SLAM

An attempt at implementing Simultaneous Localization And Mapping (SLAM). Computer Vision Final project THU Spring 2024 Both LIDAR 2D SLAM and Visual SLAM are implemented.

The SLAM Problem

Given:

• A robot's controls
  • U = {u_1, u_2, ..., u_k}

The odometry measurements over all time frames from t=0 to t=k (speedometer, gyroscope, etc.). Over time, if we only rely on these to determine path of robot, there will be accumulated error which leads to a grossly wrong path. Thus the need for SLAM.

• Relative observations
  • Z = {z_1, z_2, ..., z_n}

The observations taken from the robot of the landmarks. (Could be from camera, radar, lidar, etc. ?). Has some uncertainty.

Wanted:

• Map of features
  • m = {m_1, m_2, ..., m_n}

The features are the landmarks. Each m_i describes the location of the i-th landmark.

• Path of the robot
  • X = {x_0, x_1, ..., x_k}

Each x_i describes the position of the robot at time i.

Graph-Slam

We can represent our problem using Graphs (nodes connected with edges).

• Each node represents a position (location)
• Edges between two nodes represent a constraint
• Constraints can happen due to:
  • odometry measurement
  • the robot observes the same part of the environment (landmark)

Creating edges

If: robot moves from x_i to x_i+1 according to odometry measurements:

If: robot observes the same part of the environment from x_i and x_j

Nodes

Can represent

• Robot positions
• Feature (landmarks) positions

Idea of Graph-SLAM

Build the graph and find a node configuration that minimize the error introduced by the (noisy) constraints