Q2. What were the three heuristic rules used to animate flocking behavior?
Three heuristic rules were considered by Reynolds to animate flocking behavior: (1) velocity consensus, (2) center cohesion, and (3) collisionavoidance.
Q3. What is the purpose of this paper?
In this paper, a distributed leader–follower flocking algorithm for multi-agent dynamical systems has been developed and analyzed, which considers the case in which the group has one virtual leader and the asymptotic velocity is time-varying.
Q4. What is the goal of this paper?
It has been the goal of this paper to analyze different flocking algorithms by using tools fromnonsmooth analysis in combination with ideas from the study of synchronization in complex systems.
Q5. What is the f vector of the leader?
Rn are its position vector and velocity vector, respectively, and f (ro, vo) is the input vectorwhich governs the dynamics of the leader.
Q6. What is the control input for distributed flocking?
In distributed flocking algorithms, the following control input is of particular interest [20–22,24–26]:ui(t) = f (ri, vi)−∇riV (r)+ c ∑ j∈Ni aij(‖rj − ri‖)(vj − vi)+ f̃i, (3)where the first term is a nonlinear dynamical term, the second term is a gradient-based term, V is the collective potential function to be defined, the third term is the velocity consensus term, f̃i is the navigation feedback based on information about the leader, Ni = {j ∈ V : ‖rj−ri‖ ≤ rs, j 6= i} denotes the neighbors of agent i, rs is the interaction range, and c is the coupling strength of velocity.
Q7. How can flocking be achieved in multi-agent dynamical systems?
As validated by simulations and experiments, flocking can be achieved in multi-agent dynamical systems by various distributed algorithms.∗
Q8. How long can the group move with the same velocity as the leader?
In addition, as long as thevelocity vector of the leader can be observed, all the agents in the group can move with the same velocity as the leader.
Q9. What is the local minimum of V (r)?
It was pointed out [20] that the local minimum of V (r) is an α-lattice and vice versa, which is responsible for collision avoidance and cohesion in the group.
Q10. What is the definition of a set-valued map?
Suppose E ⊂ Rm. A map x → F(x) is called a set-valued map from E → Rm, if each point x in a set E ⊂ Rm corresponds to a non-empty set F(x) ⊂ Rm.
Q11. What is the generalized directional derivative of g at x in the direction w?
The generalized directional derivative of g at x in the direction w, denoted by g0(x;w), is defined asg0(x;w) ≡ lim y→x,t↓0sup g(y+ tw)− g(y)t .
Q12. How did Tanner and others design flocking algorithms?
In order to embody the three Reynolds’ rules, Tanner et al. designed flocking algorithms in [24,25], where a collective potential function and a velocity consensus term were introduced.
Q13. What is the effect of the leader-follower flocking algorithm?
It has been proved that although each informed agent can only obtain partial information about the leader, the velocity of the whole group converges to that of the leader and the centroid of those informed agents, having the leader’s position information, follows the trajectory of the leader asymptotically.
Q14. what is the directional derivative of vij?
The classical directional derivative of−Vij at rs is given by−V ′ij(rs;w) = limt↓0 −Vij(rs + tw)− (−Vij(rs)) t .Ifw ≥ 0, then−V ′ij(rs;w) = limt↓0 Vij(rs)−