E28: Mobile Robotics - Fall 2015 - HOMEWORK 7
Background
The hw7 gate.py (Python) and the hw7 gate.m (MATLAB) examples from the course website show how an artificial potential function could be used to steer a robot through a "gate" made from two pylons. Download either of the two examples, read over it, and run it before answering the following questions (please type your answers).
When you run it, you will see four plots corresponding to four different starting positions of the robot. Each plot is titled to indicate the starting point in the gate's coordinate frame, along with indications of whether the robot hit a pylon, and whether the robot successfully made it between the pylons to get through the gate. A run is considered successful when the robot doesn't hit the pylon and goes through the gate.
1. Getting through the gate
Increase the k_gate constant until the robot successfully passes through the gate from each starting point (I'd start at about 0.5 and ramp up from there). Then, gradually increase t_gate and k_gate together until the robot goes through the pylons without collisions.
a. What values worked out well for the two constants?
b. Describe what happens to the potential field (contour plot) and the resulting force vectors (arrow plot) as you modified these values.
2. Potential function
Alas, I didn't comment my code. Good thing you're here to make sense of it.
a. What is the purpose of the U_x component of the potential? The U_y component? U_obs?
b. Consider the two infinite rays extending up and down along the y-axis from the points at y ± gate_rad. Explain how the d_obs variable computes the distance from any point (x, y) to the nearest point on either ray. Why does computing the absolute value |y| come into play here?
c. What is the purpose of the variable close being used as an index into the d_obs array?
d. Sketch (or graph) a plot of the relationship between d_obs (independent variable) and the U_obs potential component (dependent variable). Clearly indicate where t_gate is on the x-axis.
3. Getting stuck
Why does the robot seem to get stuck when you set k_gate to 3.0 and t_gate to 1.0? What undesirable phenomenon does the potential function develop?
4. Checking for collisions
Explain how the collision checking code involving dpy1on works.
5. Computing forces
Explain how the code inside force_at can be said to be taking a "poor man's gradient" of the potential function. Why is this easier to code than computing the correct analytic gradient?
6. Integrating forces
Outline the method being used to simulate the robot motion in integrate_forces. What configuration space does our simulated robot live in? Are we explicitly modeling the robot's orientation?
Attachment:- Assignment.rar