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Cooperative Salvo Guidance over Leader-Follower Network with Free-Will Arbitrary Time Convergence

Rajib Shekhar Pal, Shashi Ranjan Kumar, Dwaipayan Mukherjee

TL;DR

The paper tackles cooperative salvo guidance for multiple interceptors targeting a stationary target by enforcing consensus on time-to-go within a user-defined settling time using a leader-follower network. It develops two guidance laws addressing ideal and first-order autopilot dynamics, enabling the leader's time-to-go to reach a desired trajectory and the followers to converge to the leader's value in a finite, arbitrarily chosen time. Key contributions include a free-will arbitrary time convergence framework for time-to-go consensus, a two-stage leader-follower control design, and extensive simulations demonstrating robustness and scalability across varying initial conditions and interceptor speeds. The results show reliable, synchronized interception at a prescribed impact time $T_d$, with practical insights into actuator saturation and network considerations, offering a path toward more flexible and reliable salvo guidance in complex multi-agent settings.

Abstract

A cooperative salvo strategy is proposed in this paper which achieves consensus among the interceptors within a pre-defined arbitrary settling time. Considering non-linear engagement kinematics and a system lag to capture the effect of interceptor autopilot as present in realistic interception scenarios, the guidance schemes use the time-to-go estimates of the interceptors in order to achieve simultaneous interception of a stationary target at a pre-determined impact time. The guidance scheme ensures that consensus among the time-to-go estimates of the interceptors is achieved within a settling time whose upper bound can be pre-specified arbitrarily independent of the initial conditions or design parameters. The efficacy of the proposed guidance strategy is demonstrated using numerical simulations with varied conditions of initial position, velocities and heading angle errors of the interceptors as well as different desired impact times.

Cooperative Salvo Guidance over Leader-Follower Network with Free-Will Arbitrary Time Convergence

TL;DR

The paper tackles cooperative salvo guidance for multiple interceptors targeting a stationary target by enforcing consensus on time-to-go within a user-defined settling time using a leader-follower network. It develops two guidance laws addressing ideal and first-order autopilot dynamics, enabling the leader's time-to-go to reach a desired trajectory and the followers to converge to the leader's value in a finite, arbitrarily chosen time. Key contributions include a free-will arbitrary time convergence framework for time-to-go consensus, a two-stage leader-follower control design, and extensive simulations demonstrating robustness and scalability across varying initial conditions and interceptor speeds. The results show reliable, synchronized interception at a prescribed impact time , with practical insights into actuator saturation and network considerations, offering a path toward more flexible and reliable salvo guidance in complex multi-agent settings.

Abstract

A cooperative salvo strategy is proposed in this paper which achieves consensus among the interceptors within a pre-defined arbitrary settling time. Considering non-linear engagement kinematics and a system lag to capture the effect of interceptor autopilot as present in realistic interception scenarios, the guidance schemes use the time-to-go estimates of the interceptors in order to achieve simultaneous interception of a stationary target at a pre-determined impact time. The guidance scheme ensures that consensus among the time-to-go estimates of the interceptors is achieved within a settling time whose upper bound can be pre-specified arbitrarily independent of the initial conditions or design parameters. The efficacy of the proposed guidance strategy is demonstrated using numerical simulations with varied conditions of initial position, velocities and heading angle errors of the interceptors as well as different desired impact times.
Paper Structure (17 sections, 3 theorems, 41 equations, 11 figures, 1 table)

This paper contains 17 sections, 3 theorems, 41 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Main Results
  5. Salvo guidance with ideal autopilot
  6. Salvo guidance with first-order autopilot
  7. Simulation results and discussions
  8. Results for salvo guidance with ideal autopilot
  9. Effect of heading angle errors
  10. Effect of the choice of free-will arbitrary settling time $t_f$
  11. Effect of the choice of desired impact time $T_d$
  12. Effect of different initial positions
  13. Effect of different interceptor speeds
  14. Results for salvo guidance with first-order autopilot
  15. Simulations to demonstrate scalability of the algorithm
  16. ...and 2 more sections

Key Result

Lemma 1

Consider the nonlinear dynamical system $\dot{\mathbf{x}} = \mathbf{f}(t,\mathbf{x},\bm{\alpha}),~\mathbf{x}(t_0)=\mathbf{x}_0$ where $\mathbf{x} \in \mathbb{R}^n$ denotes the system states, and $f:\mathbb{R}_{\ge 0} \times \mathbb{R}^n \to \mathbb{R}^n$ and $\bm{\alpha} \in \mathbb{R}^l$ denote the $\forall \mathbf{x} \in \mathcal{D}, ~ \forall t \in [t_0,t_f)$ then $\mathbf{x}=\mathbf{0}$ is fre

Figures (11)

  • Figure 1: Planar engagement geometry.
  • Figure 2: Communication topology with 1 leader and 4 followers for simulations.
  • Figure 3: Simulation results of cooperative guidance strategy for interceptors with ideal interceptor autopilot.
  • Figure 4: Simulation results with reduced bound on settling time $t_f$.
  • Figure 5: Simulation results with reduced desired impact time $T_d$.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Lemma 1: Pal2020a Theorem 1
  • Lemma 2: Tran2022 Lemma 2
  • Lemma 3: Tran2022 Lemma 3
  • Remark 1