"路径跟踪与编队控制下的多主体协同运动研究"

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The research discussed in this paper focuses on the cooperative control of multiple agents moving along a set of given curves. Specifically, the study examines a group of double-integral agents coordinated to move in a specified manner along a set of predefined curves. A projection tracking design method is proposed to design path tracking control and formation protocols, ensuring that a multi-agent system maintains formation motion under directed communication graphs. Conditions for obtaining control gains to solve coordination issues are established when the directed communication graph has globally reachable nodes. Simulation results of ground-level movement among three agents demonstrate the effectiveness of the proposed method. This research, published in J Syst Sci Complex in 2011, presents a valuable contribution to the field of cooperative control of multi-agent systems moving along specified trajectories.

634 YANGYANG CHEN · YUPING TIAN

where x ∈ R and f

is a C

smooth function of x.

In consideration of a given curve followed by a moving agent, the main idea involved in our

derivation of the path-following control is to vertically project agent i on its given path Γ

and

then to drive agent i to approach to its projection β

asymptotically (see Figure 1). Due to the

fact that the horizontal coordinate of its projection β

is the same as agent i, one can easily

ﬁgure out the position of its projection β

from the dynamics of agent i such that

=[x

]

=[x

)]

. (3)

Normal vector

along the path

Tangent vector

along the path

Figure 1 Path following frame

Let d

(t) denote the diﬀerence in the longitudinal coordinate between agent i and its cor-

responding projection β

. The path following for each agent is achieved by manipulating d

(t)

and its derivative r

(t)=dd

(t)/dt to zero, i.e.,

lim

t→∞

(t)=0, lim

t→∞

(t)=0. (4)

Each agent’s acceleration along the normal vector with respect to its curve will be designed to

meet this requirement.

When each agent moves along its given curve, the description of formation for multiple

agents degenerates into the agreement of positions and velocities of the agents along their given

curves. Noticing the special form (2) of each given curve, only one value of y

associates with

agivenx

. Once the relative abscissa of each pair agents is decided, the relative positions

of agents are uniquely conﬁrmed. Also, the relative positions of agents correspond with one

relative abscissa for each pair. Thus, it is a one-to-one correspondence between the formation

pattern and the relative abscissas of agents. In the simplest case, curve Γ

is obtained by moving

a template curve (e.g., the desired trajectory of the group center) along a desired formation

vector h

=[h

]

as shown in Figure 2. The desired formation z

(t) − z

(t)=h

− h

equal to the form x

(t) − x

(t)=h

−h

. Furthermore, it is obvious that this formation can

be ensured by the consensus of both x

(t) − h

and ˙x

(t). In reality, formation patterns are

complicated and path-dependent. It is hard to use the consensus of x

(t) − h

and ˙x

(t)to

solve all the complicated formation problems. For instance, consider the coordination depicted

in Figure 3, where agents 1 and 2 must follow path Γ

and Γ

while maintaining agent 1 “to-

the-right-ahead” agent 2, that is, along straight line that makes an angle of 150 degree with

the positive direction of path Γ

. Obviously, the relative position for agents 1 and 2 should

satisfy x

(t)=4x

(t). If we choose ξ

= x

and ξ

=4x

, one can easily observe that the

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