Linear Quadratic Guidance Law for Joint Motion Planning of a Pursuer-Turret Assembly

TL;DR

This work addresses joint motion planning for a pursuer with an attached rotating turret, aiming to capture a maneuvering target by ensuring the target lies within the turret's field of view and sensing range at final time. It develops a linear-quadratic guidance law obtained by linearizing the engagement about the collision triangle, reducing the problem to a two-dimensional transformed state with an analytic closed-form control law that jointly optimizes pursuer acceleration and turret slew. The key contributions include a terminal-projection-based reduction, a convex quadratic formulation with bound constraints, and a receding-horizon implementation that leverages real-time estimates from measurable quantities. The results demonstrate that turret-pursuer cooperation can significantly reduce pursuer effort and still guarantee terminal constraints, with practical applicability demonstrated through numerical simulations; limitations include time-to-go approximations and potential extensions to hard-constraint handling.

Abstract

This paper presents joint motion planning of a vehicle with an attached rotating turret. The turret has a limited range as well as the field of view. The objective is capture a maneuvering target such that at the terminal time it is withing the field-of-view and range limits. Catering to it, we present a minimum effort guidance law that commensurate for the turn rate abilities of the vehicle and the turret. The guidance law is obtained using linearization about the collision triangle and admits an analytical solution. Simulation results are presented to exemplify the cooperation between the turret and the vehicle.

Figures (3)

• Figure 1: Engagement Geometry
• Figure 2: Variation of Trajectories with $\alpha$
• Figure 3: Variation of Trajectories with Target's Speed, Acceleration, and Launch Angles