hungdche / 2d-localization

Interactive Simulation for 2D Localization

2D Localization

This is an interactive simulation to visualize 2D Simulation using SDL graphic library. This project was developed mainly as a way for me to wrap my head around different techiniques in robotic localization, and what is more beginner-friendly that starting things off in 2D?

I have also compiled this project into WebAssembly and deployed it on Github, which is available here: hungdche.github.io/2D-Localization

Prerequisites

• SDL2: Make sure to have installed SDL2 Version at least 2.0.20. Visit https://wiki.libsdl.org/SDL2/Installation for installation instruction. It is recommded that you install from source instead of libsdl2-dev from apt, since SDL version on apt is 2.0.10.
• Eigen: If you want to build with Emscripten, clone this repo recursively.
• yaml-cpp: Instruction on how to download is here: https://github.com/jbeder/yaml-cpp

Installation

    git clone https://github.com/hungdche/Localization-Simulation.git
    cd 2D-Localization
    mkdir build && cd build 
    cmake ..
    make -j

Features

In this simulation, a vehicle (grey square). is equipped with a camera, IMU, and Lidar. To replicate the real world scenario, IMU and Lidar data is infused with additive zero-mean Gaussian noise, modal as below. (Camera are mostly for direction visualization, and does not affect localization).
The task is to use each or a combination of sensors to try and localize the vehicle using Kalman Filter and its derivative. The cyan square indicated the estimated pose of the vehicle.

The basic movements are:

• Left, Right button: steer left/right
• Up button to accelerate in the positive direction
• Down button to accelerate in the negative direction
• n to reset the predicted pose
• l to switch between editting mode and simulating mode
• Space to brake
• Enter to randomly spawn obstacles of random sizes, can be drag around

You can specify things like max speed, noises and biases for sensors, and noise covariance matrices in configs/config.yaml. You can add more parameters by modifying include/core/parser.hpp

Method

The state vector that we always want to estimate is $\mathbf{x} = \left[ x,y,\theta \right]^T$, where $[x,y]$ is the location, and $\theta$ is the angle with respect to the y axis.

IMU Simulation Model

To try and replicate real-world IMU data, both the accelerometer and gyroscope are influenced by additive white noise and random walk.

• $\tilde{a}(t) = a(t) + b_a(t) + n_a(t)$ and $\tilde{w}(t) = w(t) + b_w(t) + n_w(t)$
  • noise can be simulated as follows: $n[k] = \sigma_{d}w[k]$
    • where $w[k] \sim \mathcal{N}(0,1)$ and $\sigma_{d} = \sigma \dfrac{1}{\sqrt{\Delta t}}$
  • bias can be simulated as follows: $b[k] = b[k-1] + \sigma_{d}w[k]$
    • where $w[k] \sim \mathcal{N}(0,1)$ and $\sigma_{d} = \sigma \sqrt{\Delta t}$

For more information, refer here:

• https://github.com/ethz-asl/kalibr/wiki/IMU-Noise-Model
• https://www.mathworks.com/help/nav/ref/imusensor-system-object.html