WP3-14 2 - Revision history

Grolleaue: /* Distributed control of multi-drone system */

2023-03-10T08:31:46Z

Distributed control of multi-drone system

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	\|-		\|-
	\| TRL \|\| 4		\| TRL \|\| 4
			\|-
			\| Contact \|\| patrick.coirault at univ-poitiers.fr
	\|}		\|}

Grolleaue: /* Simulations */

2022-03-31T14:04:03Z

Simulations

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	[[File:wp3-14_2_03_3.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]		[[File:wp3-14_2_03_3.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]

	[[File:wp3-~~14_2_04~~.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]		[[File:wp3-14_2_04_2.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]

	Siemens Simcenter AMESIM tool is also used to test the designed formation tracking scheme in more realistic environment. Following results is showing formation tracking of a follower with position offset as f_x=1m,f_y=-2m,f_z=0m.		Siemens Simcenter AMESIM tool is also used to test the designed formation tracking scheme in more realistic environment. Following results is showing formation tracking of a follower with position offset as f_x=1m,f_y=-2m,f_z=0m.

Grolleaue: /* Simulations */

2022-03-31T14:02:15Z

Simulations

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	[[File:wp3-14_2_03_2.png\|frame\|center\|Communication topology]]		[[File:wp3-14_2_03_2.png\|frame\|center\|Communication topology]]

	[[File:wp3-~~14_2_03~~.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]		[[File:wp3-14_2_03_3.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]

	[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]		[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]

Grolleaue: /* Simulations */

2022-03-31T14:00:54Z

Simulations

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	Siemens Simcenter AMESIM tool is also used to test the designed formation tracking scheme in more realistic environment. Following results is showing formation tracking of a follower with position offset as f_x=1m,f_y=-2m,f_z=0m.		Siemens Simcenter AMESIM tool is also used to test the designed formation tracking scheme in more realistic environment. Following results is showing formation tracking of a follower with position offset as f_x=1m,f_y=-2m,f_z=0m.

	[[File:wp3-~~14_2_05~~.png\|frame\|center\|Formation tracking simulation in AMESIM]]		[[File:wp3-14_2_05_2.png\|frame\|center\|Formation tracking simulation in AMESIM]]

	==Reference==		==Reference==
	[1] Ajwad, Syed Ali, Emmanuel Moulay, Michael Defoort, Tomas Menard, and Patrick Coirault. [https://hal.archives-ouvertes.fr/hal-02508376/file/CDC19.pdf Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data.] Nonlinear Dynamics (2022): 1-16.		[1] Ajwad, Syed Ali, Emmanuel Moulay, Michael Defoort, Tomas Menard, and Patrick Coirault. [https://hal.archives-ouvertes.fr/hal-02508376/file/CDC19.pdf Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data.] Nonlinear Dynamics (2022): 1-16.

Grolleaue: /* Reference */

2022-03-31T13:58:58Z

Reference

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	==Reference==		==Reference==
	[1] Ajwad, Syed Ali, Emmanuel Moulay, Michael Defoort, Tomas Menard, and Patrick Coirault. "Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data." Nonlinear Dynamics (2022): 1-16.		[1] Ajwad, Syed Ali, Emmanuel Moulay, Michael Defoort, Tomas Menard, and Patrick Coirault. [https://hal.archives-ouvertes.fr/hal-02508376/file/CDC19.pdf Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data.] Nonlinear Dynamics (2022): 1-16.

Grolleaue at 13:56, 31 March 2022

2022-03-31T13:56:50Z

← Older revision		Revision as of 13:56, 31 March 2022
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	[[File:wp3-14_2_05.png\|frame\|center\|Formation tracking simulation in AMESIM]]		[[File:wp3-14_2_05.png\|frame\|center\|Formation tracking simulation in AMESIM]]

			==Reference==
			[1] Ajwad, Syed Ali, Emmanuel Moulay, Michael Defoort, Tomas Menard, and Patrick Coirault. "Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data." Nonlinear Dynamics (2022): 1-16.

Grolleaue: /* Simulations */

2022-03-31T13:56:24Z

Simulations

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	[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]		[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]

	~~[[File:wp3-14_2_05~~.~~png\|frame\|center\|Inter~~-~~drone distance~~, ~~in meters]]~~		Siemens Simcenter AMESIM tool is also used to test the designed formation tracking scheme in more realistic environment. Following results is showing formation tracking of a follower with position offset as f_x=1m,f_y=-2m,f_z=0m.

	~~The simulation results show the stability of the system with the designed algorithm for formation~~ tracking~~. However,~~ simulation results are not sufficient to prove the stability of the system. Therefore, a rigorous mathematical proof has been also carried out to ensure the formation tracking and stability of the closed loop system with the designed controller.		[[File:wp3-14_2_05.png\|frame\|center\|Formation tracking simulation in AMESIM]]

Grolleaue: /* Controller design and Implementation */

2022-03-31T13:48:24Z

Controller design and Implementation

← Older revision		Revision as of 13:48, 31 March 2022
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	[[File:wp3-14_2_02.png\|1000px\|thumb\|center\|Overall control scheme for formation tracking]]		[[File:wp3-14_2_02.png\|1000px\|thumb\|center\|Overall control scheme for formation tracking]]

	'''Formation controller''': The basic idea is to use a classical continuous linear consensus controller for MAS of second order dynamics. By introducing the auxiliary controller, the position dynamics can be represented as double integrator. However, trivial formation controller requires both position and velocity in continuous time. A continuous-discrete-time high-gain observer is used to compute both position and velocity from available discrete position data. Each follower has a local observer which not only estimates the agent’s own states but also the states of its neighbours. The structure of the proposed observer-based formation tracking algorithm also has some advantages when it comes to communication delays and data packet dropouts. As each controller is using the estimated states provided by the local observer, by time stamping the measured position data, the estimation can be provided as soon as the data is received, even with a delay, by compensating it through increasing the computation speed of the observer. Moreover, if the information packet is lost during communication, the observer could still provide an estimation.		'''Formation controller''': The basic idea is to use a classical continuous linear consensus controller for MAS of second order dynamics. By introducing the auxiliary controller, the position dynamics can be represented as double integrator. However, trivial formation controller requires both position and velocity in continuous time. A continuous-discrete-time high-gain observer is used to compute both position and velocity from available discrete position data.

	~~An Artificial Potential Function (APF) based repulsive controller is~~ also ~~incorporated with~~ the ~~formation controller to avoid any kind~~ of ~~collision among the agents and with obstacles~~. ~~APF provides a repulsive force whenever~~ the ~~distance between two bodies becomes less than~~ some ~~threshold~~. It is ~~considered that each drone~~ is ~~equipped~~ with ~~some kind~~ of ~~proximity sensor to detect anything in its path~~.		Each follower has a local observer which not only estimates the agent’s own states but also the states of its neighbors. The structure of the proposed observer-based formation tracking algorithm also has some advantages when it comes to communication delays and data packet dropouts. As each controller is using the estimated states provided by the local observer, by time stamping the measured position data, the estimation can be provided as soon as the data is received, even with a delay, by compensating it through increasing the computation speed of the observer. Moreover, if the information packet is lost during communication, the observer could still provide an estimation.

	'''Attitude controller''': For the Matlab simulations, the desired attitude is computed through the auxiliary controller and then a finite-time attitude controller is used to compute the required torques to achieve this desired attitude.

	'''~~Simulations~~''': The ~~designed control scheme~~ is ~~simulated for~~ a ~~group of one leader~~ and ~~three follower quadrotors where followers~~ are ~~required~~ to ~~make a triangle around~~ the ~~leader in xy-plane and maintain~~ the ~~same altitude as~~ of the ~~leader~~. Figure ~~58 illustrates~~ the ~~formation with a stationary~~ leader ~~while Figure 59 shows~~ formation tracking ~~results with a moving leader~~. ~~The threshold distance for~~ the ~~repulsive force~~ is ~~considered as 2 meters~~ while the ~~protection radius around each drone~~ is ~~0.5 meter. Figure 60 shows that~~ the ~~inter-agent distance always remains greater than 1 meter which implies that~~ the ~~agents never collide during~~ the ~~whole process~~.		'''Attitude controller''': The desired attitude and thrust is computed through the auxiliary controller and then a finite-time attitude controller is used to compute the required torques to achieve this desired attitude. These required thrust and torques are then fed to the motor mixer which generate the motor speed commands for all four motors which are required for the quadrotor desired motion.

			The stability of the proposed controller is proved through rigorous mathematical analysis and the results have been published in [[#Reference\|[1]]].

			==Simulations==

			The designed control algorithm is verified using MATLAB simulation. Communication topology (see Figure) is used to the MATLAB simulation purpose where 0 represents the leader. The results of formation tracking are shown on the next figure. In the first scenario, the leader is hovering at the altitude of 10m while the followers start from their initial position and make the required formation. In the second scenario, the leader is moving with some acceleration while the followers track the leader’s trajectory while keeping the desired formation.

			[[File:wp3-14_2_03_2.png\|frame\|center\|Communication topology]]

	[[File:wp3-14_2_03.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]		[[File:wp3-14_2_03.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]

Grolleaue at 13:42, 31 March 2022

2022-03-31T13:42:42Z

← Older revision		Revision as of 13:42, 31 March 2022
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	[[File:wp3-14_2_01_3.png\|frame\|center\|Thrust and mass]]		[[File:wp3-14_2_01_3.png\|frame\|center\|Thrust and mass]]
			==formation geometry==

	==~~Design and Implementation=~~=		The desired formation pattern can be defined by a formation vector F(t)=[f_1 (t)^T.... f_N (t)^T ] where f_i (t)=[f_(i,ξ)^T,f_(i,v)^T ] satisfies f ̇_(i,ξ)=f_(i,v).

	Since the drone is an under-actuated system (e.g. quadrotor has 6 states and 4 controllable rotor speeds), the design of controller is not straightforward. To achieve the desired formation of a swarm of drones, the overall dynamics of the drone is divided into two blocks namely position dynamics and attitude dynamics with a strong nonlinear coupling among them. The idea is to introduce an auxiliary position controller ~~and~~ design it while keeping all the above mentioned constraints in mind. The required thrust and attitude then can be computed through this auxiliary position controller. An attitude controller then can be designed to achieve the required attitude by the drone and which makes the drone to reach to the required position to achieve the desired formation shape. Figure 57 shows the block diagram of the overall control architecture of one drone to achieve formation tracking of the swarm of drones. The position controller computes auxiliary position controller which is then used to compute desired roll and pitch through nonlinear decoupling equations. These desired roll and pitch angles act as a reference input to the attitude controller which computes the required torques to track these desired angles.		f_(i,ξ) and f_(i,v) are the corresponding position and velocity offsets of quadrotor “i” with respect to the reference trajectory. To further explain the notation of formation vector f_i (t) let us consider a network of quadrotors with a leader and three followers. Let the formation vector be chosen as

			[[File:wp3-14_2_01_4.png\|frame\|center\|Formation vector]]

			for i=1,2,3. This formation vector defines that the followers move around the leader in a circle of radius 10m with a phase difference of 2π/3. The altitude position offsets are constant with values -3m, 0m and 3m for follower 1, 2 and 3 respectively. A visual illustration of this formation is provided in the following figure.

			[[File:wp3-14_2_01_5.png\|frame\|center\|An example of time-varying formation]]

			==Controller design and Implementation==

			Since the drone is an under-actuated system (e.g. quadrotor has 6 states and 4 controllable rotor speeds), the design of controller is not straightforward. To achieve the desired formation of a swarm of drones, the overall dynamics of the drone is divided into two blocks namely position dynamics and attitude dynamics with a strong nonlinear coupling among them. The idea is to introduce an auxiliary position controller μ=[μ_x;μ_y;μ_z ]^Tand design it while keeping all the above mentioned constraints in mind. The required thrust and attitude then can be computed through this auxiliary position controller. An attitude controller then can be designed to achieve the required attitude by the drone and which makes the drone to reach to the required position to achieve the desired formation shape. Figure 2 shows the block diagram of the overall control architecture of one drone to achieve formation tracking of the swarm of drones. The position controller computes auxiliary position controller μ which is then used to compute desired roll and pitch through nonlinear decoupling equations. These desired roll and pitch angles act as a reference input to the attitude controller which computes the required torques to track these desired angles.

	[[File:wp3-14_2_02.png\|1000px\|thumb\|center\|Overall control scheme for formation tracking]]		[[File:wp3-14_2_02.png\|1000px\|thumb\|center\|Overall control scheme for formation tracking]]

Grolleaue: /* Quadrotor mathematical model */

2022-03-31T13:39:55Z

Quadrotor mathematical model

← Older revision		Revision as of 13:39, 31 March 2022
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	[[File:wp3-14_2_01_2.png\|frame\|center\|(1) Position dynamics for quadrotor, (2) Attitude dynamics]]		[[File:wp3-14_2_01_2.png\|frame\|center\|(1) Position dynamics for quadrotor, (2) Attitude dynamics]]

	where T_i and m_i are the total thrust and mass of quadrotor “i” while Ω_i=〖[ω_(i,1) ω_(i,2) ω_(i,3) ]〗^T, I_i=diag{I_(i,1),I_(i,2),I_(i,3) }, τ_i=〖[τ_(∅_i ) τ_(θ_i ) τ_(φ_i ) ]〗^T and		where T_i and m_i are the total thrust and mass of quadrotor “i” while Ω_i=〖[ω_(i,1) ω_(i,2) ω_(i,3) ]〗^T, I_i=diag{I_(i,1),I_(i,2),I_(i,3) }, τ_i=〖[τ_(∅_i ) τ_(θ_i ) τ_(φ_i ) ]〗^T and

			[[File:wp3-14_2_01_3.png\|frame\|center\|Thrust and mass]]

	==Design and Implementation==		==Design and Implementation==

← Older revision		Revision as of 14:02, 31 March 2022
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	[[File:wp3-14_2_03_2.png\|frame\|center\|Communication topology]]		[[File:wp3-14_2_03_2.png\|frame\|center\|Communication topology]]

	[[File:wp3-~~14_2_03~~.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]		[[File:wp3-14_2_03_3.png\|frame\|center\|Formation tracking with stationary leader, distances in meters]]

	[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]		[[File:wp3-14_2_04.png\|frame\|center\|Formation tracking with a moving leader, distances in meters]]