Augmented Cucker-smale Flocking Model with Collision Avoidance, Finite-time Control and Chorus-line Effects

Ma, Jing
Lai, Edmund M-K
Moir, Tom
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Doctor of Philosophy
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Auckland University of Technology

Cucker-Smale model is a velocity alignment model that has been used to study the emerging behavior of flocking of multiple self-propelled agents. It has been studied from many different perspectives. In this thesis, several issues that will impact deployment of this model to real physical agents such as robots are studied.

The first issue relates to whether the Cucker-Smale model is actually a flocking model. A technical definition of flocking that involves velocity alignment and a concept introduced here called flock diameter is first proposed. While the original Cucker-Smale model can produce velocity alignment, it has been shown to be inadequate in controlling the flock diameter. There is also no guarantee that collisions among agents will not occur. A new augmented Cucker-Smale model is proposed that can potentially be used to control the flock diameter and to prevent agent collisions. This augmented model is based on the use of cohesive and repulsive forces and is simpler in form compared with similar models in the literature. A bounded symmetric cohesion and repulsion function is also proposed to be used with this model. Its boundedness allows it to be implemented in real systems and therefore more practical than unbounded repulsive forces proposed in existing literature.

The second issue relates to how fast the Cucker-Smale system could achieve flocking from a random initial configuration. In order to derive an upper bound on the flocking time, finite-time control is applied to the augmented Cucker-Smale model. We are able to mathematically prove that this finite-time controlled model converges both asymptotically and in a finite time. Simulation confirmed that the results are correct although this bound is not tight. It has also been discovered that the finite-time control parameters should be at the lower end of the allowable range in order to obtain the best flocking times.

The third issue is to do with the fact that the clocks of physical agents are typically not synchronized. A block-sequential approach, rather than random delay used in existing literature, is used to model the fact that each agent’s state is updated or computed at regular time intervals according to its own clock. Simulations show that asychronicity does increase the flocking time in a significant way. Furthermore, results seem to suggest that this added time is relatively immune to the degree of asynchronicity as the size of the flock becomes larger.

The fourth issue is related to the uncertainty in estimating a neighbor's velocity and the round-off errors in computation. These are modeled as additive noise to the update equation of the model. It is confirmed that a small amount of noise reduces the velocity alignment time. However, large noise could destabilize the system.

The remaining two issues are associated with perturbation to the flocking state. They are related to a leader-follower Cucker-Smale system where there is a leader agent and the rest of the agents use the Cucker-Smale update method to align with the leader. In the context of human-swarm or human-flock interaction, we need to know how often could a human operator issue change-of-direction commands to the flock without it becoming dispersed. Our study shows that the realignment time could be used as a design guide for neglect benevolence. If change-of-direction commands are issued too frequently, the cohesiveness of the flock will be destroyed. The second is based on an observed phenomenon known as the chorus-line effect. It is also a sudden change in direction initiated by one or a few birds. But the speed by which the rest of the flock follows this change appears like to speeding propagating wave. Previous research on the chorus-line effect that has been observed in bird flocks used the wave propagation approach. However, this approach could not be transformed into an agent-based model for implementation. An adaptation of the Cucker-Smale model, called the CS-CL model, to incorporate the chorus-line effect is proposed for the first time. Simulations show that realignment times could be reduced using this model.

Cucker-Smale , Flocking , Collision avoidance , Finite-time control , Chorus-line effects
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