Renren potential field method

Hello everyone , I meet you again , I'm your friend, Quan Jun .

The artificial potential field method is Local path planning A common method of . This method assumes that the robot moves in a virtual force field .

One 、 brief introduction

As shown in the figure , The robot moves in a two-dimensional environment , The figure shows the robot , The relative position between the obstacle and the target .

This figure clearly illustrates the role of the artificial potential field method , The initial point of the object is at a higher “ Hilltop ” On , The target point to reach is “ foot of a hill ” Next , This forms a potential field , The object is guided by this potential , Avoid obstacles , Reach the target point .

Artificial potential field includes gravitational field and repulsive field , Where the target point generates gravity on the object , Guide an object towards its motion （ It's a bit like A* Algorithm Heuristic function in h）. Obstacles repel objects , Avoid collision with objects . The resultant force on an object at each point in the path is equal to the sum of all repulsion and gravity at this point . The key here is how to construct the gravitational field and repulsive field . Let's discuss them separately ：

Gravitational field ：

The commonly used gravitational function ：

there ε It's the scale factor .ρ(q,q_goal) Indicates the distance between the current state of the object and the target . The gravitational field has , Then gravity is the derivative of the gravitational field with respect to distance （ Analogical physics W=FX）：

The gradient algorithm can refer to relevant materials , To put it briefly , The gradient of a binary function is purple [δx,δy], This sign is the partial derivative , Not quite right , Forgive me .

Fig . Gravitational field model

Repulsive field ：

The formula （3） Is the traditional repulsion field formula , It's not clear how it was derived . In the formula η Is the repulsion scale factor ,ρ（q,q_obs） Represents the distance between an object and an obstacle .ρ_0 Represents the influence radius of each obstacle . In other words , Leave a certain distance , Obstacles have no repulsive effect on objects .

Repulsion is the gradient of the repulsive field

Fig Repulsive field model

The total field is the superposition of the gravitational field in the case of repulsion , That is to say U=U_att+U_rep, The total force is also the superposition of the corresponding component forces , As shown in the figure below ：

Two 、 The problem is

（a） When the object is far from the target point , Gravity will become very large , The relatively small repulsion force is even negligible , Obstacles may be encountered in the path of the object

（b） When there is an obstacle near the target point , The repulsion will be very large , Gravity is relatively small , It's hard for an object to reach the target point

（c） At some point , Gravitation and repulsion are just equal , In the opposite direction , Then the object is easy to fall into local optimal solution or oscillation

3、 ... and 、 Various improved versions of the artificial potential field method

（a） For problems that may encounter obstacles , It can be solved by modifying the gravitational function , Avoid excessive gravity due to too far away from the target point

and （1） Compared with ,（5） The formula adds a range limit .d*_goal A threshold is given to limit the distance between the target and the object . The corresponding gradient, that is, gravity, becomes ：

（b） There are obstacles near the target point, which leads to the problem that the target is unreachable , A new repulsion function is introduced

Here, based on the original repulsive field , Plus the influence of the distance between the target and the object ,（n Positive number , I saw a document n=2）. Intuitively speaking , When the object approaches the target , Although the repulsive field increases , But the distance is decreasing , Therefore, it can drag the repulsive field to a certain extent

The corresponding repulsion becomes ：

So you can see that gravity here is divided into two parts , Pay special attention when programming

（c） The local optimization problem is a big problem of the artificial potential field method , Here you can add a random disturbance , Let the object jump out of the local optimal value . Similar to the solution of local optimal value of gradient descent method .

Four 、 Code sorting

online matlab The code written is mixed ,bug quite a lot , Validating , It will be posted after passing .

It integrates various codes on the Internet , The discovery is basically from one person matlab code, Then change it to your own . But which version did you start with code There should be a lot of mistakes , In particular, it focuses on calculating the sub functions of angle and repulsion , After many people's modification , This code has been relatively improved , Sort it out , Specific implementation can refer to ： Improved version maltab Program

A foreign friendly matlab Artificial potential field method program （ Detailed description document attached ）

The data link

A preliminary study of path planning algorithm http://blog.csdn.net/u011978022/article/details/49912515

Research on artificial potential field method http://kovan.ceng.metu.edu.tr/~kadir/academia/courses/grad/cs548/hmws/hw2/report/apf.pdf

Artificial potential field method http://letsmakerobots.com/artificial-potential-field-approach-and-its-problems

An improved version of the artificial potential field method http://www.doc88.com/p-738493052458.html

Artificial potential field method Forum http://www.ilovematlab.cn/thread-188840-1-1.html

Artificial potential field method matlab Program end shock version ：http://download.csdn.net/detail/programming2015/8589191#comment

Introduction to artificial potential field method PPThttp://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf

Artificial potential field method matlab Program improvement successful version ：http://www.ilovematlab.cn/thread-93531-1-1.html

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