Algorithm

Tianbotmini is a platform for quick introduction to the theory and knowledge of mobile robots.

Mobile robot kinematics model

Tianbotmini is a two-wheel differential mobile robot, which can be simplified to the motion of a particle and a kinematic model is established.

The kinematic equation of the mobile robot can be expressed as:

\[\begin{split}\begin{cases}\dot{x}=v\cos(\theta) \\\dot{y}=v\sin(\theta) \\\dot{\theta}=\omega \end{cases}\end{split}\]

Paths and trajectories

The path of the mobile robot is only related to the position, and the trajectory is not only related to the position, but also constrained by time.

Multiple mobile robots

Multiple mobile robots exhibit better performance and become a hot field of mobile robot research.

Leader follower formation

The formation of the leader and the follower requires the leader and the follower to maintain a relative positional relationship. We determine the positional relationship by setting relative distance and relative angle. As shown in the image below:

According to the geometric relationship in the figure, we can get the following equation:

\[\begin{split}\begin{cases}l_{x}=\left(x_{L}-x_{F}-d\cos\left(\theta_{F}\right)\right)\cos\left(\theta_{L}\right)+\left(y_{L}-y_{F}-d\sin\left(\theta_{F}\right)\right)\sin\left(\theta_{L}\right) \\l_{y}=-\left(x_{L}-x_{F}-d\cos\left(\theta_{F}\right)\right)\sin\left(\theta_{L}\right)+\left(y_{L}-y_{F}-d\sin\left(\theta_{F}\right)\right)\cos\left(\theta_{L}\right) \end{cases}\end{split}\]

We need to know how the error changes, after derivation of the above formula, we can get the following equation: Here, we use a control law that linearizes the input and output.

\[\]

textbf{e}=-textbf{k}dot{textbf{e}}

Formation change

When multiple mobile robots move in a certain formation, they will switch formations according to the needs of the task. The following are common formations.

References

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