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EE 7500 Notes

This markdown keeps all my notes for the RoSE 25 paper which is the final project for EE 7500 MPC class.

TODOS

  • Carefully finish the forward kinematics explanation from Dr. Haber and go through all the 13.3 chaper tutorials from here: https://modernrobotics.northwestern.edu/nu-gm-book-resource/13-3-1-modeling-of-nonholonomic-wheeled-mobile-robots/
  • Find a detailed resource to properly understand the differential drive model. Use [6], [7] or [8] to indicate parameters but be uniform
  • Create a DiffDrive vehicle kinematic model. Note down where Numba based acceleration may be possible.
  • Test DiffDrive model with MPPI on path (1) and save video
  • Put slides togerther and then if time permits try another path

Before submitting report

  • Create a notebook to visualize a different reference path. We showcase at least two paths
  • Test DiffDrive+MPPi on a path 2 (s-curve) and save video
  • Generate ATE error metric and plots
  • Finish report
  • Submit report

For writing report / slide presentation

Paper references

Some papers to quickly write up the EE 7500 report: https://github.com/MizuhoAOKI/daily_paper?tab=readme-ov-file#Model-Predictive-Path-Integral-Control

According to Chatgpt o1 preview, the cost function of Nav2's MPPI controller is as follows

  • Slide showing the steps of sampling-based MPPI controller:

An example image

  • Path tracking error: $C_{\text{path}} = w_{\text{path}} \sum_{t=1}^{N} \left( \text{distance}\left( x_t, \text{path}_t \right) \right)^2$
  • Obstacle Cost: $C_{\text{obstacle}} = w_{\text{obstacle}} \sum_{t=1}^{N} \text{costmap}\left( x_t \right)$

Paper note

  • The test problem is formulated as finite-horizon optimal control problem [1]
  • Mention uses cases such as Tube-based MPPI, Robust MPPI, Covariance Control MPPI, MPOPI, Mode-based Reinforcement Learning
  • We compare the vanilla MPPI controller in MPPI-Generic vs vanilla MPPI controller in Nav2
  • Use the MPPI-Generic paper to write out the initial dynamics equation.

Why chose MPPI

  • [12]
  • [1] and [2] paper

Notes on the skid-steering control model

Modelling and Control of a Skid-Steering Mobile Robot for Indoor Trajectory Tracking Application: This paper validated the dynamics model on the clearpath husky which is what we will use. This will be another way we will verify that the chosen model is valid. video1: Evaluation of Skid-Steering Kinematic Model for Subartic enviornment Modelling, Simulation and Control of a 4-wheeled mobile robot

Notes from Aggressive Driving with Model Predictive Path Integral Control [1]

  • Algorithm 1

An example image

MPPI-Generic

  • Understand how to put the skid-steering kinematics model for a 4 wheel robot. Go through the master thesis and book given by Farid

  • Start a separate repo for a ROS 2 wrapper for MPPI-Generic. Figure out if we can create a node to run the cartpole example correctly.

code, paper, video, website

  • CUDA/C++ accelerated general purpose implementation containing multiple dynamics and cost functions
  • Custom cost function and dynamics can be used
  • Algorithm 1 shows a much more cleaner steps of a general purpose MPPI

An example image

  • The library has 6 core classes

    • Dynamics
    • Cost functions
    • Controllers
    • Sampling Distributions
    • Feedback Controllers
    • Plants

  • By default Feedback controllers are disabled

  • Plants: Is a wrapper around the controller. It handles communication between the controller and the system, like receiving data (e.g., system state) and sending control commands. For platforms like ROS, the Plant sets up subscribers (to get data like robot state) and publishers (to send control outputs) while also converting ROS messages into a format the controller (like MPPI) can use.

  • Considerations for the Plant function: "The Plant houses methods to obtain new data such as state, calculate the optimal control sequence at a given rate using the latest information available, and provide the latest control to the external system while providing the necessary tooling to ensure there are no race conditions."

  • So we need a node class that will implement a MPPI-Generic-Plant object.

  • For this project we don't need to understand how to separate computation of Dynamics and Cost function blocks.

  • Three levels of API structure

    • Beginners: use a provided Dynamics, Cost Function and Controller to control a system. A minimal working example is the cartpole_example.cu
    • Intermediate: Talks about custom dynamics and cost function. Depending on the use-case, some of the methods will be implemented twice, one for CPU and one for GPU.

TO use Mamba in Windows

Open a terminal and paste C:\Users\azmyi\mambaforge-pypy3\Scripts\activate