Safe Circumnavigation of a Hostile Target Using Range-Based Measurements

TL;DR

The paper addresses safe circumnavigation of a hostile target by a nonholonomic robot using only range and range-rate measurements. It introduces an auxiliary circle and a barrier Lyapunov-function (BLF) based control law to enforce a safety constraint while driving the robot onto a prescribed orbit of radius $r_d$ around the target, with $r(t)\ge r_s$ at all times. A design parameter $\delta$ is derived from the radii of three circles ($r_d$, $r_a$, $r_s$) to guarantee stability; the control law $\Omega$ combines a heading-term, a geometric term, and a BLF term with gain $\kappa$, ensuring convergence to $(r_d,\pi/2)$ and avoidance of the safety circle. The method is validated through simulations and experiments on a Khepera IV in a MoCap environment, and the results show robust circumnavigation even with multiple auxiliary-circle entries when $\kappa$ is small. The work advances range-based, safety-critical circumnavigation in GPS-denied settings and highlights avenues for CBP-based extensions.

Abstract

Robotic systems are frequently deployed in missions that are dull, dirty, and dangerous, where ensuring their safety is of paramount importance when designing stabilizing controllers to achieve their desired goals. This paper addresses the problem of safe circumnavigation around a hostile target by a nonholonomic robot, with the objective of maintaining a desired safe distance from the target. Our solution approach involves incorporating an auxiliary circle into the problem formulation, which assists in navigating the robot around the target using available range-based measurements. By leveraging the concept of a barrier Lyapunov function, we propose a novel control law that ensures stable circumnavigation around the target while preventing the robot from entering the safety circle. This controller is designed based on a parameter that depends on the radii of three circles, namely the stabilizing circle, the auxiliary circle, and the safety circle. By identifying an appropriate range for this design parameter, we rigorously prove the stability of the desired equilibrium of the closed-loop system. Additionally, we provide an analysis of the robot's motion within the auxiliary circle, which is influenced by a gain parameter in the proposed controller. Simulation and experimental results are presented to illustrate the key theoretical developments.

Figures (6)

• Figure 1: Illustration of the problem and solution methodology.
• Figure 2: Geometry when robot's velocity vector is tangent to $\mathcal{C}_a$ at time instant $t_0$.
• Figure 3: Trajectory of the robot when it enters inside $\mathcal{C}_a$ (a) only one time with $\kappa = 0.05$ (b) multiple times with $\kappa = 0.015$.
• Figure 4: Evolution of range $r(t)$, bearing angle $\theta(t)$ and control law $\Omega$ with time for multiple entry case in Fig. \ref{['multi_entry']}.
• Figure 5: Trajectory of Khepera IV robot in multiple entry case.

Theorems & Definitions (22)

• Lemma 1: Convergence under BLF tee2009barrier
• Lemma 2
• proof
• Theorem 1
• proof
• Lemma 3
• proof
• Remark 1
• Theorem 2
• Lemma 4