Worksheet

U2.6 Go to a point

Kinematics and frames · University · about 25 min

What this lesson is about

The first useful controller: a vector to the target, straight through the inverse kinematics.

• What is going on
• Where the position came from
• Stopping

Questions 6 marks in all

1. [1 mark]The go-to-point controller sets its speed from the gap to the target. What does this print?

   for gap in (60.0, 28.0, 10.0, 3.0):
       speed = min(14.0, max(4.0, 0.5 * gap))
       print(gap, speed, "stop" if gap < 4 else "drive")

2. [1 mark]The target is 30 cm east and 40 cm north of the robot. What does this print?

   import math
   dx, dy = 30.0, 40.0
   gap = math.hypot(dx, dy)
   speed = min(14.0, max(4.0, 0.5 * gap))
   wx, wy = speed * dx / gap, speed * dy / gap
   print(gap, speed, round(wx, 1), round(wy, 1))

3. [1 mark]A student writes wx, wy = speed * dx, speed * dy, leaving out the division by gap. What goes wrong?

   1. AThe effective gain depends on how far away the target is, so the robot behaves differently on long and short runs
   2. BThe robot heads in the wrong direction
   3. CNothing, because speed is already capped at 14
   4. DThe robot can never get within 4 cm, because the velocity is always zero

4. [1 mark]How should the stopping threshold, gap < 4, be chosen?

   1. ALarger than the distance the robot coasts from the speed it arrives at, or it sails past and hunts
   2. BAs small as possible, since a smaller threshold is always more accurate
   3. CEqual to the robot's radius
   4. DSmaller than the noise on position(), so noise cannot trigger a stop

5. [1 mark]The robot starts at world (60, 60), and position() counts from where it started. How far is a target at world (100, 45) from the start, in cm to one decimal place?

6. [1 mark]This controller reads position(), which U1.3 called the lab's overhead camera. Why is that acceptable here?

   1. AThe subject is kinematics for now, and from U6 an estimate the robot works out for itself replaces it under the same loop
   2. Bposition() is what a real robot would use for this controller
   3. CThe inverse kinematics only works with a perfect position
   4. Dodometry() is in the body frame, so it cannot be used with world targets

The task: go to a point

Drive to world (140, 150) and stop within 10 cm of it. The robot starts at (60, 60) facing the wrong way, and position() counts from where it started.

from bugbot import *
import math
connect()

V_MAX, V_LAT = 20.0, 15.0
TX, TY = 80.0, 90.0        # the target, in cm from the start

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/u2-6-go-to-a-point/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Add a heading term so the robot also finishes facing a chosen direction, without changing the path.
2. Feed it a list of points and drive them in order, without stopping at each one.
3. Replace position() with odometry() and run it again. How close does it get now, and how much worse does it get on a longer run?