IEEE Robotics & Automation Magazine - September 2021 - 97

CNH Controller
Initial
Configuration
Target Assigner
Target
Configuration
-
φ:= φattr + φcoop + φrepl
s0
CAPF
FSM
α
β
Position
Measurement System
(a)
u := -k∇φ
s1
Achieved
Coordination
Astrobots
(b)
(c)
(d)
(e)
Figure 5. Seeking completeness using the CNH control strategy. (a) The control architecture. (b)-(e) A typical coordination process
governed by CNH control, starting from a random initial configuration and progressing to a synchronized one.
temporarily leave its final spot to provide free space for the
others. This strategy successfully yields a completeness condition
that can be locally evaluated based on the specifications
of astrobots in various states, e.g., their initial and target spots.
In particular, it is formally shown that, if all the neighborhoods
are completely coordinated, the coordination of the
whole swarm is globally complete [17], [18]. Thus, the nonlinear
hybrid control discussed in the previous section is
replaced with the paradigm of cooperative nonlinear hybrid
(CNH) control, as depicted in Figure 5(a). Figure 5(b)-(e)
illustrates the steps of a coordination process governed by the
CNH scheme, in which an initial amorph configuration is
coordinated to a synchronized one.
The CNH control scheme efficiently realizes complete
coordination. However, it is computationally impossible to
formally verify the safety and correctness of the solutions it
obtains. Thus, one has to employ a set of simulations to
check whether the generated signals fulfill the requirements
of their coordination process. Such numerical verification
procedures are time consuming and need excessive computational
resources. Alternatively, supervisory control theory
[19] and discrete-event systems are legitimate options to
yield verifiability. In this regard, a new derivation of the
attraction field idea [20], i.e., backtracking forcibility, can
be effectively used to coordinate astrobot swarms, as well.
In particular, the authors of [21] established a verifiable
supervisory coordination solution that determines whether
a particular observation setup of astrobots can be completely
coordinated.
Supervisory coordination pursues completeness feasibility
checking, as demonstrated in Figure 6. First, astrobots' continuous
working space is discretized to be embedded into discrete-event
models. Then, each astrobot is encoded by a
Astrobots Targets
Motion Discretization
Plant
Specification
Supervisor Synthesis
Coordination Supervisor
Complete Coordination Checking
Input/Output
Operation
Figure 6. Seeking completeness via supervisory coordination.
SEPTEMBER 2021 * IEEE ROBOTICS & AUTOMATION MAGAZINE *
97
Targets

IEEE Robotics & Automation Magazine - September 2021

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2021

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