Distributed control of heterogeneous multi-agent systems

1. A system for controlling motion of a vehicle in a group of vehicles, the system comprising

a communication interface;

a vehicle platform for travelling among the group of vehicles; and

an electronic processor configured to

determine a local virtual tracking error signal,

determine a controller state signal, and

determine a self-navigation input control signal based on the local virtual tracking error signal and the controller state signal,

wherein the self-navigation input control signal is for navigating the vehicle platform when travelling as a member of the group of vehicles, wherein a trajectory of an exosystem is based on a boundedness condition, wherein the trajectory of the exosystem including external disturbances and a trajectory of a leader vehicle of the group of vehicles, wherein the vehicle communicates with other vehicles in the group of vehicles via a fixed augmented directed connected communication graph topology, wherein each vehicle in the group of vehicles is stabilizable, wherein each vehicle in the group of vehicles satisfies a transmission zero condition, wherein design matrices of the vehicle satisfy an internal model principle,

wherein the self-navigation input control signal, u i (t), is defined by:

u i ( t )= K i z i ( t ),

wherein K i is a controller gain and z i (t), is the controller state signal at time, t, and wherein the controller state signal, z i (t), is defined by at least one of:

ż i ( t )= M 1i z i ( t )+ M 2i e vi ( t )

wherein M 1i and M 2i are design matrices and e vi (t) is the local virtual tracking error signal at the time, t,

wherein the controller gain, K i , is selected such that an agent-wise local gain condition is less than one, and wherein a locally-controlled agent matrix of the vehicle is Hurwitz, or

ż i ( t )= M 1i z i ( t )+ M 2i e vi ( t )+ M 3i y mi ( t ),

wherein M 1i , M 2i , and M 3i are design matrices, e vi (t) is the local virtual tracking error signal at the time, t, and y mi (t) is a local measurement output signal at the time, t,

wherein the controller gain, K i , is selected such that an agent-wise local gain condition is less than one, wherein a locally-controlled agent matrix of the vehicle is Hurwitz, and wherein an observer gain, H i , is selected such that the locally-observed agent matrix on the vehicle is Hurwitz.

2. The system of claim 1 , wherein each vehicle of the group of vehicles is detectable based on an output matrix.

3. The system of claim 1 , wherein the controller state signal, z i (t), is defined by

z i ( t )= M 1i z i ( t )+ M 2i e vi ( t )+ M 3i y mi

wherein each vehicle of the group of vehicles is detectable based on a measurement output matrix, wherein the system further comprising a plurality of vehicle sensors, and wherein the electronic processor is further configured to

determine the local measurement output signal based on data received from the plurality of vehicle sensors, and

determine the self-navigation input control signal based on the local measurement output signal.

4. A method for controlling motion of a vehicle in a group of vehicles, the method comprising

determining, with an electronic processor of the vehicle, a local virtual tracking error signal;

determining, with the electronic processor, a controller state signal; and

determining, with the electronic processor, a self-navigation input control signal based on the local virtual tracking error signal and the controller state signal,

wherein the self-navigation input control signal is for navigating a vehicle platform of the vehicle when travelling as a member of the group of vehicles, wherein a trajectory of an exosystem is based on a boundedness condition, wherein the trajectory of the exosystem including external disturbances and a trajectory of a leader vehicle of the group of vehicles, wherein the vehicle communicates with other vehicles in the group of vehicles via a fixed augmented directed connected communication graph topology, wherein each vehicle in the group of vehicles is stabilizable, wherein each vehicle in the group of vehicles satisfies a transmission zero condition, wherein design matrices of the vehicle satisfy an internal model principle,

wherein the self-navigation input control signal, u i (t), is defined by:

u i ( t )= K i z i ( t ),

wherein K i is a controller gain and z i (t) is the controller state signal at time, t, and wherein the controller state signal, z i (t), is defined by at least one of:

ż i ( t )= M 1i z i ( t )+ M 2i e vi ( t )

wherein M 1i and M 2i are design matrices and e vi (t) is the local virtual tracking error signal at the time, t,

wherein the controller gain, K i , is selected such that an agent-wise local gain condition is less than one, and wherein a locally-controlled agent matrix of the vehicle is Hurwitz, or

ż i ( t )= M 1i z i ( t )+ M 2i e vi ( t )+ M 3i y mi ( t ),

wherein M 1i , M 2i , and M 3i are design matrices, e vi (t) is the local virtual tracking error signal at the time, t, and y mi (t) is a local measurement output signal at the time, t,

wherein the controller gain, K i , is selected such that an agent-wise local gain condition is less than one, wherein a locally-controlled agent matrix of the vehicle is Hurwitz, and wherein an observer gain, H i , is selected such that the locally-observed agent matrix on the vehicle is Hurwitz.

5. The method of claim 4 , wherein each vehicle of the group of vehicles is detectable based on an output matrix.

6. The method of claim 4 , wherein the controller state signal, z i (t), is defined by

ż i ( t )= M 1i z i ( t )+ M 2i e vi ( t )+ M 3i y mi ( t ),

wherein each vehicle of the group of vehicles is detectable based on a measurement output matrix, and wherein the method further comprising

receiving, at the electronic processor, data from a plurality of vehicle sensors of the vehicle;

determining, with the electronic processor, the local measurement output signal based on the data received from the plurality of vehicle sensors; and

determining, with the electronic processor, the self-navigation input control signal based on the local measurement output signal.

7. The method of claim 4 , further comprising

determining, with the electronic processor, a self-state signal; and

determining, with the electronic processor, the self-navigation input control signal based on the self-state signal.

8. A system for controlling motion of a vehicle in a group of vehicles, the system comprising

a communication interface;

a vehicle platform for travelling among the group of vehicles; and

an electronic processor configured to

determine a local virtual tracking error signal,

determine a controller state signal,

determine a self-state signal, and

determine a self-navigation input control signal based on the local virtual tracking error signal, the controller state signal, and the self-state signal,

wherein the self-navigation input control signal is for navigating the vehicle platform when travelling as a member of the group of vehicles, wherein a trajectory of an exosystem is based on a boundedness condition, wherein the trajectory of the exosystem including external disturbances and a trajectory of a leader vehicle of the group of vehicles, wherein the vehicle communicates with other vehicles in the group of vehicles via a fixed augmented directed connected communication graph topology, wherein each vehicle in the group of vehicles is stabilizable, wherein each vehicle in the group of vehicles satisfies a transmission zero condition, wherein design matrices of the vehicle satisfy an internal model principle,

wherein the self-navigation input control signal, u 1 (t), is defined by:

u i ( t )= K 1i x i ( t )+ K 2i z i ( t ),

wherein K 1i and K 2i are controller gains, x i (t) is the self-state signal at time, t, and z i (t) is the controller state signal at the time, t, wherein the controller state signal, z i (t), is defined by:

ż i ( t )= G 1i z i ( t )+ G 2i e vi ( t )

wherein G 1i and G 2i are design matrices, and e vi (t) is the local virtual tracking error signal at the time, t.

9. The system of claim 8 , wherein the vehicle platform comprises an underwater, ground, aerial, or space vehicle.

10. The system of claim 8 , wherein the group of vehicles travel over time in a one-dimensional spatial system, a two-dimensional spatial system, or a three-dimensional spatial system.

11. The system of claim 8 , wherein the internal model principle comprises an N p-copy internal model principle.

12. The system of claim 8 , wherein the group of vehicles travel over time to reach a common destination.

13. The system of claim 12 , wherein the common destination comprises a fixed destination or a destination that changes over time.