Publish and Subscribe-Based Formation and Containment Control of Heterogeneous Robotic System with Actuator Time Delay
Abstract
:1. Introduction
1.1. Motivation
1.2. Related Research
- the influence of the information transmission between the agents has been identified as a crucial factor in performance and reliability of the control design;
- the presence of parameters’ uncertainties and external disturbances may critically influence the performances of the prior.;
- application of the DDS middleware technique augmented with the flocking approach has not been applied for heterogeneous systems, which is closer to the real-word robotic applications.
- A robust architecture for the formation control design of heterogeneous systems has been developed.
- A robust navigation system for the containment control design of heterogeneous systems has been proposed and designed.
- The navigation algorithm avoids obstacles while still maintaining the required formation or containment.
- Reliable middleware for data transmission has been developed.
2. Preliminaries
2.1. Data Distribution Service (DDS)
- Durability: Determines whether or not the previous data sent by the publisher has been received by a new subscriber.
- Reliability: Specifies whether or not the publisher will resend information lost over the network. Reliability involves two setups: BEST EFFORT (not re-send data lost) and RELIABLE (resend data lost).
- History: Determines a publisher’s preservation of the data received or sent to a subscriber. History involves two setups: KEEP LAST and KEEP ALL.
- Ownership: Determines whether a subscriber will simultaneously accept new samples from multiple publishers. Ownership involves two setups: SHARED and EXCLUSIVE.
2.2. Dynamics of Quadrotor
2.3. Dynamics of Underwater Vehicles
3. Multiple AUVs-UAVs Control Design
3.1. L1 Adaptive Control with Actuator Time Delay
3.2. Flocking and Boids Mode
- Separation: The separation force is utilized for avoiding collision between the UAVs and AUVs, which is defined as follows:
- Alignment: The matching average velocity of the agents is defined as follows:
- Cohesion: The cohesion force is utilized to calculate the AUVs attraction to the desired position based on the UAVs leader’s position, which is defined as follows:
- Obstacle Avoidance: The obstacle avoidance force is utilized for avoiding collision between the obstacles and the agents (UAVs and AUVs), which is defined as follows [34]:
4. Simulation Results
4.1. Formation Control Based on L1 Adaptive Control with Actuator Time Delay
- AUVs-UAVs formation control without disturbance and uncertain parameters. Figure 2 illustrates a group of AUVs in a triangular formation tracking their UAVs leader and coordinating themselves around it in 2D space. At the same time, Figure 3 depicts the 3D space of the set of three AUVs without disturbance and uncertainty in the inertia matrix.
- Formation of AUVs-UAVs with disturbance and uncertainty in parameters. In Figure 2 and Figure 3, the disturbance and parameter uncertainties (water density and the inertia matrix) were not taken into account. Figure 4 and Figure 5 show the 2D space and the 3D space of the group of three AUVs with disturbance and uncertainty in water density and inertia matrix. Figure 6 and Figure 7 illustrate the formation control of three AUVs in triangular form and one UAV avoiding some obstacles during their movement in 2D and 3D space. One can observe that during this maneuver, the controller still maintains the formation.
4.2. Containment Control Based on L1 Adaptive Control with Actuator Time Delay
- AUVs–UAVs containment with disturbance and uncertain parameters: The disturbance and the parameter uncertainty were not considered in Figure 9 and Figure 10, but now it is considered. Figure 11 and Figure 12 show the 2D space and 3D space of the set of five AUVs with disturbance and uncertainty in water density and the inertia matrix. Figure 13 and Figure 14 illustrate the containment control of five AUVs and four UAVs avoiding some obstacles during their movement in 2D and 3D space. One can see that during this maneuver the controller maintain the containment and the formation of the followers within their leaders.
5. Results Discussion and Comparative Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
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For the UAV | |
the vector representing z, y, and x coordinates. | |
the vector of Euler angles yaw (), pitch (), and roll (). | |
g | represents the gravity acceleration. |
m | represents the mass. |
is the drag coefficient. | |
u | is the total thrust force input created by the 4 propellers. |
represents the quadrotor’s inertia. | |
is the angular velocity. | |
is equal to . | |
represents the propeller inertia. | |
represent the rotational drag. | |
× | is the cross product. |
For the AUV | |
is the inertia matrix. | |
is the coriolis matrix. | |
is the damping matrix. | |
is the gravitational vector. | |
is the input control signals. | |
is the rigid body’s inertia matrix. | |
represents the additional momentum and forces. | |
is the gravity vector. | |
is the 3-by-3 identity matrix. | |
is the inertia tensor. |
Properties | Unit | Value |
---|---|---|
Mass | m | 0.52 kg |
Gravity Acceleration | g | 9.8 m/s |
Drag’s Translational | ||
Drag’s Rotational | ||
Ratio of Drag & Thrust | d | 7.5 × 10 kg × m |
Inertia of x-axis | 0.0069 kg × m | |
Inertia of y-axis | 0.0069 kg × m | |
Inertia of z-axis | 0.0129 kg × m | |
Arm Length | L | 0.205 m |
Propeller Inertia | kg × m |
Properties | Value |
---|---|
Length | 1.5 m |
Diameter | 20 cm |
Weight in air | 32 kg |
Depth rating | 100 m |
Propulsion | 2 horizontal + 2 vertical thrusters |
Horizontal velocity | 0–1.5 m/s, variable |
Energy | Li-Ion batteries, 600 Wh |
Autonomy/Range | about 10 h/40 km |
Properties | Value [] |
---|---|
Properties | Value | Unit |
---|---|---|
−1.74 | kg | |
kg | ||
−4.12 × 10 | kg | |
kg × m | ||
−6.07 | kg × m | |
−6.40 | kg × m | |
kg × m | ||
kg × m | ||
kg × m | ||
kg × m | ||
kg × m | ||
kg × m | ||
kg × m | ||
kg × m |
QoS Policies | QoS Value |
---|---|
Publisher/Subscriber | |
Durability | Volatile |
Reliability | Reliable |
History | Keep All |
Ownership | Shared |
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Elkhider, S.M.; Al-Buraiki, O.; El-Ferik, S. Publish and Subscribe-Based Formation and Containment Control of Heterogeneous Robotic System with Actuator Time Delay. Appl. Sci. 2021, 11, 9145. https://doi.org/10.3390/app11199145
Elkhider SM, Al-Buraiki O, El-Ferik S. Publish and Subscribe-Based Formation and Containment Control of Heterogeneous Robotic System with Actuator Time Delay. Applied Sciences. 2021; 11(19):9145. https://doi.org/10.3390/app11199145
Chicago/Turabian StyleElkhider, Siddig M., Omar Al-Buraiki, and Sami El-Ferik. 2021. "Publish and Subscribe-Based Formation and Containment Control of Heterogeneous Robotic System with Actuator Time Delay" Applied Sciences 11, no. 19: 9145. https://doi.org/10.3390/app11199145
APA StyleElkhider, S. M., Al-Buraiki, O., & El-Ferik, S. (2021). Publish and Subscribe-Based Formation and Containment Control of Heterogeneous Robotic System with Actuator Time Delay. Applied Sciences, 11(19), 9145. https://doi.org/10.3390/app11199145