Distributed Control of Robotic Networks

Abstract

DCRN Chapter 4: Rendezvous {true, false} for S is the coordination task defined by T rndzvs (x [1] ,. .. , x [n]) = true, if x [i] = x [j] , for all (i, j) ∈ E cmm (x [1] ,. .. , x [n]), false, otherwise. Next, assume that, for the same network S = ({1,. .. , n}, R, E cmm), the robots' physical state space is X ⊂ R d. It is convenient to review some basic notation consistent with what we adopted in Chapter 2. We let P = {p [1] ,. .. , p [n] } denote the set of agents' location in X ⊂ R d and we let P be an array of n points in R d. Furthermore, we let avrg denote the average of a finite point set in R d , that is, avrg({q 1 ,. .. , q k }) = 1 k (q 1 + • • • + q k). For ε ∈ R >0 , the ε-rendezvous task T ε-rndzvs : (R d) n → {true, false} for S is defined as follows: T ε-rndzvs is true at P if and only if each robot position p [i] , for i ∈ {1,. .. , n}, is at distance less than ε from the average position of its E cmm-neighbors. Formally, T ε-rndzvs (P) = true ⇐⇒ p [i] − avrg {p [j] | (i, j) ∈ E cmm (P)} 2 < ε, i ∈ {1,. .. , n}. 4.1.3 The connectivity maintenance problem Assume that the communication graph, computed as a function of the robot positions, is connected: How should the robots move in such a way that their communication graph is again connected? Clearly, the problem depends upon: (1) how the robots move; and (2) what proximity graph describes the communication graph or, in the case of relative-sensing networks, what sensor model is available on each robot.

Distributed Online Patrolling with Multi-agent Teams of Sentinels and Searchers

“…Commonly used objectives in such patrol problem formulations include minimizing the average or worst case revisit rate to return to a given location, which has correspondence to measures of service rates and wait time in queuing theory models [7,12]. Other metrics, such as maximized area coverage for sensor deployments [13,2], enable decentralized control laws to govern persistent surveillance of areas. However, these previous models do not incorporate the possibility of imperfect detections of the events, for which Bayesian methods found in probabilistic search theory [6,5] provide key insights.…”

“…Different assumptions can be made on how sub-portions are defined and where sentinels are positioned. For example, if a Voronoi partition is used, the sentinel could occupy the generator points associated with each partition [2]. Consistent with our sensor model, we adopt a representation based on probabilistic quadtrees [4].…”

Unifying Geometric, Probabilistic, and Potential Field Approaches to Multi-robot Coverage Control

“…This property is often called supermodularity, and has been exploited in a rather different way in [16]. Surface plots of g α (f 1 , f 2 ) for α = −1, 1, and 2 are shown in Figures 2(a), 2(b), and 2(c), respectively, and the decrease in g α (·) as the number of arguments grows is shown in 4 We know lim β→∞ [ Including this mixing function in the cost function from (1) gives…”

“…This inherently geometric strategy has seen many recent extensions to robots with a limited sensing radius in [7], to heterogeneous groups of robots and nonconvex environments in [3,21], and to incorporate learning of unknown environments in [24]. A recent text that presents much of this work in a cohesive fashion is [4] and an excellent overview is given in [20]. Coverage controllers also have been successfully implemented on robotic systems in [22,23].…”

Decoupled Formal Synthesis for Almost Separable Systems with Temporal Logic Specifications

“…Thus a variety of robot architectures and control methods have been proposed that avoid this by various assumptions about communication among the agents, types of tasks, and allocation of responsibility [16], [15], [8], [5]. Relatively little prior work considers distributed robotics where tasks are formally specified using LTL.…”