Target Motion Model

In the robot soccer game, the realization of the vision-based motion state of the target such as the position, speed and acceleration is the basis of the multi-robot's passing coordination, defensive interception, more precise motion planning and control and more effective tactical behavior.

　　Although the motion of the soccer robot is flexible and unpredictable, it is not completely random, and has some inner rules to follow . For example, the motion of a robot is usually to achieve some kind of tactical action, such as moving a position, chasing a ball, playing with the ball, blocking the defense, passing the match, etc. In these cases, the motion of the robot exhibits obvious regularity. For example, the goal of the chase and intercept defensive movement is the soccer and the robot with the ball, the end of the ball movement is the goal position and so on. It is only when the robot fails that a completely irregular movement can occur .

Secondly, the soccer robot is autonomous operation, its internal law is determined by its control algorithm to a certain extent. Conversely, if we can make reasonable assumptions about the control algorithm adopted by the tracked target, we can grasp the motion law of the target. Moreover, the range of motion of a soccer robot is limited. For example, a functioning robot does not run out of the site area, and as a physical system, the robot's ability to move is limited by motor power, wheel and ground friction. These factors can be used as a priori knowledge in the tracking filtering algorithm of soccer robot to improve the accuracy and pertinence of the algorithm .

Selecting the appropriate target motion model is an important part of the design of tracking filter algorithm, and establishing a reasonable motion model can help to predict the future state or trajectory of tracked target accurately, which is an important condition to realize accurate tracking control. In the research of tracking problem, the motion model of the target is mainly represented by the state space model:

$$\textbf{x}_{k+1}=f_k (\textbf{x}_k,u_k,w_k) $$

Among them, the XK is the target state, the UK is the control input, the WK is the process noise, and the FK is the time-related vector function, which determines the motion rule of the target; K is the sampling time and usually corresponds to the time when the measurement is obtained. Because it is not possible to know the true control of the target input UK, it is generally ignored and treated as part of the noise.

1. Quiesce model

In all models, the simplest and most basic model is the stationary model, which is

$$\DOT{X} (t) =w (t) \approx 0$$

where state x=[x] contains only the position component of the target, W (t) is a white noise with a 0 mean and a variance of σ2. The corresponding discrete models are:

$$\textbf{x}_{k+1}=\textbf{x}_k+w_k$$

The stationary model considers that the target is not in motion, and all the unpredictable control and error are white noise interference. Because the model is too idealistic or the target is almost impossible to be stationary, the usual target tracking problem does not take into account the static model described above. However, in a soccer robot game, the target is still in a very high probability, such as the gatekeeper robot in most cases is static, and other play defensive or offensive role of the robot to reach its defensive position or the passing point will also stop to wait for further development of the situation. In these cases, only the stationary model is most consistent with the actual situation of the target movement. Higher-order or more complex motion models take a long time to converge to the stationary state, resulting in greater error.

2. Constant and uniform acceleration motion model

The second-order uniform motion (CV) model is a more common model, also known as a non-motorized model, relative to the stationary model.

$$\begin{bmatrix}\dot{x}\\ \ddot{x}\end{bmatrix}=\begin{bmatrix}0&1 \ 0& 0\end{bmatrix}\begin{bmatrix}x\\ \dot{x}\end{bmatrix}+\begin{bmatrix}0\\ 1\end{bmatrix}w (t) $$

Where the state variable x contains the position and velocity of the target, W (t) is a white noise with a 0 mean. The corresponding discrete model is

$$\begin{bmatrix}x_{k+1}\\ \dot{x}_{k+1}\end{bmatrix}=\begin{bmatrix}1&t \ 0& 1\end{bmatrix}\begin{ bmatrix}x_k\\ \dot{x}_k\end{bmatrix}+\begin{bmatrix}\frac{t^2}{2}\\ t\end{bmatrix}w (T) $$

where T is the sampling interval.

The CV model argues that although the presence of disturbances alters the speed of movement of the target at the next moment, the target is generally uniform motion (non-motorized). The greatest advantage of this model is the simple form, when the target maneuver amplitude is very small or the sampling interval is very short, the motion of the target can effectively approximate to uniform motion . But also as its name, the model is not suitable for occasions where the target movement occurs frequently or drastically.

In the soccer robot game, the target uniform motion usually occurs during the long distance movement. Because the acceleration performance of soccer robot is more prominent, usually only need 0.5~1s time to accelerate from stationary to the desired or even the highest speed, so the soccer robot will usually complete the long distance movement at (highest speed) uniform motion way.

There is also a uniform acceleration (CA) model based on the CV model, in the form of

$$\begin{bmatrix}\dot{x}\\ \ddot{x}\ \ \dddot{x} \end{bmatrix}=\begin{bmatrix}0&1 &0\\ 0& 0&1 \\0 &0&0 \end{bmatrix}\begin{bmatrix}x\\ \dot{x} \ \ddot{x}\end{bmatrix}+\begin{bmatrix}0\\ 0 \\1\end{bmatrix}w (t) $$

In practice, the likelihood of a soccer robot (or other target) to really absorb and accelerate the motion is very small, or it lasts for a very short time. The main function of CA model is to introduce the acceleration state $\ddot{x}$ of the target, and to derive a more reasonable model based on the CA model and to improve the precision and robustness of the tracking filtering algorithm by introducing the acceleration constraint condition.

Reference:

"Robot Vision System Research" Science Press

Target Motion Model