「3pi Line Follower」
「Heuristic-based Algorithm」
- 直接看Line Follower在程式核心部份所使用的heuristic演算法
// This is the "main loop" - it will run forever.
while(1)
{
// Get the position of the line. Note that we *must* provide
// the "sensors" argument to read_line() here, even though we
// are not interested in the individual sensor readings.
unsigned int position = read_line(sensors,IR_EMITTERS_ON);
if(position < 1000)
{
// We are far to the right of the line: turn left.
// Set the right motor to 100 and the left motor to zero,
// to do a sharp turn to the left. Note that the maximum
// value of either motor speed is 255, so we are driving
// it at just about 40% of the max.
set_motors(0,100);
// Just for fun, indicate the direction we are turning on
// the LEDs.
left_led(1);
right_led(0);
}
else if(position < 3000)
{
// We are somewhat close to being centered on the line:
// drive straight.
set_motors(100,100);
left_led(1);
right_led(1);
}
else
{
// We are far to the left of the line: turn right.
set_motors(100,0);
left_led(0);
right_led(1);
}
}
- 我們發現, heuristic演算法靠著sensor所回傳的黑白比例, 來做為左右轉或直走的依據; 並且, 轉彎時始終保持單一速度。
「PID control-based Algorithm」
PID分別為proportional–integral–derivative的縮寫, 它被廣泛應用在溫度、流量或是電機傳動等等的控制上, 其理論基礎這篇文章沒辦法細說, 但概念上我們可以透過下面的說明來瞭解。 首先以Line Follower這個例子來講, 底下我們分別說明proportional、integral及derivative:- Proportional: 「比例」, 經由sensor所傳回量化後的值, 我們可以算出3pi位於白底或黑線上的比例為何, 這就是「P」值
- Integral: 「積分」, 「I」值紀錄了3pi的活動軌跡, 也就是在一段運行時間中, 其「P」值的加總
- Derivative: 「微分」, 「D」值紀錄了前後「P」值的「差」
[註一]: 目前weighting值是turing得到的(所以稱為magic number), 但是, 有許多的研究針對「如何turing」提出很多新的方法, 底下截圖來自wiki [1]上針對不同方法的優缺點所做的整理, 有興趣的話倒是可以試試這些方法
- PID Algorithm的Source Code
// This is the "main loop" - it will run forever.
while(1)
{
// Get the position of the line. Note that we *must* provide
// the "sensors" argument to read_line() here, even though we
// are not interested in the individual sensor readings.
unsigned int position = read_line(sensors,IR_EMITTERS_ON);
// The "proportional" term should be 0 when we are on the line.
int proportional = ((int)position) - 2000;
// Compute the derivative (change) and integral (sum) of the
// position.
int derivative = proportional - last_proportional;
integral += proportional;
// Remember the last position.
last_proportional = proportional;
// Compute the difference between the two motor power settings,
// m1 - m2. If this is a positive number the robot will turn
// to the right. If it is a negative number, the robot will
// turn to the left, and the magnitude of the number determines
// the sharpness of the turn.
int power_difference = proportional/20 + integral/10000 + derivative*3/2;
// Compute the actual motor settings. We never set either motor
// to a negative value.
const int max = 60;
if(power_difference > max)
power_difference = max;
if(power_difference < -max)
power_difference = -max;
if(power_difference < 0)
set_motors(max+power_difference, max);
else
set_motors(max, max-power_difference);
}
- PID short summary
PID control uses continuous functions to compute the motor speeds, so that the jerkiness of the previous example can be replaced by a smooth response. [2]
- 上面這句話是節錄自3pi的使用文件中, 這句話完全說明了整個PID control的精神, 以及使用後所帶來的好處。
- 如果翻成中文, 再加上自己的一些解釋之後, 可以這麼說的: 在Heuristic Algorithm下運作的3pi流暢度低於PID control Algorithm, 因為PID control Algorithm使用了連續函式, 物理意義上可以說它考慮了前後軌跡, 來做為下一個行進路線的參考, 相較於Heuristic Algorithm忽略前面一個軌跡, 3pi在使用PID control Algorithm的行進當然會比較順!
「Experiments」
- 實驗目標及方向很明確, 我們想要證明: 3pi在使用PID control-based Algorithm時會比使用Heuristic Algorithm走得順, 沒錯, 就是要證明一個字 → 順!
- 底下我們直接展示兩種不同演算法在3pi上的成果, 相信大家都看得出來哪一個比較smooth
- Heuristic Algorithm
- PID control-based Algorithm
「Conclusion」
Line Follower, 常被拿來當成機器人競賽的項目, 而賽車比賽中的勝負常常在轉彎的時候來決定, 從本篇文章實驗的部份就可發現不同的方法影響了轉彎時不同的流暢度, 它靠的是PID control-based Algorithm比Heuristic-based Algorithm多考慮了歷史的軌跡。然而, PID control-based Algorithm畢竟採用的是magic number, 如何讓這些參數變得更有意義將會是未來研究上的議題。
「Reference」
- http://en.wikipedia.org/wiki/PID_controller
- http://www.pololu.com/docs/0J21/7
