Coordination of nonholonomic mobile robots for diffusive threat defense

Abstract

This paper studies coordination of a team of nonholonomic mobile robots with smart actuators for defending against invasive threat to a planar convex area. The threat refers to a kind of harmful substance such as chemical pollutant appearing outside and moving towards the area. The invasion of threat can be modeled by a 2D unsteady reaction-diffusion process. To reflect the adverse effect of threat on the area, a so-called risk intensity field is introduced. The value of risk intensity is equal to the concentration of threat measured by a static mesh sensor network. Based on this risk intensity field, a coordination control scenario using Voronoi tessellation is formulated. In order to minimize the actuator performance loss and reduce the total average risk intensity simultaneously, a generalized centroidal Voronoi tessellation (CVT) algorithm including optimal motion control and risk mitigation control is designed. The proposed algorithm is gradient-based and guides mobile robots to track their optimal trajectories asymptotically. Meanwhile, two conditions of choosing control gains are derived to keep the total average risk intensity below a safety level. Several simulation examples with different cases of threat invasion are provided and the advantage of proposed algorithm over traditional control method is presented.

Introduction

Learning from universal collective behavior in nature and society [1], distributed coordination control of multi-agent systems is currently receiving great attention from both academic communities and engineering field [2], [3], [4], [5]. Recently, the use of networked mobile sensors and/or actuators for environmental monitoring and protection has been an area of intensive research [6], [7], [8]. In this paper, a team of nonholonomic mobile robots with communication capability forms a mobile actuator network which is driven to defend against invasive threat to a bounded convex area. The threat here refers to a kind of harmful substance such as chemical pollutant which leaks outside and moves towards the area. Thus the invasion of threat can be simulated as a 2D unsteady reaction-diffusion process. The adverse effect of threat on the area is modeled by a spatial-temporal scalar field, named risk intensity field. The value of risk intensity is equal to the concentration of threat measured by a fixed mesh sensor network. Under the assumption that smart actuator embedded on each mobile robot can spray neutralizers at a steady rate, the risk intensity of diffusive threat can reduce continually. In order to minimize actuator performance loss of mobile robots, an optimal deployment strategy combined with risk mitigation control is designed. The study of this problem can help us to efficiently complete many practical tasks such as area coverage, intruders detection, containment and defense in environmental or military applications. One of these applications is the coordination of marine vehicles for harbor protection [9], where a group of mobile agents is spread out over the harbor to detect and accordingly react to various potential threats. In present work we focus on monitoring the area of interest while simultaneously reducing the adverse effects of invasive threat.

The above objective is related to multi-agent coverage of an area governed by a spatially distributed process, where agents with collocated or non-collocated sensors and actuators are deployed to monitor the area and control the process. Often, the process is modeled by partial differential equations (PDEs) with different types. See for example the representative literature [10], [11], [12], [13], and the references therein. In [10], a Lyapunov-based guidance control scheme of mobile sensor and actuator networks is introduced, and a spatial gradient following law is used to control a 2D diffusion PDE system. Using adaptive control method, this work is extended in [11] by considering terrain vehicle dynamics. In a similar stability analysis fashion, a sampled-data controller implemented by stationary sensors/actuators is designed in [12] for a class of uncertain semilinear parabolic systems on a finite sampling period. Another distributed event-triggered control scenario is developed for the same kind PDE in [13]. However, the process control scenarios above mainly consider how to stabilize a distributed parameter system with measurable process state. As a result, deployment strategy of stationary or mobile sensors/actuators is non-optimal when coverage-type performance measure is taken into consideration. Adapting notions from locational optimization, distributed coverage control of mobile sensors for minimizing the sensing cost is first adopted in [14] by using Voronoi tessellations and Lloyd descent algorithm. This Voronoi-based optimal deployment strategy is then utilized in [15], [16] to address a diffusion process control problem by mobile actuators. Using a new CVT algorithm based on fractional-order PI controllers, similar control problem is further investigated in [17].

For multi-agent coverage control problem, the important feature of environment is often modeled by a spatial density field [18], [19], [20], [21]. In contrast to most existing problem formulations in the literature [22], [23], [24], [25], where the density distribution of the environment is not affected or controlled by mobile agents, in our work the density is not only determined by its intrinsic dynamics, but also by feedback control of agents, i.e., the scalar density field is a closed-loop feedback system. For this case, we can no longer just use a non-autonomous time-varying density distribution, as mentioned in area coverage problems [22], [23], to reflect the measure of relative importance of points in the environment. In this paper, we focus on coordination problem of invasive threat defense by mobile robots with smart actuators. The external threat invades mission area across its boundary, which can be modeled by a diffusion process. A static mesh sensor network is mounted to monitor the whole mission area gathering threat concentration information while mobile robots equipped with limited range actuators spray neutralizers to reduce the concentration of threat. Motivated by the diffusion control scenario proposed in [17], we use a risk intensity field to evaluate the adverse effect of diffusive threat to mission area. The risk intensity value is equal to the measured concentration of threat. Using generalized Voronoi Tessellations, a more general objective function considering actuator performance loss is provided. In order to optimize the objective function and reduce the average risk intensity as well, an optimal motion control law plus risk mitigation control law is designed to generate trajectories of mobile robots for minimizing the actuator performance loss and reducing the total average risk intensity.

The major contributions of this paper are threefold. First, a coverage control method of multi-agent system is applied in a static sensor-plus-mobile actuator network to monitor the environment as well as to influence it. The interest of environment is monitored and changed simultaneously by mobile robots. It is shown that encoding density feedback control into the coverage related problems facilitates mobile agents to handle complex tasks in hazardous environment. Second, subject to the nonlinear dynamics of mobile robots with nonholonomic constraints, a modified optimal deployment strategy considering the time-varying effect of environment is proposed. Different from previous works [15], [16], [17], which use traditional Lloyd’s CVT method to solve area coverage problem governed by a spatially distributed process, our modified generalized CVT algorithm is more suitable for the environment with time-dependent objective function. Finally, a modified correction controller for reducing the total average risk intensity is designed. It is guaranteed that mobile robots converge to generalized Voronoi centroids even if risk mitigation control is adopted.

This paper is organized as follows. In Section 2, mathematical modelling and problem formulation are given. Based on the risk intensity field, a coordination control scenario using Voronoi tessellation for diffusive threat defense is proposed in Section 3. In Section 4, numerical simulations with two cases are presented to verify the effectiveness of proposed algorithm. Some future research directions are discussed in Section 5. Main results of this research is concluded in Section 6.