Multirobot systems (MRSs) are capable of solving task complexity, increasing performance in terms of maximizing spatial/temporal/radio coverage or minimizing mission completion time. They are also more reliable than single-robot systems as robustness is increased through redundancy. Many applications such as rescue, reconnaissance, and surveillance and communication relaying require the MRS to be able to self-organize the team members in a decentralized way. Group formation is one of the benchmark problems in MRS to study self-organization in these systems. This paper presents a hybrid approach to group formation problem in multi-robot systems. This approach combines the efficiency of the cellular automata as finite state machine, the interconnectivity of the virtual grid and its bonding technique, and last but not least the decentralization of the adaptive dynamic leadership.
Any group of robots in a multirobot system (MRS) moving and coordinating together will always require the ability to quickly change group formation to adapt to the environment. All the robots within this system cooperate with each other to achieve the common goal of having the best group formation with decentralized communication between the robots in that system. This means that each robot has to consider the environmental changes, positions of other robots, and the global goal.
The multi-robot systems consist of either homogenous or heterogeneous robots. Homogenous robot system consists of a number of robots with the same properties, capabilities, configuration, and shape. On the other hand, heterogeneous robot system consists of robots that have different capabilities, properties, configuration, and shapes which makes task of implementing an algorithm to control their group formation without a centralized controller/coordinator difficult. Search and destroy, search and rescue, surround and conquer, and many military applications require multi-robot systems that are able to form a group and to adapt robustly.
In order to solve the group formation problem in MRS, it is required to model the relationship between robots in the same system, avoid clashes between robots, obstacles and goal, build all desired formations, coordinate the motion of each robot, maintain formation while in motion, develop an approach that ensures adaptability of the formation.
This paper presents a hybrid approach to group formation problem in multi-robot systems. This approach combines the efficiency of the cellular automata as finite state machine, the interconnectivity of the virtual grid and its bonding technique, and last but not least the decentralization of the adaptive dynamic leadership.
The remainder of this paper is organized as follows. Section
Section
Section
Section
MRS is a group of robots that operate in the same environment and are designed with an aim of performing collective behavior. However, robotic systems may range from simple sensors, acquiring and processing data, to complex human-like machines, able to interact with the environment in fairly complex ways. Some tasks may be quite complex for one robot to achieve or even impossible to be done, and when many robots try to achieve a goal it is high likely to be finished faster than if only one robot trying to accomplish that task and so the task completion time of a MRS would be minimal. Moreover, a MRS is more reliable than one robot, because, in a MRS, if one robot fails, there is always a substitute for that robot unlike the scenario for a single-robot system. The main advantage of a MRS is that it depends on “Power in numbers” which means that building several resource-bounded robots is easier and more economical than building a single powerful robot.
Group formation is observed in many animal species like flock of birds and school of fish, where members of a formation stay at a specific orientation and distance with respect to each other while moving, or fill a specific area as homogeneously as possible in an attempt to maintain a specific shape for their group. Group formation has permitted sophisticated behaviors that would have never been achievable by individual members. These behaviors include, but are not limited to, cooperative foraging, defense, search, or exploration. Most of the group formation techniques force the members of the group to move in a cohesive way as a whole.
Nearly all the work in cooperative mobile robotics began after the introduction of the new robotics paradigm of behavior-based control [ Communication. The issue of communication in MRS has been studied extensively since the inception of distributed robotics research and has been divided into two paradigms: explicit and implicit communications [ Localization, mapping, and exploration. An extensive amount of research has been carried out for single autonomous robots but only fairly recently has this been applied to MRS. Architectures, task planning, and control. The research area in this field addresses the issues of action selection, the delegation of authority and control, the communication structure, heterogeneity versus homogeneity in robots, achieving coherence in local actions, the resolution of conflicts, and other related issues. Object transport and manipulation. Enabling multiple robots to carry, push, or manipulate common objects cooperatively has been a longstanding, yet difficult, goal of any MRS. Many research projects have dealt with this topic area; few have been demonstrated on physical robot systems [ Motion Coordination. Research themes in this domain that have been particularly well studied include path planning, traffic control, formation generation, and formation keeping. Most of these issues are now fairly well understood, although demonstrations of these techniques in physical multi-robot teams (rather than in simulation) have been limited [
The domain of traffic and transportation is geographically and functionally distributed to have a high degree of autonomy. Due to these very characteristics, many applications in this domain can be adequately modeled as a MRS. As a result of this modeling, it could be also possible to meet the growing interest in making traffic and transportation more efficient, resource saving, and ecological [
Moreover, applications of search and rescue requires large number of agents to solve the problem of the coverage area and so increase the efficiency of the system. Also, MRS can also be used in health care and medical curing such as eliminating cancer cells [
Some effort has been put into the development of architectures that are optimized for space applications and include behavioral and cooperation patterns. The following is one of the space applications that involves MRS. Automatic Rendezvous and Docking, the automatic docking and rendezvous of spacecraft has been shown by a few space agencies. The first successful mission was by the Soviet Space Program in 1967. The satellite Kosmos-188 (SIZE-ALONE) achieved the world’s first automatic docking with the artificial Earth satellite Kosmos-186 [
There are many generic problems facing group formation in any MRS; the following is some of these problems. Modeling of the relationship between robots in the same system: a mathematical or physical connection that relate all the members with each other. Avoiding clashes between robots, obstacles, and goal: this problem depends not only on how agents are organized in a formation, but also it depends on the sensors (hardware) installed on the members. Coordination of the motion of each robot: it includes formation control and coordination between the members of a system in order to maintain the formation while in motion. Determining the reaction of other robots due to change in motion: ability to predict changes through learning. Finding the best path: determining the shortest and most efficient path regarding the consumption of energy.
There are many algorithms mimicking the group formations in nature such as birds flocking, fish schooling, and quadrupeds herding. These groups are considered effective if members attain performance goals regarding quality, quantity, and timeliness of work results. Generally, maintaining a formation is accomplished in two steps: a perceptual process, detect-formation-position, determines the robots proper position in formation based on current environmental data; the second step is the motor process maintain formation where commands are sent to motors to direct the robot toward the correct location.
Behavior-based approach desires to prescribe specific behavioral characteristics to each robot, but it is difficult to analyze the approach by theoretical formalization and so it is not easy to guarantee the convergence of the robots into the desired formation. Flocking is a coordinate and cooperative behavior easily conspicuous in a large number of beings, ranging from simple bacteria to mammals. This salient behavior is predominantly based on the principle that there are safety and strength in numbers [
The virtual structure approach which models each robot as a particle in a single structure and the control of robot formation is straight forward, but this approach requires huge communication bandwidth between members of the formation.
Virtual spring between agents.
Small virtual grid.
Large virtual grid.
Cai and Yang [
Introducing a new technique to effectively change the centralized approaches into decentralized ones, the dynamic leadership rules are to be embedded within each robot in a formation to ensure that all robots will abide by the same rules. Simply, these rules are just standards that identify the leader of the formation for an undefined time only bounded by the fitness of the current leader. A robot is considered fit to be a leader of a formation only if this robot is superior to all other robots in the formation regarding the leadership rules, for example, closeness to goal or better connection to large number of members within the formation. These rules force the change of the leader frequently according to the fittest robots position. As seen in Figure
Choosing a leader.
A hybrid approach mixing the well-established automata theory, virtual grid, and the newly proposed dynamic leadership algorithm to tackle the problem of the group formation is presented in this section.
Automata is the plural of automaton, and it means “something that works automatically.” An automaton is a pointed, observable representation of an algebraic structure [
As mentioned in the previous section, virtual grid can be used as an internal bonding structure that relates agents in a system to each other and so build a virtual connection between the agents. The new bounding relation that is created by the virtual grid acts as a cohesive force. The smaller the cells in the grid are, the stronger the cohesive force is. However, this strength comes with a cost of longer computational time and unstable control of the system due to the small allowed error tolerance. Therefore, it is required to assess the importance of having a stiffer bond over an unstable system, and this assessment could take into consideration the task that this formation will be executing.
This algorithm rules are to be embedded within each robot in a formation to ensure that all robots will abide by the same rules. Simply, these rules are just standards that identify the leader of the formation for an undefined time only bounded by the fitness of the current leader. A robot is considered fit to be a leader of a formation only if this robot is superior to all other robots in the formation regarding the leadership rules.
DAC is distance from agent to corner.
Other objective functions such as maximizing the battery life or minimizing the power consumed might be also developed by decreasing the time used for communication between robots in the MRS.
If the environment is unknown, therefore there is no target location known to the system and so the parameter responsible for the weight given to the closeness of the target (goal) would be 0; Algorithm
(1) Assign the Leadership to any random agent within the (2) (3)
(4)
(5)
(6)
The proposed approach to tackling the problem of the group formation is a hybrid approach mixing the well-established automata theory, virtual grid, and the newly proposed dynamic leadership. However, the automata theory has a disadvantage of having rigid states, that is, an agent is not considered in a state unless it has reached a specific position while not taking into consideration that there are always practical errors and divergence when it comes to agents’ motion. This rigidity is considered as disadvantages to the automata theory if used in this approach. Also, the virtual grid technique has a disadvantage of either it allows a tolerance in the displacement between agents that might cause large divergence from the desired positions or an unstable control system if the grid cells were too small and does not allow any tolerance.
On the other hand, the automata theory has an advantage of ensuring that the desired goal is achieved in form of milestones (checkpoints) and so provide the system with prompt feedback about the formation status, while the virtual grid provides the agents in the system with an interconnection technique that bonds the agents together and controls their behavioral activity. In this hybrid approach the rigidity of the automata theory is balanced by combining the allowance (tolerance) of the virtual grid technique with it, that is, allowing an agent to be considered in a state if its position is within the cell of the virtual grid. Therefore, this hybrid approach targets the efficiency and the mathematical model of the automata theory, the interconnectivity of the virtual grid and its bonding technique, and last but not least the decentralization of the adaptive dynamic leadership. Basically, this approach is a sum of the advantages and suppressant of the disadvantages of its ingredients. Figure
Hybrid approach.
Discretized states.
If
Figure
5 Agents rectangular formation.
(1) (2) End position (3) Assigned position (4) (5) (6) position + ( (7) Assigned position
(8) Get End position from
Figure
Seven agents rectangular formation.
Motion to goal scenario.
The automata theory provided the hybrid approach with a method to continuously have feedback whether the desired action was performed or not. This method is the states (checkpoints) at which the agent broadcasts its current reached state to the whole MRS and so it can be determined if the desired goal was reached; if the goal is not reached, then the agent that did not reach the checkpoint continues to alter its position. The following steps are executed to reach the final goal position.
Assign a leader using Algorithm
Assign a goal position to each agent, shown in Figure
Pathway.
Each agent discretizes its pathway into foreseen checkpoints (Figure
Broadcast.
Each agent moves towards its checkpoints as shown in Figures
Scene 1.
Scene 2.
Scene 3.
Repeat Step
Final goal.
(1) call Assigning leader as in Algorithm (2) call Position Assignment {Line Formation} as in
(3) (4) (5) call Position Assignment {Current Formation} as in
The testing was set up using a free software used for simulation called Virtual Robotics Experimental Platform (V-REP) [
Setting up an experiment requires understanding both the practical and the simulation models and identifying the communication method between agents in the MRS. In all the experiments conducted, it is assumed that the leader is the initiator of the formation, and these agents building a formation will be used to build all different formations to maintain consistency in the results. All formations will have an equal chance to perform well and achieve the goals of the collaborative activity, although this may conflict with the best interest of individual agents. Therefore, to form the groups, the leader has to evaluate the collaboration goal in a way that satisfies both the task of the collaboration that the agents have to achieve as a group and the individual needs of the agent. However, the interest in collaboration in the group formation will be only regarding the process of building up a formation and maintaining this formation throughout the motion of the whole group in the environment.
A simulation environment of four agents, Figure
Four agents experiment setup.
In these experiments, the point of interest is the evaluation of the group formation in terms of how well the formation was built rather than how well the formation will perform; therefore, the collaboration goals for the agents and the formation are modeled as a set of requirements (constraints) and so the success of group formation in this context is defined by the satisfaction of the constraints that define these goals. To achieve this, the following assumptions were set. All agents within the MRS have equal communication radius. Each agent in the environment should belong to the group (i.e., no agents are delinked). All agents in the MRS should be used in the building of any formation, and all built formations are stable. Each agent is able to identify all the members of the MRS. Each agent is able to distinguish between an agent and an obstacle. All agents have the same behavioral wonder action. The error tolerance accepted would be a maximum of 15% determined by the error in the proximity sensor [
The Evaluation Metrics are classified into two categories: Individual-based EM and Collective-based EM as illustrated in Figure
Evaluation metrics.
Constraints are defined as any parameter, variable, or condition that affects the process of the group formation, that is, environment structure and position of the goal. The following is a descriptive definition of the EM used.
(1) Individual satisfaction quality (ISQ) is used to determine how well the intermediate states were satisfied in the formation of the group (allocation of agents). ISQ is classified as one of the time-based EM and is quantitatively measured by the average time taken (ATT) by each agent to reach intermediate states and finally the goal position using the following:
(2) Individual perceived formation satisfaction (IPFS) is used to refer to how pleased is the individual with being allocated at the assigned position in the formation. This metric is based on the different environmental obstacles and power needed to reach the final position. Basically, IPFS is considered as a time-based evaluation metric and it is concerned with the energy exerted by the agent in the still state while trying to reach the goal position. IPFS is computed as the battery consumption duration during still states which is determined by the following:
(3) Optimal Agent Divergence (OAD) is a metric used to determine the divergence of the agent actual state from the desired one and it sets the acceptability of this reached state with respect to a predefined tolerance which is defined by the task that the whole MRS will perform. OAD is classified as a position based evaluation metric and is calculated using the following:
(1) Formation quality (FQ) identifies how well all the agents within the group collaborated together in order to build a formation and how long it took them all to reach the desired formation. FQ is a time-based evaluation metric that is calculated using (
(2) Goal satisfaction quality (GSQ) is used to identify how well the MRS reached the goal position; this includes the different formations that were applied on the system in order to reach this goal position. GSQ is a time-based evaluation metric that determines the time taken by the whole formation to pass an obstacle and return back to the initial formation using the following:
(3) Optimal formation divergence (OFD) is a metric used to determine the divergence of the built formation from the desired one and it sets the acceptability of this built formation with respect to a predefined tolerance which is defined by the task that this MRS will perform. OFD is a position-based evaluation metric that is calculated by the following:
Since there are two desired formations under investigation, it is required to have three evaluation scenarios for each formation. For each scenario, the evaluation metrics defined in the previous subsection will be used to evaluate the validity and efficiency of the approach used. The first evaluation scenario would be the ability of the approach under investigation to build up line formation (Figure
Line formation.
The second scenario would be placing the agents in a random formation and setting a goal position to the MRS and investigating the ability of the algorithm to build a rectangle formation (Figure
Rectangle formation.
The third scenario investigates the adaptability of the algorithm where the environment is altered to have obstacles that forces the MRS to shift formation in order to pass the obstacle ahead (Figure
Rectangle formation facing narrow passage.
Line formation scenario.
Initial position
Orienting
Motion in
State 1 achieved
Final position
Rectangle formation scenario.
Initial position
Orienting
Motion in
State 1 achieved
Final position
Switching formation scenario.
Initial position
Orienting
State 1 achieved
Line formation
Switching formation
Final position
Figure
Individual behavioral EM.
Figure
Collective behavioral EM.
This paper presented a hybrid approach to group formation problem in MRS. The proposed approach is based on dynamic leadership, cellular automata, and virtual grid. The cellular automata have an advantage of ensuring that the desired goal is achieved in form of milestones (checkpoints) and so provides the system with prompt feedback about the formation status, while the virtual grid provides the agents in the system with an interconnection technique that bonds the agents together and controls their behavioral activity. In this hybrid approach the rigidity of the automata theory is balanced by combining the allowance (tolerance) of the virtual grid technique with it.
The proposed approach has been proven by the experimental work that it can solve the problem of group formation in MRS. Also, the developed approach targeted the adaptability of the formation and how robust the agents in the MRS would react when the environment is changing. Results confirmed the hypothesis that claimed that the proposed hybrid approach is a sum of the advantages and suppressant of the disadvantages of its ingredients. Adaptability of the formation was tested using 4 agents switching from one formation to another due to the presence of obstacles in the environment. Moreover, the conducted experiments were set up using heterogeneous robots and results showed that the hybrid approach is fit for solving the group formation problem. However, more experiments are needed to verify the effect of communication failure on the stability of the proposed approach, also it is required to build more formations using this approach and qualitatively and quantitatively evaluate the performance. The proposed approach will be tested using Khepera III real robots in a newly built tested arena for MRS simulations and experiments in the robotics and autonomous systems (RAS) laboratory.