Robotics is a complex engineering field, dealing with design, modeling and
control of highly intelligent systems, where the fascination to enter the field
becoming increasingly popular. At the meantime their applications also increases
where they find major roles from toys, domestic and industrial robots to sophisticated
space application with the advancement in the complexity of the embedded systems.
Robotics being a multi domain problem, therefore, modeling and simulation of
such systems requires high artifacts in their conceptual design phase rather
than their physical implementation model (Morzek, 2003).
Overall such conceptual design is difficult to achieve since they tend to be
very complex in nature and most of the currently using modeling and simulation
tools operate on a traditional single domain approach (Goodman
et al., 2002; Hing and Musa, 2008), without
intensive interaction and integration between the different entities of the
robotic system. As a result it is necessary to have the conceptual design of
such systems where the solution concepts are selected and modeled and they are
interconnected to achieve their elaborated performance as a complete integrated
system. These solutions of concepts are designed or modeled based on the functional
and behavioral synergy and by formal representation during the conceptual design
stage rather than physical structuring. Morzek (2003)
and Erden (2011) proposed two different approaches
namely visual modeling with Unified Modeling Language (UML) and Petri Net based
Design Network, for modeling multi domain reactive systems respectively. However,
modeling and integration of energy, material and information flow has different
qualitative structures and lacks formal modeling in such systems. In addition,
manipulation of conceptual design solutions of a robotic system results in considerable
effort for modeling the behavior or motion states, which exhibit highly reactive
characteristics in nature (Erden, 2011). Moreover,
systems possessing with such reactive characteristics are also considered as
a hybrid systems, which can be modeled using state based techniques which have
higher formalism in design (Arkin, 1998).
State based modeling is such a technique, which is used to model complex systems
made up of reactive approaches. State based models is often used to represent
the entire behavior of such system, for instance either by a global state machine
or by a set of communicating state machines in which each state machine describes
the complete intra-object" behavior of a complex system. The functional
interactions between the state machines are investigated in terms of state transitions
in the system either with discrete behaviors modeled by Finite State Machines
or the continuous behaviors modeled algebraically by the use of differential
As a case study to prove the effectiveness of the state based modeling or conceptual
design approach, the main objective of the present study is to model a multi-robot
formation framework combined with navigation and obstacle avoidance. The task
achieving behaviors of such systems, as represented (Chetty
et al., 2011), is modeled using finite state machines augmented with
timers, in a predefined scenario which constitutes an action when certain environmental
factors occurs in the workspace of interest. These behaviors are modeled as
combination of discrete event systems using AFSM and continuous behavior as
differential equations based on their objectives and goals. In these modeling,
the actions are modeled as state transitions and the environmental effects as
events. In order to investigate the performance of these modeling methods, simulation
studies are carried out in stateflow simulation environment, which is used for
simulating event driven systems and the methods to implement these models are
addressed in detail.
STATE BASED MODELING
The detailed description of the state based conceptual modeling methods of
a Multi robot formation control system is presented here.
State based modeling is a modeling concept used to specify the complex hybrid
control systems where the entire objective of the system is divided into set
of functional task achieving behaviors/motion states working on individual goals
concurrently and asynchronously, which upon integration yields the global objective
of the system. Therefore, this kind of modeling method is used to model the
task achieving behaviors and layers of the complex robotic systems. For readers
understanding, this paper considers the formation control framework for multi
robot control addressed in kuppan (Chetty et al.,
2011) and mentioned in the previous section as a case study.
In state based modeling, when applied for multi robot control, the first step
is to properly express the task achieving behaviors/states and the behavioral
layers based on the overall functionality of the robots in the group. Several
methods such as Stimulus-Response (SR) diagrams, functional notation and Finite
State Machines (FSM) were available in the literature (Arkin,
1998) to model the individual task achieving behaviors/motion states of
the reactive control system. However, the task achieving behaviors of the entire
layered formation framework is represented as Finite State Machines augmented
with timers, called Augmented Finite State Machines (AFSM). The use of AFSMs
results in a tight coupling of perception and action, producing the highly reactive
response characteristic of the complex behavioral control systems where entire
sets of primitive (task achieving) behaviors are swapped in and out of execution
during the accomplishment of higher-level goal. Further, they are very useful
when describing sequence of behaviors and they make explicit the behaviors/motion
states active at any given time, the transitions between them and to hold internal
data structures of the system.
The next step is to realize the input-output relationship of the task achieving
behaviors and to functionally map the inputs from the stimulus plane to the
motor plane, to have the behavioral response. This is accomplished by incorporation
of suitable behavioral transformation function βi, for the individual
task achieving behaviors, where the behavioral response is activated when the
inputs from the sensors (λ) exceed the predetermined threshold level (τ).
By altering the value of (τ) in correspondence with the task achieving
behavior, one can alter the trigger of response of the task achieving behavior
over the stimuli. Hence, the method to create this kind of functional mapping
of the stimulus plane to motor plane is called as the behavioral encoding/mapping.
Associated with a particular behavior, the behavioral mapping function β
determines the robotic motor responses, which may fall into three major categories
such as Null, Discrete and Continuous. Among all the above mapping functions,
discrete behavioral mapping is used since the task achieving behaviors have
a finite set of stimulus and response pairs.
Further, the sequence of actions for responses generated by this mapping function
for a situation is very simple and reduces the complexity of the system model
as in the case of continuous encodings formed by a mathematical function, which
transforms the sensory input to behavioral activation function. Hence, an IF-
Then rule based technique is used for representing the behavior mapping function
(β) of the task achieving behaviors such as avoid obstacle, safe wander
and Pit sensing present in the navigational part of the formation framework.
The major advantage of this rule-based technique is that at any instant more
than one rule may be used for any given situation that corresponds to the set
of responses of the behaviors. However, the continuous encoding is used as the
behavioral mapping function (β) for the supervisor level formation, since
the objective of the tracking controller is to make the robots to be in the
desired formation with its teammates. Hence (β) is made up of mathematical
formulation of the kinematics of the robots employed, as addressed in kuppan
(Chetty et al., 2011).
Finally, it is important to apply a suitable coordination and communication
mechanism to coordinate the task achieving behaviors/motion states, to yield
the global objective of robot control. Having discussed methods to describe
individual behaviors, when multiple behaviors/AFSM is employed to construct
the system, it is necessary to coordinate the emergent behavior to have the
response signal for the robotic motor actuator. Here the coordination mechanism
plays a major role as the selector/arbiter which selects the particular active
behavior. There are two primary mechanisms for behavioral coordination, which
are competitive and cooperative. In this work the competitive methods especially
priority based arbitration mechanism is used as the arbiter to select the active
behavior. A strict behavioral dominance hierarchy exists, typically through
the use of suppression which is a hall mark of subsumption based architectural
methods developed by Brooks (1990). With the above
inputs in the state based modeling technique, the active behaviors or motion
states of the multi-robot system such as the proceed, Avoid
obstacle, Safe wander, Pit sensing classified
into lower level navigational part and formation as the supervisory
level, are modeled as given in Table 1. The details of the
emergence of these behaviors or motion states could be referred in the work
reported by kuppan (Chetty et al., 2011).
With these inputs, the behaviors or motion states of the robots are modeled
and expressed in state based model as triples as:
where, * is the vector encoding the global responses undertaken by the robot;
G= [g1, g2, g3
..]T is the vector encoding gain of each behavior
βi, ; B is the Vector of all active behavior βi
at timet, B= [β1, β2, β3
]T ; S=
[s1, s2, s3
]T is the vector of all stimuli si for
each behavior at time t; and C is the Coordination/arbitration function which
is competitive or cooperative.
IMPLEMENTATION IN SIMULINK/STATEFLOW ENVIRONMENT
State flow is an interactive graphical design and development tool that works
with Simulink to model and simulate complex systems modeled as finite state
machines, also called reactive event driven systems.
|| Methods of Modeling task achieving behaviors
Event-driven systems transit from one operating mode to another in response
to events and conditions. The corresponding systems are called discrete-event
dynamic systems and are often used to model logic for controlling a physical
device such as a robot. Advantage of the state flow over traditional Matlab-Simulink
and other simulation environment is the availability of graphical objects, where
the finite state machines are designed as state transition charts. The series
of state transitions directs a flow of logic from one state to another state.
Hence, Matlab-Simulink/Stateflow environment is used as the simulation environment
to measure the performance of the layered control approach (Brooks,
1990; Stormont and Chen, 2005).
In Stateflow simulation environment, several steps are to be followed to develop
the state chart model for the reactive control architecture as given in Fig.
First step is to create a simulink model, which defines the interface of the
state chart to the necessary inputs from and the outputs to the simulink environment.
The sensory information is created as discrete events and data, in the signal
builder of the simulink environment and provided as input to the behavioural
layers. The next step is to define the hierarchical states, which are the group
of task achieving reactive behaviors/finite sate machines of the control system.
Third step is to define the actions and a variable corresponding to the task
achieving states while entering and exiting the states or while in active. This
gives the response of the active state. Finally, the Interconnections between
the states are created/modelled as state transitions that are represented by
lines with arrowheads, where the transitions from one state to another state
occurs based on the sensory information.
In the Simulink-state flow environment, in general, the task achieving behaviours/AFSM
are modelled as temporal states. These states can be of parallel and states
with dotted rectangles or sequential OR states with solid rectangles, with round
corners as shown in Fig. 2.
||Different steps used for development of state chart model
|| State chart representation of robot system
The position state is the virtual state implemented in parallel with navigational
state, in order to update the posture information of the robot irrespective
of the behaviours/states that the robot executes while navigating the environment.
Hence, the temporal states of Navigation and Position are implemented as parallel
and states in the environment. The individual task achieving behaviours of the
navigational state such as obstacle avoidance, safe wander and pit sensing are
created as sequential OR states in the simulation environment. Interconnections
between the states are modelled as state transitions that are represented by
lines with arrowheads, where the transitions from one state to another state
occur based on the sensory information and the state transition conditions.
The arrow heads represents the flow transition from one state to another. The
arrowheads with the dotted end represent the default/initial behaviours/states
of the model. The sensory information is created as discrete events and data,
in the signal builder of the simulink environment and provided as input to the
behavioural layers through state flow chart.
Obstacles and pits in the environment are modelled such that the sensors provide
a logically high signal in the time frame whenever it perceives the obstacle
and pit information and present them as inputs to the robots. The avoid obstacle
behavioural response for the sensory events is modelled such that the robots
make a change in orientation by prescribed θ degrees. This
in turn changes its direction of motion towards left or right based on the position
of the obstacles with respect to the current posture of the robot. For the pit
sensing behaviour, the response of the behaviour is modelled such that initially
it backs up for a distance of d and starts to navigate the environment
by changing its direction towards left or right. Based on the sensory information
and the conditions, the control to the robot actuator takes place by switching
the task achieving behaviours/states in out of execution by means of suitable
Implementation of the multi-robot formation control model in the stateflow
simulation environment is shown in Fig. 3. Three robots R1,
R2 and R3 are employed in the formation framework and
they are modelled as parallel AND states to have identical control architecture
as mentioned in the previous section. These AND states consist of two temporal
states which are the representation of the individual lower level navigation
and supervisor level formation layers. As mentioned earlier, the sub states
of the navigation and formation are implemented as sequential OR states with
priority and interconnected with suitable state transition functions. State
transition between the navigational and formation behaviour is carried out based
on the obstacle information perceived by the follower robot and the communication
For example, w.r.t Fig. 2, the entry variable of the avoid
obstacle behaviours are the range and angular orientation of the obstacle perceived
by the robot sensor with respect to the current pose of the robot. The output
of the behaviour is the motor control data which is generated by the while execution
of the corresponding active obstacle avoidance state. Similarly, for the behaviour
of safe-wander, the entry variables are the sensor data, time and the previous
direction of turn and the exit variables are the motor control data which directs
the robot motion.
By default, in the simulation model represented by Fig. 3,
the Robot R1 has the highest priority over the other robots in the
group to gain the leadership and executes the navigational behavior. The other
robot such as R2 and R3, as shown in the formation framework
mentioned above takes the role as the follower and executes the formation state.
The formation state has the tracking controller developed in the present work,
as its behavioral transformation function. The entry variables of this formation
behaviour are the posture and velocity information of the leader robot R1
obtained by means of inter-robot communication mechanism. In addition, the desired
linear and angular separation between the robots, which depicts the topology
of formation, is also provided as the entry variables. The exit variables are
the current pose of the robot R2 designated as the follower. The
response output of the corresponding behaviour is the separation errors and
the motor control data, which are obtained as the result of execution of the
state by the conditions that are given (Chetty et al.
||State modeling and implementation of layered control architecture
in the simulation environment for three robots in closed defined formation
||State modeling and implementation of layered control architecture
in the simulation environment for three robotsoutputs, formation errors
and postures of both the robots are recorded and are interconnected with
the simulation environment for data logging
The control out puts, formation error and postures of both the robots are recorded
and are interconnected with the simulation environment for data logging.
One of the important aspects of the proposed formation control approach is
the active obstacle avoidance of the path of the follower robots, which is accomplished
by the incorporation of dynamic switching of roles by means of exchange of leadership
between the robots. The methodology adopted for such strategy is given (Chetty
et al., 2011).
|| Trajectory of robots in the workspace exhibiting dynamic
switching of roles
Figure 4 shows the execution of formation behaviors and how
the dynamic switching of roles between the robots is implemented in the state
flow environment in detail, when Robot R2 acts as follower and obstacle
is on R2 or R3 or on both R2 and R3. The follower state
has three sub states such as Robot R1 as leader, Robot R3 as leader and a temporary
state. These states are selected and implemented to avoid the confusion of the
robot R2, to gather the parameters of its corresponding leader at
that instant, which are to be given as the inputs to the tracking controller.
By default, robot R1 acts as leader and at any instant Robot R3
can become the temporary leader, if it perceives an obstacle in its path. Therefore,
at any instant, there can be only one leader either R1 or R3
to the robot R2 during the formation framework. The transitions between
the states are represented by guarded state transitions.
Initially during the formation framework and assuming Robot R1 acts
as the leader, the robot R2 executes the state Robot R1
as leader. This in turn executes the formation behavior and keeps the
robot R2 in closed defined formation with the leader. When the robot
R3 gains the leadership from the robot R1, robot R2
executes the formation behavior by switching the state from Robot R1
as leader to Robot R3 as leader by means of the
state transition function guarded by the discrete event Obstacle on R3.
Simulation results: Simulation studies have been carried out to test
the performance of the control architecture for the combined objective of guiding
the group of mobile robots in the closed defined formation as a whole, while
navigating the environment by avoiding obstacles on their paths. However, the
principles behind the control architecture are not simulated. In all the simulation
studies that are performed, the robot running environment is selected to measure
all possible reactive behaviors/motion states of the layered framework without
the boundary conditions imposed in the simulation environment. Sensory signals
are created such that they produce high signals whenever they perceive obstacle
or pits in the environment, using the signal builder block of the Simulink.
Wheel velocities, wheel direction of rotation and the position and orientation
information of the robots are taken as the behavioural outputs and are logged
into the data loggers. Simulation parameters and the threshold values for the
behavioural activation are provided in the simulation environment taking the
kinematics of the robots into account. The wheel velocities obtained as behavioural
outputs are constrained and bounded by the conditions v <vmax
<300 mm/s and ω < ωmax <50°/s.
Figure 5 to 7 show the results of the simulation
studies in state flow that are carried out to measure the performance of the
Multi robot systems modelled using state based technique. Figure
5 shows the trajectories of three robots in a closed defined formation having
the desired linear and angular separation between them during the fly while
navigating the environment. Further, it can also be observed form the encircled
portion of the figure, that the state transition in the model makes the robots
to switch their roles in order to avoid the obstacles in their path, without
disturbing the spatial pattern between the robots R1, R2 and R3.
The sensory information for robots R1, R2 and R3
representing the obstacle and pit in the environment are created as logical
high signal in the simulation environment as shown in Fig. 6.
Figure 7 shows the emergence of individual behaviours of
the robots R1, R2 and R3 as state outputs,
whenever the robots perceives the sensory information given by Fig.
6. The logical 1 represents the emergent states that are active
at that time instant to have control over the robot.
It could be observed from the above result that the state based modeling through
motion states of the robot provide efficient control in achieving the overall
task of the robot by switching the states based on the sensory perception.
|| Sensor signals of robots modeled as logic high in Signal
builder of Simulink
|| Sensor signals of robots modeled as logic High in Signal
builder of simulink
The switching of motion states in and out of execution through the state transition
routes the response of the emergence behavior to the robot actuator, which governs
the motion of the robots.
In this study, a state based modelling methodology is addressed to model the
complex reactive multi domain systems. The proposed state based model represents
the entire behavior of the complex system by a global state machine or Augmented
Finite state machines, describing the complete intra-object behavior of the
system. The multi robot formation approach is considered as a case study and
it is modeled using the state based method and the implementation of such model
as state charts in Simulink/Stateflow is also addressed in this paper. The efficiency
of the modeling method is also investigated through simulation studies and it
is found out that the Stateflow specifies the complete behavior of the system
using the state chart formalism without considering the physical nature of the
system. Therefore it is evident that any multi-domain system could be modeled
with visualization, performance and formalism.
First author would like to thank Robotics Automation and Manufacturing research
strength of Monash University Sunway Campus for providing the opportunity to
visit IIT Madras, India as visiting researcher to carry out this work. Author
would also like to thank Precision Engineering and Instrumentation laboratory
of IIT Madras, for offering visiting researcher position. Further, Authors would
also like to thank Ministry of Higher Education (MOHE), Malaysia to support
this work through the project Exploratory Research on the behavior based planning
and control of formations in WMR.