View source for Projects:2019s2-23301 Robust Formation Control for Multi-Vehicle Systems

[[Category:Projects]]
[[Category:Final Year Projects]]
[[Category:2019s2|23301]]
Formation control has been widely used in the control of robots, sicne it can improve the overall efficency of the system. In this project, we aim to design a robust formation control for multi-vehicle system, in which the system can deal  with  at  least  one  network  problem  or physical  failure. 
== Introduction ==

Formation control of multi-agent systems (MASs) has been widely used for cooperative tasks in such applications as terrain exploration, mobile networks and traffic control. However, the communication-induced problems and the high failure risk of increasing equipments has created a number of challenges for the security of MASs. The objective of this project is to design a robust formation  control  strategy  for  a  multi-vehicle  system  against communication and physical failures (e.g., network attacks, link failures, packet dropouts, sensor/actuator faults).  

The vehicles are designed to detect the local environments by visual navigation and achieve a self-organisation formation. The robust fault-tolerant control  strategy is investigated to deal with at leas one network problem or physical failure. The effectiveness of the formation control strategy and its robustness  should be verified by both simulations and experiments. Potential applications are in large flexibility MASs and high-security Cyber-Physical Systems. Currently, our lab is equipped with a multi-vehicle platform, consisting of quadrotors, ground robots and camera location systems. Algorithms are developed by either Matlab Code or C language. MATLAB, Simulink, OpenGL, Motive and Visual Studio are possible softwares to be chosen for this project.

=== Project team ===
==== Student members ====
* Abdul Rahim Mohammad
* Jie Yang
* Kamalpreet Singh
* Zirui Xie

==== Supervisors ====
*Prof. Peng Shi
*Prof. Cheng-Chew Lim

==== Advisors ====
*Xin Yuan
*Yuan Sun
*Yang Fei
*Zhi Lian

=== Objectives ===
Design a robust formation control approach for multi-vehicle system to achieve:

*Self-decision making
*Environment detection
*Communication
*Obstacle avoidance
*Tolerance to physical or network problem

== Background ==
=== Autonomous Control System ===
Autonomous control system has the power and ability for self-governance in the performance of control functions. They’re composed of a collection of hardware and software, which can perform the necessary control functions without intervention, or over extended time periods. There’re several degrees of autonomy. Conventional fixed controllers can be considered to have a restricted class of plant parameter variations and disturbances, while in a high degree of autonomy, controller must be able to perform a number of functions beyond conventional functions, such as regulation or tracking.

=== Agent ===
For the most part, we are happy to accept computers as obedient, literal, unimaginative servants. For many applications, it is entirely acceptable. However, for an increasingly large number of applications, we require systems that can decide for themselves what they need to do in order to achieve the objectives that we delegate to them. Such computer systems are known as agents. Agents that must operate robustly in rapidly changing, unpredictable, or open environments, where there is a significant possibility that actions can fail, are known as intelligent agents, or sometimes autonomous agents.

=== Multi Agent System ===
A group of loosely connected autonomous agents act in an environment to achieve a common goal. This is done by cooperating, and sharing knowledge with each other 
Multi-agent systems have been widely adopted in many application domains because of the beneficial advantages offered. Some of the benefits available by using MAS technology in large systems are
* An increase in the speed and efficiency of the operation due to parallel computation and asynchronous operation
* A graceful degradation of the system when one or more of the agents fail. It thereby increases the reliability and robustness of the system
* Scalability and flexibility- Agents can be added as and when necessary
* Reduced cost- This is because individual agents cost much less than a centralized architecture
* Reusability-Agents have a modular structure and they can be easily replaced in other systems or be upgraded more easily than a monolithic system

=== Formation Control ===
Formation of a multi-agent system is a composed of a group of specific agents, communication among agents, and geometrical information of agents. This project focuses on the formation control of the multi-vehicle system. The aim of formation control is to design a controller that has the ability to bring the agents to a desired geometric shape by assigning local control laws to individual agents.

== Methodology ==

=== Detection ===
# Detect objects in immediate surroundings using LiDAR for distance measurement and monovision sensor for object classification
# 
# Use angular rotation from IMUs and distance to object as polar coordinates for localisation
# 
# Calculate global coordinate points of objects based on polar coordinates
# 
# Pass object data to Agent unit for formation control
 
The detection module is used to detect localised environmental information using its many sensors such as vision sensor, SONAR Ultrasonic sensor, LiDAR ToF (Time-of-Flight) sensor and IMU. The detection module achieves sensing through heterogeneous acquisition mechanism also referred to as multimodal sensing. Multimodal sensing is necessary because it allows us to capture environmental information more vividly than using single sensor based ranging. Data gathered from various sensors is fused together within the agent through the process called Data fusion which allows multimodal data streams to jointly analyze captured sensing data. LiDAR and SONAR sensors will provide ranging information for object detection during the hypothesis generation and the vision sensor will provide the system with object’s shape parameters for hypothesis verification phase.  
The detection module uses ultrasonic sensors for their wide cone of detection and LiDAR for its accuracy to sweep the immediate area, this allows the rovers to mark any obstacles within its path. This is in contrast to using multiple sensors for ranging which increases computational needs and power consumption on low energy hardware where the rovers will be ultimately planned to be deployed.
Detection occurs in two phases, first of which is the hypothesis generation phase. Hypothesis generation phase is when the ranging sensors detect an obstacle within their detection zone and consider the hypotheses that the obstacle is a fellow agent. The rover will then focus its efforts towards identifying the obstacle through the use of vision sensor. The second phase, hypothesis verification phase will use the vision sensor to verify our hypotheses. The vision sensor will extract frames through the real time feed and passes these frames to our YOLOv3 model that has been pretrained with a classifier. The classifier is trained using 800 images manually labelled to train the classifier. The model was trained for 900992 images with an average loss ratio of 0.016559. To ensure robustness within the system and to optimize the detection rate and computational needs, the vision sensor only captures frames every 100 milliseconds and process these frames through the object detection model. 
[[File:Detection Flowchart.png|thumb|right|Fig 1]]
 
The distance data is filtered through Alpha trimmed mean filter and a Kalman filter before being packed from the main function to support functions indicated with “Filtered Distance Data” in the Fig 2. Orientation data is filtered through complementary filter and sent from the main function to support functions for the hypothesis generation phase. Hypothesis is verified in the Hypothesis verification phase when data from the vision sensor returns a state value which is “0” for no rover detection and “1” for any rover detected. The data is then fused together and passed to the support function that calculates rectangular coordinates using the polar coordinates from distance for radius and angle from IMU sensor. The rover is now localized within its frame and this value is passed over to support functions. Support functions calculate the global frame using the rover’s coordinates as a reference point. Adding the local coordinates to the self-reference point allows us to locate rovers in the global frame.
[[File:Detection Flowchart II.png|thumb|right|Fig 2]]



The following filters are necessary for robust performance of the detection module, they also provide a level of fault tolerance to the system.

==== Kalman Filter ====
Kalman filter is a recursive algorithm that provides the optimal estimate of the system state, given the noise in the system. It tries to achieve the optimal estimation of the unknown configuration based on the previous estimate and new measurement data. The ﬁlter updates at fixed time intervals specified in the model. Kalman filter is used as a fault tolerant system that will estimate the optimum distance to the object even if the LiDAR and SONAR ranging sensors provide faulty ranging data. The filter will approach the optimal estimate with increase in iterations of the filter.

==== Complementary Filter ====
Complementary filter is a recursive algorithm that provides the optimal estimate of the gyration data. It tries to achieve the optimal estimation of the angular position and gyration based on the previous estimate and a combination of low pass and high pass filters.
Complementary filter is used to take slow moving signals from accelerometer and fast-moving signals from a gyroscope and combine them as sensor fusion. Data from accelerometer and gyroscope are enough to estimate angular positions as such there are the only inputs to the Complementary filter. Data from the gyroscope is used because it is very precise and not susceptible to external forces. Data from the accelerometer is used as it is less susceptible to noise due to drift. The ﬁlter updates these measurements at fixed time intervals specified in the model considering previous measurements while estimating new data. 

==== Alpha Trimmed Mean Filter ====
Alpha trimmed mean filters are a variation of adaptive mean filters that are especially effective against additive gaussian noise. The filter is an adaptation from image processing used to remove impulse noise as they are a good compromise between moving mean  filter and median filter. They are used if the nature of noise in the system deviates from the gaussian with impulsive noise components. The filter is a moving window-based filter which iterates over the continuous stream of data from ranging sensors over a given window size of w and trimming factor of α. Adaptive alpha trimmed filters allow for the flexibility of choosing α based on the local noise statistics.

===Obstacle Avoidance ===

====Artificial Potential Field method (APF)====

The Artificial Potential Field method (APF), which was generated by Khatib in 1986<ref> O. Khatib. “Real-Time Obstacle Avoidance for Manipulators and Mobile Robots”,  The International Journal of Robotics Research, March 1986 </ref>, is introduced in this project to help robots to avoid obstacles. As shown in the Fig 4, the robot’s moving area is simplified into 2D-plan (a virtual potential field). In addition, the robot, obstacles and the desired location are all simplified into points. In this area, obstacles provide the repulsion to the robots, and the repulsion must become bigger when the robots are closer to the obstacles. It should be noted that there is a detection range of the obstacle. In other words, if the robots are in this range , then the robots must be affected by the repulsion from the obstacles. Otherwise, the repulsion is zero. 
The desired location provides the traction to the robot, and the traction must become smaller when the robots are closer to the desired location. Eventually, the robots must move under the resultant of the repulsion and the traction.
[[File:APFCOL.jpg|thumb|right|Fig 3]]

====Issues with APF & Improved APF====
The APF has some issues, including the unreachable target issue and the local minima issue. The unreachable target means the robot cannot achieve the desired location, and the robot can be in a state of shock, like the Fig 4 shown. To be detailed, the unreachable target issue happens when the obstacles are close to the desired location. At the same time, the robot and the desired location are both in the detection range of the obstacle. In this case, the desired location is located between the robot and the obstacle. In addition, as mentioned above, the repulsion from the obstacle must become bigger when the robot is closer to the obstacle. However, the traction must become smaller when the robot is closer to the desired location. As a result, the robot must be pushed back by the repulsive force when the robot becomes closer to the desired location and the obstacle. After this, the traction must become bigger and the repulsion must become smaller, since the distance between the robot and the desired location (and the obstacle) becomes bigger now. As a result, the robot must be pulled forward by the traction. Eventually, the robot must repeat the process of “back and forward” (in a state of shock).  For the issue of the local minima, the resultant of the repulsion and the traction is zero in some points, which are not the desired location, so that the robot stops moving and cannot arrive the desired location.

[[File:Localmin.jpg|thumb|right|Fig 4]]
[[File:APF comparison.png|thumb|left|Fig 5]]

For the unreachable target issue, the relative distance between the robot and the desired location must be introduced into the repulsive field function. Therefore, the procedures of this method just need to update the equation of the repulsive field function, and other procedures are all the same as the traditional one.  In terms of the local minima issue, the “Virtual Obstacle” method is introduced. The difference between traditonal APF approach vs the improved APF are shown in the Fig 5

The procedures of the strategy to escape the local minimum point are:  
* Identify if the robot is in the local minimum point every 2 steps. 
* If the robot is trapped in the local minimum point, then the strategy of escaping the local minimum point must be activated. 
* The strategy here is that the robot must treat the current local minimum point as a “virtual obstacle”. Then, the system re-calculates the forces around the robot. Finally, the system finds out the direction of the resultant force.   
* The robot moves toward this direction with a small step


=== Formation Control ===
==== Time-varying Formation Control ====
The major task of formation control is to calculate desired positions by individual agents themselves. It takes positions and velocities information from the detection module and output a controlled output which in our implementation is velocities and accelerations. The control input is the formation position we delegated for the system and the state vector is the positions and velocities information of each nodes. These two variables form the node dynamics of the system. A consensus protocol has been designed to control these variables for each agent.

In our system, the main focus is the design of achieving desired position with desired velocity. Therefore, on the formation control level the system can be literally simplified as a second order linear system. A double integrator can approximately describe the dynamics of each as:

[[File:Node dynamic.png|thumb|center]]

where x and v refer to the positions and velocities of each agent respectively and u is the control input of the 𝑖th agent.As the motion of agents along each axis is independent, this control law can also be adapted to higher dimensional cases with using Kronecker product.

Let <math> \Theta_i(t)=[x_i(t),v_i(t)]^T </math>, <math> B_1=[1,0]^T </math>, and <math> B_2=[0,1]^T </math>. The time-varying system for agent dynamics can then be reformatted as:

<math> \dot{\Theta_1}(t)=B_1 B^T_2 \Theta_i(t)+B_2 u_i(t) </math>

Define <math> h_(t)=[h_(ix)(t),h_(iv)(t)],i=1,2,...,N </math> as the desired position and velocity of agent <math> i </math> where <math> h_i(t) </math> is a continuously differentiable vector. <math> h(t)=[h^T_1(t),h^T_2(t),...,h^T_N(t)]^T </math> is a column vector that contains desired formation for all the agents. A graphical explanation of these variables has been shown in the figure below

[[File:Formation in XY plane for N=4 agents.png|thumb|center]]

A time-varying formation can then be descripted by <math> h_i </math> for an MVS. For the system to achieve the desired formation function, there will be a controller that perform the <math> \Theta_i </math> under certain initial condition <math> \Theta_(i0) </math> and input <math> h_i </math> such that <math> \lim_{t \to \infty} (\Theta_i(t)-h_i(t))=0 </math>.

MVSs in the above form is considered achieve consensus if for any initial condition, there will be a consensus function <math> s(t) \in \mathbb{R}^3 </math> such that <math> \lim_{t \to \infty} (\Theta_i(t)-s(t))=0 </math>. Therefore, an MVS in this form achieves consensus when it achieves the formation stated which means that the consensus function is now equivalent to the formation function. Thus, the consensus problem can be considered as a special case of formation control problem. In other words, the formation control problem has been transformed into consensus problem.

Based on the aforementioned theories, a time-varying formation protocol:

[[File:Formation protocol.png|thumb|center]]

where <math> i=1,2,...,N </math>, <math>K_1=[k_11,k_12]</math> is the design of motion dynamic of the time-varying formation, <math>K_2=[k_21,k_22]</math> can be designed to drive the ground vehicles to achieve desire formation.

==== Formation Optimising ====
To achieve an optimal formation with respect to the current position, it is necessary to map the formation first before generating the output <math>\dot{\Theta(t)}</math> for each agent. The target agent positions <math>h_x(t)</math> has been defined previously. Then, the associated assignment to the agent set 𝜎 is aimed to minimize the sum of squared travelled distances. The studies indicate that with assignment <math>\sigma</math>, the objective of the assignment function can be formulated by <math> \Theta_x(t) \to h_x(t) </math> minimising:

[[File:Formation optimisation.png|thumb|center]]

There are several solutions based on local interactions that are able to find the optimal assignment to obtain the least cost for the system. In out implementation of the system, we introduce Kuhn-Munkres algorithm to generate the minimum cost for forming the formation.

Kuhn-Munkres algorithm (also known as Hungarian algorithm) is an efficient algorithm to solve the assignment problem. The formation mapping strategy first generates an n-by-n matrix containing the cost of assigning n of each agent a task, that is the distance. The algorithm performs row operations on the matrix by subtract the lowest value with the row. This leads to at least one zero in row. It repeats for all rows and obtain at least on zero per row. These zeroes can be the lowest cost for each assignment of agents. In general, it may turn out that the matrix at this stage cannot be used for assigning. So, it needs to again repeat the same procedure to columns. At this stage, it probably will get the result. As a result of the assignment, each agent can obtain a desired position that cost the least for the entire system.

==== Collision Free with Edge-tension Function ====
Let <math>\delta</math> be a safety distance between each agent. If the distance between any two of the agents is always greater than <math>\delta</math>, we can consider the system as collision free. Now we defined an edge-tension function:

[[File:Edge-tension.png|thumb|center]]

Where <math>l_{ij}</math> is the distance between agents, <math> K_{ij}</math> and <math>\alpha_{ij}</math> are constant number, and <math>V_{ij}</math> is a differentiable nonnegative function of <math>l_{ij}</math>  such that <math>V_{ij}</math> attains a unique minimum at <math>l_{ij}=d_{ij}</math> where <math>d_{ij}=\delta+ (K_{ij}/2) * \log(3+2\sqrt{2})</math>.

Considering this edge-tension function, now the control low can be further designed as:

[[File:Edge-tension control law.png|thumb|center]]

where <math>\Delta_{x_i}V_{ij} </math> is the gradient of <math>V_{ij}</math> with respect to <math>x_i</math>. Now the control output can achieve a collision-free control for the agent system to obtain the formation <math>h_i</math> by remaining the distance always greater than <math>\delta</math>.

Furthermore, if we consider <math>\Delta_{x_i}V_{ij}=w_{ij}(x_i-x_j) </math> where <math>w_{ij}</math> the weight of Laplacian matrix and defined as <math> w_{ij}=l_{ij} </math> for all <math>i \neq j</math> and <math>w_{ij}=\sum_{j \neq i}w_{ij}</math> for all <math>I=j</math>, the control law can rewritten as:

[[File:Edge tension control law.png|thumb|center]]

where <math>[f_1,f_2]=[1/N,(1+a_22)/N]</math>, <math> L_w</math>is the weighted Laplacian matrix related to <math>w_{ij}</math> we defined above. This control output is in the format of aforementioned time-varying system model and can be combined with the formation controller. As indicated previously, the motion along each axis is independent. So, we can use Kronecker product to adapt this control law into a three degree-of-freedom system.

=== Motion Control===
[[File:Refrencevelocities.png|thumb|right|Fig 8]]
[[File:Wheelmodel.png|thumb|right|Fig 9]]
The formation control and obstacle avoidance algorithms were formed in MATLAB which would provide the continuous stream of final points. An algorithm to send these data points from MATLAB to CoppeliaSim was deigned by the motion control module. These final points were then fed into the embedded Lua script and the coordinates were sent to CoppeliaSim by the help of remote API method.

As seen in Fig 8, MATLAB is used to form a connection with the CoppeliaSim scene through a function MoveSpin which contains necessary commands that help in establishing a connection and asking the user for the final points to be transferred to CoppeliaSim.

This packed data from the MATLAB was transferred into a child script attached to a object which acted as a connection maker in the system. data points are sent to the respective robot, the next process is the planning path of the motion. In a robotic Lua script, the desired points are read and fed into the control. the initial and the final points interact points to find d and θ shown in Fig 9. These velocities (v_x (t),v_y (t) and ω(t)) are the global velocities that help in planning the path but they need to be changed into the reference frame velocities((v (t), v_n (t), ω(t))) also seen in Fig 9
* x,y,θ- Robots position (x,y) and the angle that is relative to the front 
* d[m]- the distance between the wheels and centre
* v_0,v_1,v_2(m/s)- wheel linear velocities
* ω_0,ω_1,ω_2 (rad/s)- wheels angular velocities 
* f_0,f_1,f_2 (N)- wheel traction force
* T_0,T_1,T_2 [N.m] – torque on the wheels
* v,vn [m/s]- Robot linear velocity
* ω[rad/s]-Robot Angular velocity
* F_v,F_vn [N]-Robot traction force along v,vn
  
T[N.m]-Robot torque(respect to ω)

== Results ==

===Detection===

====Local and Global Coordinates====

The system is capable of calculating local and global coordinates based on the ranging data provided by LiDAR sensor. Local coordinates are based on the local frame where the center of the rover on which the sensors are mounted, this is referred to as self-reference. The local frame assumes the center of the coordinate plane (0,0) as the center of the rover and the distance of the object detected as input to support functions. The support functions transform the polar coordinates to rectangular coordinates LiDAR’s distance(r) and IMU rotation(θ). Global coordinates are calculated by using the position of the current rover in simulation space accessed through the CoppeliaSim’s Remote API functions. The local frame is then concatenated to the rover position in the rectangular coordinates. Fig 1 shows the local coordinates and global coordinates displayed in the output of object detection.

[[File:Global coordinates.png|Fig 1|thumb|left]] 



{| class="wikitable" style="display: inline-table;"
|-
! Actual Distance (m) !! LiDAR Distance !! Kalman Filtered(1st iter) !! Kalman Filtered (3rd iter)
|-
| 1.650 || 	1.649 || 	1.669 || 	1.651
|-
| 1.154 || 	1.154 || 	1.171 || 	1.158
|-
| 1.018 || 	1.017 || 	1.030 || 	1.022
|-
| 1.652 || 	1.649 || 	1.670 || 	1.653
|}


[[File:KFgraph2.png|thumb|Fig 2]]

Although the LiDAR sensor is accurate in ranging operations, it becomes necessary to filter out noise within the system introduced over time either due to the rover’s own movement or environmental conditions. Kalman filter is used as a fault tolerant system that will estimate the optimum distance to the object even if the LiDAR and SONAR ranging sensors fail or provide faulty estimates. 
Kalman filter works by estimating Kalman gain which is derived from the incoming sensor data like LiDAR ranging data, and prediction-based estimates from the mathematical model of the system designed beforehand. Every iteration of the Kalman filter increases the accuracy of the estimates giving robust ranging data even under unsuitable environmental conditions or faulty sensor data. Kalman filter, however, does not account for the complete sensor failure as it relies on incoming data to estimate the distance. Fault tolerance in that case is achieved by using the alternate ranging sensor such as SONAR or in cases when both sensors fail, active triangulation can be fed as an input to the filter. The Kalman estimates are consistently 3-10 mm higher than the actual distance, this is due to imperfect modelling of the system in the filter, some calibration of the model is required before the filter can be used for maximum accuracy. 

{| class="wikitable" style="display: inline-table;"
|-
! Actual X(in meters) !! Actual Y !! Localised X !! Localised Y
|-
| 1.90 || 1.05 || 1.40 || 1.10
|-
| 1.34 || 1.03 || 1.66 || 1.07
|-
| 1.07 || 2.10 || 1.069 || 1.99
|-
| 3.99 || 2.01 || 3.76 || 2.13
|}

[[File:Actual coordinates vs Localised coordinates.png|thumb|right|Fig 3]]

As can be seen from Fig 3 and the table, there is some discrepancy in the accuracy of the localized coordinate frames. This is due to the constant rotation of the rover that changes the IMU’s rotation data that in turn affects the polar to rectangular coordinate transformation. This error can be mitigated to by using only the first measured distance (first detection values) as the only measurement to consider as the accurate measurement. The error in the distance is an average of 0.265m i.e. 26mm. This error is due to the nature of detection at the point of contact of LiDAR instead of the center of the rover as the actual coordinates denote. This error can be compensated by adding the half width of the rover as calibration data to the distance measured.<br>

===Obstacle Avoidance===
The program starts from setting the coordinates for the initial positions, the desired location, the obstacles’ positions and the parameters of obstacle avoidance algorithm. Then, the system must judge if the robot arrives the desired location. If the robot arrives the desired location, the program can be end. Otherwise, the program must compute the traction force (vector). The program must judge if the robot is affected by the obstacles around it before computing the repulsion force (vector). After that, the program must add traction vector and repulsion vector so that the resultant force vector can be obtained. It should be noted that the resultant vector can be used to find out the direction of the resultant force. Then, the robot must move toward this direction that is provided by last step with a step size, which is must be small enough so that no collision is possible when robot moves to next position.  
In addition, the size of the robot and the obstacles are set. A method of setting size of obstacles and robots is introduced in <ref>B. Yan, P. Shi, C.C. Lim, et al. “Optimally distributed formation control           with obstacle avoidance for mixed-order multiagent systems under switching topologies.” IEEE Digital Library, 2018</ref>. In this method, the size of robot is suggested to be added to the size of the obstacle. In conclusion, in this method, the robot is still a point and the size of obstacle is combined with the size of robot and the size of the original obstacle.
The improved APF simulation results show that both local minima issue and unreachable target issue can be overcome. The simulation results for the local minima issue are shown in Fig 4 and simulation results for the unreachable target issue are shown in Fig 5. 

[[File:APF2.png|thumb|center|Fig 4]] [[File:Unreachable target.png|thumb|center|Fig 5]]

===Formation Control===

The controller we designed is able to track time-varying formation input, in this case, we simulated this kind of input for the purpose of analysing the performance of the formation controller. The simulation result is shown in the following figure.

[[File:Simulation result.png|thumb|center]]

The input, which is the desired formation position and speed, is designed as a time-varying square with each rover drawing a circle while the whole formation can still remain a square. The trajectory we designed is a circle with radius 𝑟 = 1 for each agent. Since the performance for individual agent is the same as this is a decentralised system, the figure only shows the tracking ability for the agent 1. Result for other agents should be similar. As shown in the figure, the agent is able to track the input of both speed and position effectively. The response of the controller can be considered to be effective. It can also be seen from the result that due to the introduction of the edge-tension function, this formation can attain a collision free trajectory in which the agents will not crash with each other.

===Motion Control===
[[File:Traj both.png|thumb|right|Fig 6]]
The Motion control algorithm created the following trajectories(Fig 6). The blue trajectory is formed by the two-wheel differential drive and the green trajectory is formed by the 3-wheel Omni wheel drive.

<br>
The test was run for 3 times in both the cases and the graphs clearly show that the trajectory formed by the Omni wheel drive is more in shape than the counterpart. It is important to identify the far corners of the trajectories, the corners for the 3-wheel drive are more pointed than the 2-wheel drive. The above observation took place because the differential drive had a front face because of which it could not align itself towards the desired position. Since any robot path planning is the smallest path due to non-alignment with the desired point it could not move in the backward direction because of which the circular curves were formed at the ends of the graph that moved the robot to first align itself and then follow the trajectory. On the contrary, in a 3-wheel drive, there was no front face and the robot could align to the desired point and moved along the trajectories. The mean deviation in the 2-wheel drive case was 28% more than the 3-wheel drive case (compared along the y-axis of the movement). Hence three-wheel robots were selected over the 2-wheel differential drive.



===PID===

PID controllers are an important part in the motion control. Since the motion also brings the concept of momentum, a robot while moving in any direction tends to stay in motion even if the desired point is achieved. This phenomenon brings an overshoot in the system. <br>
[[File:Robust system config.png|thumb|right|Fig 7]]
<br>

* CASE I-The velocity constant was kept at 40 m/s and the value of Kp and Kd was 0.6 and 2 respectively.
* CASE II- The velocity constant was kept at 45 m/s and the value of Kp and Kd was 0.7 and 1.75 respectively.<br>
* CASE III- The velocity constant was kept at 60 m/s and the value of Kp and Kd was 0.6 and 3 respectively.

Case II indicated as yellow lines in both the graphs showed a medium quality profile with the period of 5.78 seconds, peak overshoot of 0.0156m, the constant error of 0.0028 meters and average speed of 0.85 m/s. This was the recommended constant values that were to be used in the system.

One of the aims of the project was to develop a robust system. The robustness in the motion module can be analysed by keeping the velocity of one wheel to be zero or in other terms if one wheel in the 3-wheel system does not work. The normal system with two wheels might not work due to the dependence of the system on the motion of 2 wheels but the 3 wheel system is geometrically structured such that the rollers in the third wheel act as a third wheel in the system with the driving force from the other two wheels. The healty system is represented as dashed line, when all the 3 wheels in the system are working and the blue line shows the faulty system that indicates only 2 wheels are operational(Fig 7).

== Conclusion ==

In this project, we have considered basic problems of formation control for MVS. Based on that, we have proposed several research questions for this project. In regard to the previous related works, the desired objective has been clarified as a decentralised system with detection and communication. This system consists of four sub-modules including host, detection, control and motion modules as a reliable system structure. To improve the robustness of the system, we have considered some control strategies based on literature studies. The main contribution of this project is that we research, test, and integrate several approaches to achieve the requirement of submodules. We have also established a feasible plan to apply the control theory to actual platform.

A multi-vehicle system has been created with detection of various robots and obstacles by camera and infrared sensors, controlled remotely in python. A formation control with optimised path planning and obstacle avoidance has been achieved and successfully simulated in V-REP. Motion control in V-REP embedded script and remote API connection with MATLAB for reaching the targeted position  generated from formation control algorithm. A design of local understanding of global position systems for agents has been performed.

== Reference ==
[1] Wooldridge, M (2002). An Introduction to MultiAgent Systems. John Wiley & Sons. ISBN 978-0-471-49691-5

[2] Balaji, P., & Srinivasan, D. (2010). An introduction to multi-agent systems. Studies in Computational Intelligence, 310, 1-27.

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