Nature-inspired dynamic control for pursuit-evasion of robots

TL;DR

This paper addresses pursuit-evasion for robots modeled as unicycles, proposing a nature-inspired dynamic framework that captures the speed-versus-m maneuverability trade-offs observed in predators and prey. It introduces the Alert-Turn algorithm, a hybrid control with long-distance and short-distance phases that governs both pursuers and evaders under velocity and turning constraints, and proves a sufficient-capture condition for single-pursuer scenarios. The framework is extended to multi-agent settings using aggregation and a target-changing mechanism, with a selfish parameter $\alpha$ that modulates cooperative versus selfish escape patterns and a statistical analysis of how the number of pursuers and target-change policies affect capture outcomes. Numerical simulations and replication studies show that the approach reproduces natural chasing behaviors and provides actionable design insights for multi-robot pursuit-evasion, including optimal detection frequencies and dispersion strategies. The work lays groundwork for obstacle-aware pursuit-evasion and invites exploration of inverse optimal control to learn biologically plausible objectives.

Abstract

The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of years of evolution, animals have developed effective and efficient strategies for both pursuit and evasion. In this paper, we provide a dynamic framework for the pursuit-evasion problem of unicycle systems, drawing inspiration from nature. First, we address the scenario involving one pursuer and one evader by proposing an Alert-Turn control strategy, which consists of two efficient ingredients: a sudden turning maneuver and an alert condition for starting and maintaining the maneuver. We present and analyze the escape and capture results at two levels: a lower level of a single run and a higher level with respect to parameters' changes. In addition, we provide a theorem with sufficient conditions for capture. The Alert-Turn strategy is then extended to more complex scenarios involving multiple pursuers and evaders by integrating aggregation control laws and a target-changing mechanism. By adjusting a 'selfish parameter', the aggregation control commands produce various escape patterns of evaders: cooperative mode, selfish mode, as well as their combinations. The influence of the selfish parameter is quantified, and the effects of the number of pursuers and the target-changing mechanism are explored from a statistical perspective. Our findings align closely with observations in nature. Finally, the proposed control strategies are validated through numerical simulations that replicate some chasing behaviors of animals in nature.

Figures (13)

• Figure 1: Illustration of the Alert-Turn Algorithm. $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $V_e^{\max}=0.6$, $V_p^{\max}=1.2$, $W_e^{\max}=2$, $W_p^{\max}=1$, $a_e=0.25$, $a_p=0.6$, $r_e=0.2$, $r_p=0.1$, $t_f=5.8$.
• Figure 2: Illustration of escape patterns. The first column figures show the trajectories of agents. The second column shows the moment the evader escapes at its first turning maneuver. The third column figures present how the velocities evolve with time. (a) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.16$, $r_p=0.2$, $c_e=0.1$, $c_p=0.3$, $a_e=0.3$, $a_p=0.6$, $t_f=80$. (b) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.3$, $a_e=0.15$, $a_p=0.2$, $t_f=100$. (c) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.3$, $a_e=0.6$, $a_p=0.6$, $t_f=150$. (d) $\varepsilon_1=2$, $\varepsilon_2=0.05$, $r_e=0.25$, $r_p=0.1$, $c_e=0.05$, $c_p=0.3$, $a_e=0.3$, $a_p=0.6$, $t_f=100$.
• Figure 3: Illustration of capture patterns. The first column figures show the trajectories of agents. The second column presents how the velocities evolve with time. (a) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.23$, $r_p=0.1$, $c_e=0.1$, $c_p=0.05$, $a_e=0.3$, $a_p=0.2$, $t_f=30$. (b) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.3$, $a_e=0.35$, $a_p=0.6$, $t_f=20$. (c) $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.3$, $a_e=0.1$, $a_p=0.5$, $t_f=20$. (d) $\varepsilon_1=1.4$, $\varepsilon_2=0.1$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.43$, $a_e=0.2$, $a_p=0.6$, $t_f=40$.
• Figure 4: Simulation results with respect to the parameters' ranges. The common parameter values are $V_e^{\max}=0.6$, $V_p^{\max}=1.2$, $W_e^{\max}=2$, $W_p^{\max}=1$, $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $a_e=0.3$, $a_p=0.6$, $t_f=120$. Left: The minimum distance during the pursuit-evasion process with respect to different parameters. Right: The corresponding escape and capture results. (a) Results with respect to the ranges of $r_e$ and $r_p$ given $c_e=0.1$, $c_p=0.3$. (b) Results with respect to the ranges of $r_e$ and $c_p$, given $r_p=0.1$, $c_e=0.1$. (c) Results with respect to the ranges of initial conditions $\Delta \theta_0$ and $\Delta d_0$, given $c_e=0.1$, $c_p=0.3$, $r_e=0.2$, $r_p=0.1$.
• Figure 5: Simulation results with respect to the parameters' ranges. The common parameter values are $V_e^{\max}=0.6$, $V_p^{\max}=1.2$, $W_e^{\max}=2$, $W_p^{\max}=1$, $\varepsilon_1=1.4$, $\varepsilon_2=0.04$, $r_e=0.2$, $r_p=0.1$, $c_e=0.1$, $c_p=0.3$, $t_f=120$. Left: The minimum distance during the pursuit-evasion process with respect to different parameters. Right: The corresponding escape and capture results. (a) Results with respect to the ranges of $a_e$ and $\Delta d_0$, given $a_p=0.6$. (b) Results with respect to the ranges of $a_e$ and $\Delta \theta_0$, given $a_p=0.6$. (c) Results with respect to the ranges of initial conditions $a_e$ and $a_p$.

Theorems & Definitions (4)

• Theorem 1
• Remark 1
• Theorem 2
• Remark 2