udacity lesson 5: robot motion

19. FEBRUARY 2014

UDACITY LESSON 5:ROBOT MOTION

Agenda›Path Smoothing›PID

2

Motivation› In motion planning, we learned to plan a path

› But how do we turn that discrete path into an actual continuous path, that the robot can follow efficiently?

› Additionally, how do we get the robot to follow the path – how do we control its motion?

3

Path Smoothing›Until now, all paths have been straight and discrete, divided into grids, like this:

4

Path Smoothing›We’d rather have a line that a robot can follow at a constant speed, and as short as possible. A bit like this:

5

Path Smoothing

6

›The first criterion minimizes distance between original and smooth -> favors the original path

›The second criterion minimizes distance within the smoothed path -> favors a pile of points in one place

Path Smoothing›Weighing these terms can yield a smooth path:

7

Path Smoothing›We can use gradient descent optimization with the following update rules for each iteration:

›Where they each correspond to one of the previously stated terms

8

Path Smoothing›Finally, we might want to add a term that avoids obstacles to our system:

9

Path Smoothing›Demo: ›Pathsmooth.m

10

PID control›Control theory is about how to adjust our system to interact with the real world.

›In the case of a robot, it will mostly be connected to moving around.

›We use sensor input as the robots “senses”. The controller is then the brain that takes this input and converts it to the correct motion.

11

PID Control›The most common type of controller is the PID:

12

PID Control›P: Proportional control. Drives the system based on the current error.

›I: Integral control. Drives the system based on an integral of past errors. Removes steady state error.

›D: Derivative control. Drives the system based on a derivative of past errors 13

PID Control›So how to implement this?

›Or maybe in code:

14

PID Tuning›We need values for Kp, Ki and Kd.

›These must fit the physical properties of the system we control. Motor speed, robot weight, turn radius etc.

15

PID Tuning›There are a lot of methods for finding these parameters. Two examples:

›Twiddle›Ziegler-Nichols

16

17

Ziegler-Nichols›All gains are set to zero›P is increased until the system oscillates with a constant amplitude. The gains can then be found as:

18

PID Control›Demo:›PIDSmooth.py

19

Discussion

20