuit strategy.