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Python代写|Assignment代写 - CSC477 – Introduction To Mobile Robotics

时间：2020-11-12

CSC477 – Introduction To Mobile Robotics

assignment 3, 15 points

due: Nov 18, 2020, at 3pm

Course Page: http://www.cs.toronto.edu/~florian/courses/csc477_fall20

Overview: This assignment deals with estimation and mapping. You will implement occupancy grid

mapping based on 2D LiDAR observations and known poses. You will also implement a simplified version

of GraphSLAM for range observations to uniquely identifiable landmarks. Finally, you will write down the

main components of an Extended Kalman Filter for a localization problem.

1 Occupancy grid mapping (5pts)

In this exercise you are going to implement parts of the occupancy grid mapping system discussed in class.

In particular, you are going to map an environment based on known odometry estimates and known 2D laser

scans. Do git pull under your CSC477 repository to get the starter code. The functionality that you need

to implement is marked using to-do comments in the file estimation_assignment/python/occupancy_

grid_mapper.py. To run your code, cd path/to/csc477_fall20/estimation_assignment and execute

the following commands on three different terminals:

rosbag play laser_and_odometry.bag

roslaunch estimation_assignment occupancy_grid_mapping.launch

odometry_orientation_noise_std_dev:=2.5

odometry_position_noise_std_dev:=0.1

rosrun rviz rviz

When rviz initializes, go to File > OpenConfig and then load the configuration file in estimation_

assignment/resources/comp417.rviz which is going to start the visualization of laser scan messages,

frames of reference, and debugging visualizations. Save this configuration file as the default in your

/home/username/.rviz/default.rviz, so you won’t have to do this every time you restart rviz. In

the roslaunch command given above, the standard deviation of the odometry orientation noise is given

in degrees. In this example the true yaw of the robot is corrupted by random noise from N (0, 2.52).

Similarly, the true position is corrupted by random noise from N (0, 0.12), which is expressed in meters.

laser_and_odometry.bag is a recording of laser scans and odometry data in the environment you used in

Assignment 1. The expected result for perfect odometry looks similar to Figure 1.

Figure 1: Part of the robot’s mapping task during the (0,0) noise trajectory.

What you need to submit: 5 images of maps produced by your mapper, with noise parameters (0, 0), (2.5,

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CSC477: Introduction to Mobile Robotics - Assignment 3

0), (5, 0), (2.5, 0.1), (5, 0.1) respectively. Your images should be named map_[0|1|2|3|4]_firstname_

lastname.png. Also, submit a video recording of the rviz visualization for the odometry noise combi-

nation (0,0), demonstrating your map being built from beginning to end. Your video should be named

map_0_firstname_lastname.mp4/avi/ogg.

2 Least squares localization (5pts)

In this exercise you are going to solve the localization problem in a map of known landmarks. In partic-

ular, assume your robot has 2D state xt = [px(t) py(t)]

T and an omnidirectional motion model xt+1 =

xt + utδt + wt, where wt ∼ N (0, σ2wI) is zero-mean Gaussian noise. The robot is moving through an en-

vironment that has L static landmarks l1, ..., lL whose positions are known. Occasionally, the robot makes

the following set of measurements: z

(i)

t = ||xt − li|| + nt where nt ∼ N (0, σ2n), for some of the available

landmarks. Your goal is to estimate the sequence of states x1:T by minimizing a least squares cost function.

You can find starter code in estimation_assignment/python/localization.py. It provides the set of

measurements made at each timesteps. Your task is to implement the cost function using numpy and the

nonlinear least squares solver in scipy.optimize.least_squares. There are to-do comments in the code

that explain in detail what you need to implement. After you are done with your implementation, the

expected outcome is the following figure:

Figure 2: The robot starts at (0,0) and moves throughout the world, making measurements of static, known

landmarks.

What you need to submit: your code in the file estimation_assignment/python/localization.py.

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CSC477: Introduction to Mobile Robotics - Assignment 3

P.S.: You can think of cell phone localization based on static cell towers as a particular application of

this problem.

3 Extended Kalman Filter (5pts)

Assume you have a robot that follows Dubins car dynamics on the plane. Its state is xt = [px(t) py(t) θ(t)].

Also assume that you have three landmarks li = [l

(i)

x l

(i)

y ] in the world. At each point in time the robot

observes all three landmarks, with some sensor noise. The measurement model consists of the Euclidean

distances from the robot’s current state to each of the three landmarks, plus noise. Formulate an EKF

estimator for this problem. Specifically, formally define the dynamics model, the observation model, their

Jacobians, and the covariances of their noise processes. There is no implementation required for this question,

but if you want to do it, you can find starter code at path/to/csc477_fall20/filtering_examples/

python. Submit your work for this question as a pdf document or as a scanned image of your handwritten

solution.

4 How to submit

Submit all your work in a file called estimation_assignment.zip that contains your extensions to the

provided starter code, as well as the five images, the video, and the pdf file. Submissions will be done on

Quercus.

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