Concept

Software-in-the-loop: Execute at least some part of the software that would run on the robot for simulation or validation.

Hardware-in-the-loop: Execute at least some part of the software on the robot for simulation or validation.

Typical Example: PX4

• PX4 is a software stack for Pixhawk flight controllers
• PX4 uses NuttX as embbedded real-time operating system (Posix)
• The Posix standard allows to compile parts of the firmware on linux as executables
• Used for simulation (PX4 has state estimators and controllers)

Details

Typical Example: Crazyflie

• Crazyflie uses FreeRTOS, not Posix-compliant
• Parts of the firmware can be compiled as library, with Python bindings
• Testing/simulation can be done using Python

Advantages / Disadvantages

History

• 2006: Toy project at Mozilla research
• 2009: Official work at Mozilla (10 engineers)
• 2015: first stable release
• 2021: Rust foundation formed (AWS, Huawei, Google, Microsoft, and Mozilla)

Current Usage (According to Github 2023)

Current Usage (According to Github 2023)

Current Usage (According to Stack Overflow 2024)

Source

Current Admiration (According to Stack Overflow 2024)

Source, Blue=Admired, Red=Desired

Use Cases

Professional Usage

• Firefox Browser
• Datacenter backend (Cisco, AWS)
• Linux drivers (since 2023)
• Rust Case Study (Fulton et al. 2021)

Academia

• Why Scientists Are Turning to Rust (Perkel 2020)

Core Concepts

• Syntax similar to C/C++
• Compiled, strongly typed
• No garbage collection
  • Compile-time checks for memory safety (Borrow-checker)
• Integrated build system and package manager

Learning Resources

• https://www.rust-lang.org/learn

Comparison to Other Languages

• Python
  • Compiled (instead of interpreted), strongly typed (rather than scripting language), harder to use, fewer packages/libraries
• C
  • More features (some of which are not embedded friendly), memory safety guarantees
• C++
  • better module system (integrated package manager), fewer features, fewer packages/libraries

Interoperability (e.g., calling Rust from C/C++ and vice versa) possible

Why Rust in this Course?

A Typical Simulator

x = initial_state()
delta_t = 0.01 # some timestep
t = 0
while KeepRunning:
    y = computeObservation(x) # state estimation
    u = robotBehavior(y, ...) # control / planning
    x = integrateDynamics(x, u, delta_t) # dynamics
    t = t + delta_t

• In the simplest case we have
  • computeObservation(x)=x
  • robotBehavior(...)=fixed value
• integrateDynamics(x, u, delta_t) initial value problem (ODE solver!)

Euler Integration

\[ \mathbf{x}_{t+\Delta t} = \mathbf{x}_t + f(\mathbf{x}_t, \mathbf{u}_t) \cdot \Delta t \]

Classic Runge–Kutta Method (RK4)

\[ \begin{align} \mathbf{x}_{t+\Delta t} &= \mathbf{x}_t + \frac{\Delta t}{6} (k_1 + 2 k_2 + 2 k_3 + k_4)\\ k_1 &= f(\mathbf{x}_t, \mathbf{u}_t)\\ k_2 &= f(\mathbf{x}_t + \Delta t \frac{k_1}{2}, \mathbf{u}_t)\\ k_3 &= f(\mathbf{x}_t + \Delta t \frac{k_2}{2}, \mathbf{u}_t)\\ k_4 &= f(\mathbf{x}_t + \Delta t k_3, \mathbf{u}_t) \end{align} \]

Setting Up Rust

curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
rustup update
cargo new lecture1a
cd lecture1a
cargo build
cargo run

Physics

struct Multirotor1dState {
    z: f32,
    z_dot: f32,
}
struct Multirotor1dAction {
    f1: f32,
}
struct Multirotor1d {
    mass: f32,
    g: f32,
    dt: f32,
    x: Multirotor1dState,
}

impl Multirotor1d {
    fn step(&mut self, action: Multirotor1dAction) {
        let z_new = self.x.z + self.x.z_dot * self.dt;
        let z_dot_new = self.x.z_dot + ((action.f1 / self.mass) - self.g) * self.dt;

        self.x.z = z_new;
        self.x.z_dot = z_dot_new;
    }
}

Physics Demo

fn main() {
    let mut robot = Multirotor1d { 
        mass: 0.1, g: 9.81, dt: 0.1, 
        x: Multirotor1dState { z: 0.0, z_dot: 0.0 } };
    println!("{:?}", robot);
    for _ in 1..100 {
        robot.step(Multirotor1dAction { f1: 1.0 });
        println!("{:?}", robot.x);
    }
}

(Demo the code)

Visualization

Meshcat

• Server runs in the browser (using three.js)
• Client available for Python, C++ (as part of Drake), and Rust

(Small demo of meshcat Rust)

pip install meshcat
meshcat-server --open
cargo new lecture1b
cd lecture1b
cargo add meshcat

1D Multirotor Demo

(Demo the provided example code)

Learned Today

1. Types and use cases of flying robots
2. Dynamics of multirotors (1D and 2D)
3. How to build a simple simulator in Rust

References

Questions