Mitsubishi Heavy Industries Technical Review Vol. 61 No. 1 (March 2024)
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Development for Navigation and Formation Controlof Multiple Autonomous Vehicles
Based on Broadcast Control

DAIKI FUJIKURA*1

YASUO FUJISHIMA*1

A need to realize so-called "swarm control" - a technique to complete tasks with multiple
vehicles operated in a coordinated manner - has arisen for autonomous vehicle products that
Mitsubishi Heavy Industries, Ltd. (MHI) is developing. When taking the task of navigating multiple
vehicles as an example of swarm control, the operational efficiency can be improved if there's amethod that can navigate any number of vehicles since such method can handle many vehicles atonce. Therefore, MHI has developed a technology to navigate multiple autonomous vehicles basedon broadcast control, which is one of the swarm control methods that can control any number ofvehicles. We plan to conduct actual vehicles verification using this technology and to proceed withthe development, aiming at its application to products.

|1. Introduction
MHI has developed a number of autonomous vehicle products that operate either on land,
water surface, underwater, or in the air. For some of these products, a need has arisen to realize
swarm control, in which multiple vehicles are operated in a coordinated manner to complete a task
in order to satisfy customers' demand for improved operational efficiency. One of the main tasks
expected to be achieved by utilizing the swarm control technology is a navigation of a swarm system
consisting of multiple vehicles. For such task, it is desirable that the control technology can change
the formation of the vehicles according to the environmental conditions, in order to cope with theappearance of obstacles such as pedestrians and other vehicles or with changes in the width of theroad.
Among methods that achieves both formation control and group navigation, some requirevehicle-to-vehicle communication for mutual information sharing. However, as the number ofvehicles increases, the combination of vehicles that can communicate with each other becomeslarger, and the communication system for the entire group may become more complex since thecombination may need to be altered depending on changes in the positional relationship between thevehicles. If the complexity of the communication system needs to be reduced, the maximum numberof vehicles that can be navigated at once is limited, resulting in a limited improvement in task
execution efficiency through a swarm control.
As an approach different from the swarm control based on vehicle-to-vehicle mutualcommunication, "broadcast control"(1) has been proposed. The broadcast control is a method inwhich, a base station, which can observe the position and other conditions of the entire group and isstationary in the world coordinate system, simultaneously transmits (broadcasts) the same scalar
information to all vehicles to control the formation of the vehicles. Thanks to this feature, it ispossible to realize a communication system that is independent of the increase or decrease in thenumber of vehicles, and theoretically any number of vehicles can be controlled.
Given the aforementioned feature, in order to achieve efficient navigation of a vehicle group,
we have developed a swarm control system in which one vehicle (master) is assigned the role of thebase station in broadcast control and makes broadcast communication with the other vehicles*1

CIS Department, Digital Innovation Headquarters, Mitsubishi Heavy Industries, Ltd.

Mitsubishi Heavy Industries Technical Review Vol. 61 No. 1 (March 2024)
2(2)(slaves) . In this system, the base station moves with the slaves and is not stationary with respect tothe world coordinate system as in the conventional broadcast control system. Also, as explained later,
the state transition model of a slave defined in the developed system is different from that of theconventional method. Remainder of this report describes a method to solve the problems arising fromthese differences so as to apply broadcast control to the target system, with the results of a simulation
using a 10-slave vehicles model.

|2. Broadcast control(1)Broadcast control is a method of controlling an entire swarm consisting of multiple vehicles
by defining a base station that manages the entire swarm and then broadcasts the same control
commands to all vehicles therefrom. Figure 1 shows a block diagram of the broadcast control system.
In this chapter, a formation generation of 𝑀 vehicles with respect to the world coordinate system
will be discussed. 𝑃 𝑖 1,2, … , 𝑀 in the figure is the state transition model (vehicle kinematics)
of vehicle 𝑖, which assumes that the vehicles can move in any directions. This can be expressed as
the following formula.
𝑃:𝑥 𝑡 1𝑥 𝑡
𝑢 𝑡
Where, 𝑡 is time, 𝑥 𝑡 is the position of vehicle 𝑖, and 𝑢 𝑡 is the control input.

Figure 1

Block diagram of broadcast control system

𝐺 in Figure 1 is a base station called a global controller, which takes the position informationof all vehicles as input, calculates how close the vehicle group is to the achievement of the target
formation, in other words, the deviation between the target formation and the current formation, using
an evaluation function, and broadcasts the result to the entire group as a scalar evaluation value 𝜐.
𝐿 𝑖 1,2, … , 𝑀 is the controller of the vehicle 𝑖. The controller takes 𝜐 as input andoutputs 𝑢 𝑡 . 𝑢 𝑡 can be expressed as the following formula.
𝑐 𝑡 ∆ 𝑡
𝑢 𝑡

𝑐 𝑡

1 ∆ 𝑡

1

𝑎 𝑡

1

Δ𝜈 𝑡
∆
𝑐 𝑡 1𝑡1

𝑡0,2,4, … ,𝑡

1,3,5, …

In this equation, Δ𝜈 𝑡 is the difference between the evaluated value when 𝑡 is odd and thatsent in the previous time (time 𝑡 1), ∆ 𝑡 is a vector of random variables that output 1 or -1
with equal probability, ∆ 𝑡 is the per-element inverse of ∆ 𝑡 , and 𝑎 𝑡 and 𝑐 𝑡 areadjustment parameters. The input of the controller and the derivation equation of the control input
are the same for all slaves, and there is no information that increases or decreases with the numberof vehicles, so the scalability of the number of vehicles is maintained.

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Based on the above definitions, the broadcast control uses the formation evaluation value sentfrom the base station to converge slave vehicles to the specified formation by moving each vehicle
in such a way that the evaluation value decreases.

|3. Target swarm system
In this report, the employment of broadcast control for a swarm consisting of one master and𝑀 slave vehicles as shown in Figure 2 in which information is sent simultaneously and unilaterally
from the master to the group of slaves is considered. Figure 3 shows a block diagram of the masterand slave vehicles. The master can measure its own velocity, heading, and the slave positions withrespect to the master coordinate system whose origin exists at the master's position, and the axis ofwhich is in the direction the master is heading. Furthermore, the master can simultaneously send thesame scalar information to slaves. The master measures positions of slaves and sends information at
a fixed communication interval. With the above definitions, the role of a base station in conventional
broadcast control is assigned to the master. On the other hand, the slaves can measure their own
headings, but not their own positions with respect to the master coordinate system nor to the world
coordinate system. Both the master and slaves calculate control commands from the inputs given to
their respective controllers, and their positions are updated by their respective state transition models.

Figure 2

Swarm system discussed in this report

Figure 3

Block diagram of master and slaves

Finally, the following preconditions are defined for the swarm system considered in this report.
- The slaves have kinematics that do not allow them to move in lateral directions (i.e.,
nonholonomic constraint).
- The vehicles have restrictions on their velocity, acceleration, and angular velocity, andcannot operate beyond the upper and lower limits.

Mitsubishi Heavy Industries Technical Review Vol. 61 No. 1 (March 2024)
4- Collisions between the slaves are not considered.
- Errors in the measured information are not considered.
- There is no communication interruption between the master and the slaves.

|4. Employment of broadcast control to the swarm system
This chapter considers the employment of the broadcast control for the vehicle group systemdefined in Chapter 3. Since the system is different from that of the conventional method, thefollowing issues need to be solved.
- Issue (1): The conventional method assumes that the base station is stationary in the world
coordinate system, but in the case of the system assumed in this report, the master, whichserves as the base station, moves along with the slaves.
- Issue (2): The conventional method assumes that the vehicles can move in all directions, butthe vehicles assumed in this report have nonholonomic kinematics, which do not allow themto move in lateral directions.
To address these issues, the following measures are taken in this report.
- Measure (1): By concluding the broadcast control within the master coordinate system, thebase station (master) is made fictitiously stationary from the perspective of the slaves,enabling the employment of the conventional method. For this purpose, the movement
information of the master, such as its velocity and heading, is newly broadcast to the slaves.
- Measure (2): The path to the target position and the control commands based on it arederived considering the nonholonomic nature of the vehicles and the communicationinterval.
Based on these measures, a controller for the slave 𝑖 was devised as shown in Figure 4. Theslave 𝑖 executes this controller and calculates the control commands of its velocity and heading. In
the "Derivation of control input with conventional method" block in the controller, the derivation
formula for the control input 𝑢 𝑡 shown in Chapter 2 is applied without modification. The next
"Calculation of target position considering master movement" block corresponds to Measure (1). In
this block, 𝑢 𝑡 is regarded as the target position that the slave should reach before the nextcommunication. 𝑢 𝑡 is recalculated based on the received movement information of the master soas to realize following to the master. The last "Calculation of velocity and heading commands
considering nonholonomic nature" block corresponds to Measure (2). In this block, the route to thetarget position is obtained, the target values of velocity and heading of the slave at each time arecalculated from the generated path, and are output as command values. The path is calculated under
the constraint of using two identical radius arcs, as shown in Figure 5, to uniquely determine thesolution while considering the nonholonomic nature of the vehicle.

Figure 4 Flowchart of slave controllerMitsubishi Heavy Industries Technical Review Vol. 61 No. 1 (March 2024)
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Figure 5 Path generation method of slave totarget position|5. Simulation
To evaluate the feasibility of the developed method, the control performance of the vehicles'
formation was verified using models equivalent to actual equipment. Figure 6 illustrates theformation transition scenario in this simulation. First, a group of 10 slaves located on both sides ofthe master were asked to position on the same circumference around the master with equal spacing.
Next, they were asked to position on the same semicircle behind the master with equal spacing. For
the first target formation, the evaluation function was defined as the sum of (1) the term that requires
the slaves to stay on the same circumference and (2) the term that requires them to be as far awayfrom each other as possible. For the second target formation, the evaluation function was defined as
the sum of (1) the term that requires the group of slaves to stay on the same semicircle behind themaster, (2) the term that requires them to be as far away from each other as possible, and (3) the termthat requires them to keep the relative distance from the master below a certain value. During thesimulation, the master was kept moving straight at a constant velocity and in a constant heading.

Figure 6

Formation transition scenario in simulation

Figure 7 shows the transition of the formation of vehicles in the simulation. We confirmedthat the nonholonomic vehicles were able to change formations twice under conditions where themaster moved along with them.

Mitsubishi Heavy Industries Technical Review Vol. 61 No. 1 (March 2024)
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Figure 7

Result of formation transition|6. Conclusion
We have developed a swarm navigation technology that can control any number of vehicles
for autonomous vehicle products. This technology enables conventional broadcast control to be
employed for a vehicle system with a master and slaves in which the master moves together with theslaves. It was confirmed by the simulation result that this control technology can either maintain orchange the designated formation while allowing the slave vehicles to follow their master. As a future
work, we plan to verify the feasibility of the control using actual vehicles with the aim to apply thistechnology to products. At the same time, we will work to shorten the formation convergence timeand develop path generation that takes vehicle dynamics into account to further improve the level ofthe technology.

References(1)(2)

Azuma, S. et al., Broadcast control of multi-agent systems, Automatica Vol.49 No.8 (2013), 2307-2316.
Daiki Fujikura et al., Application of Broadcast Control Method to Nonholonomic Vehicles, The 42nd
Annual Conference of the RSJ (2023), The Robotics Society of Japan