The landscape of hardware engineering is rapidly evolving, demanding more agile and efficient development workflows, particularly for complex control systems. While Python has long been a powerhouse for algorithm development, simulation, and data analysis, its direct application in embedded hardware deployment has traditionally faced significant hurdles. Enter Archimedes, an open-source Python framework designed to bridge this critical gap, offering a “PyTorch for hardware” experience that marries Python’s productivity with the deployability of C/C++.

The Challenge of Hardware Deployment in Control Systems

Developing sophisticated control algorithms in Python is highly efficient. Engineers can leverage a rich ecosystem of libraries like NumPy, SciPy, and CasADi for rapid prototyping, complex mathematical modeling, and high-fidelity simulations. However, embedded systems, which are the backbone of most control applications, typically demand highly optimized C or C++ code for performance, memory efficiency, and real-time constraints. This often necessitates a tedious and error-prone manual translation process from Python prototypes to production-ready C/C++ code.

This manual translation introduces several problems: it slows down iteration cycles, increases the likelihood of introducing bugs, and creates a significant disconnect between the high-level design and its low-level implementation. The vision of a seamless workflow, where an algorithm developed in Python can be directly deployed to hardware, has long been a pursuit for hardware and control engineers.

Introducing Archimedes: Bridging the Python-C Divide

Archimedes emerges as a powerful solution to this challenge. It is an open-source Python framework specifically engineered for the deployment of control systems to hardware. Its core philosophy is to enable engineers to develop and analyze algorithms in a productive Python environment and then automatically generate optimized C code for embedded applications.

Inspired by the success of modern deep learning frameworks like PyTorch and JAX, which allow developers to deploy models developed in Python to various targets, Archimedes aims to bring similar capabilities to the realm of control systems and hardware. It provides a comprehensive toolkit for modeling, simulation, optimization, and, crucially, C code generation, making the transition from algorithm design to hardware deployment significantly smoother.

Key Features and Architectural Strengths

Archimedes is built on a foundation that combines powerful symbolic capabilities with intuitive interfaces, drawing parallels to well-known numerical libraries. Its key features include:

• NumPy-compatible Array API: It offers an array API that is compatible with NumPy, allowing developers to work with familiar numerical operations while benefiting from Archimedes’ underlying optimizations and capabilities.
• Efficient Execution with C++: At its heart, Archimedes can “compile” Python functions into C++ computational graphs. This means that when a compiled function is executed, the entire numerical computation runs in optimized C++ rather than interpreted Python, leading to significant speedups, often 5-10x even on simple benchmarks.
• Automated C Code Generation: This is arguably the linchpin of Archimedes. It allows for the direct generation of optimized C code for embedded applications from Python algorithms. This capability is critical for deploying complex control logic to microcontrollers and other resource-constrained hardware.
• Automatic Differentiation (Autodiff): Archimedes supports forward and reverse-mode sparse automatic differentiation, a fundamental capability for optimization and sensitivity analysis in control system design.
• Interface to Plugin Solvers: The framework provides interfaces to various “plugin” solvers for Ordinary Differential Equations (ODEs), Differential-Algebraic Equations (DAEs), root-finding, and nonlinear programming. This allows engineers to integrate advanced numerical methods directly into their hardware-deployable designs.
• Hierarchical Systems Modeling: For complex systems, Archimedes facilitates hierarchical data structures for parameters and dynamics modeling, akin to PyTorch-style module structures. This promotes modularity and scalability in design.
• JAX-style Function Transformations: It incorporates JAX-style function transformations, enabling advanced manipulation and optimization of computational graphs.

Under the hood, Archimedes leverages symbolic computation tools like CasADi to achieve its automated code generation, converting Python-defined models into efficient C++ code. This eliminates the manual translation burden, drastically reducing development time and potential human error.

The Python-to-C Bridge: A Paradigm Shift

The ability to automatically generate C code from a Python description of a control system is a significant advancement for hardware engineers. Traditionally, mechanical and control engineers, while often adept at numerical analysis, might shy away from extensive programming, especially when it involves low-level languages like C. Python’s user-friendliness, extensive scientific libraries, and automation capabilities make it an ideal language for engineering tasks, from numerical analyses with NumPy and SciPy to automating design features.

Archimedes capitalizes on these strengths. By providing a direct path from Python to C, it empowers engineers to:

• Iterate Faster: Rapidly prototype, test, and refine control algorithms in Python without the overhead of manual C/C++ rewriting.
• Reduce Errors: Minimize bugs introduced during manual code translation, ensuring higher fidelity between the simulated and deployed behavior.
• Improve Maintainability: Keep the “source of truth” in a high-level, readable Python format, making future modifications and updates simpler.
• Leverage Existing Ecosystems: Fully utilize Python’s vast ecosystem for data processing, machine learning, and visualization in conjunction with hardware design.

This approach aligns with a broader industry trend where Python is increasingly used for design automation, testing, and verification in hardware engineering, simplifying tedious tasks and enabling more sophisticated workflows.

Real-World Applications and Best Practices

Archimedes is particularly valuable in industries where complex control systems are paramount, such as aerospace, automotive, and robotics. In these fields, disciplined, systematic approaches are not just beneficial but essential for safety and performance.

A typical workflow might involve:

1. Modeling and Simulation: Defining physics models and control logic in Python using Archimedes’ NumPy-compatible API.
2. Parameter Estimation and Optimization: Calibrating models with real-world data and optimizing control strategies, leveraging Archimedes’ automatic differentiation and solver interfaces.
3. Hardware-in-the-Loop (HIL) Testing: Validating control logic against simulated or actual hardware components.
4. Automated Code Deployment: Generating optimized C code from the validated Python models and deploying it to embedded targets.

This streamlined process ensures that the intellectual property embodied in the Python algorithms is preserved and efficiently translated for high-performance hardware execution, a concept that parallels the deployment pipelines seen in modern machine learning.

Getting Started with Archimedes

As an open-source project, Archimedes can be easily installed via pip:

pip install archimedes-control

For development and access to the latest features, you can also install directly from the GitHub repository:

pip install git+https://github.com/casadi/archimedes.git

Basic Usage Example

Let’s start with a simple example that demonstrates the core workflow of Archimedes - defining a control system in Python and generating C code for deployment.

import archimedes as arch
import numpy as np

# Define a simple PID controller in Python
class PIDController(arch.Module):
    def __init__(self, kp, ki, kd):
        super().__init__()
        self.kp = kp
        self.ki = ki
        self.kd = kd
        self.integral = 0
        self.prev_error = 0
    
    def forward(self, error, dt):
        # Proportional term
        p_term = self.kp * error
        
        # Integral term
        self.integral += error * dt
        i_term = self.ki * self.integral
        
        # Derivative term
        derivative = (error - self.prev_error) / dt
        d_term = self.kd * derivative
        
        self.prev_error = error
        
        # Control output
        return p_term + i_term + d_term

# Instantiate the controller
pid = PIDController(kp=1.0, ki=0.1, kd=0.05)

# Compile to C++ for fast execution
pid_compiled = arch.compile(pid)

# Generate embedded C code for deployment
c_code = arch.generate_c_code(pid, "pid_controller")

# The generated C code can now be deployed to a microcontroller
with open("pid_controller.c", "w") as f:
    f.write(c_code)

This simple example showcases the key advantage: you write the algorithm once in Python and can both execute it efficiently in your development environment and generate optimized C code for embedded deployment.

Advanced Features and Workflows

Automatic Differentiation for Optimization

One of Archimedes’ most powerful features is its built-in automatic differentiation, which is essential for gradient-based optimization in control systems.

import archimedes as arch

# Define a cost function for model predictive control
def cost_function(state, control_input, target_state):
    # State tracking error
    state_error = arch.sum((state - target_state)**2)
    
    # Control effort penalty
    control_penalty = arch.sum(control_input**2) * 0.01
    
    return state_error + control_penalty

# Create a compiled version with automatic differentiation
cost_with_grad = arch.compile(cost_function, with_gradient=True)

# Now we can compute both the cost and its gradient efficiently
state = arch.array([1.0, 2.0, 3.0])
control = arch.array([0.5, 0.3])
target = arch.array([0.0, 0.0, 0.0])

# Compute cost and gradient with respect to control input
cost_value, grad = cost_with_grad(state, control, target)

# Use the gradient for optimization algorithms
print(f"Cost: {cost_value}, Gradient: {grad}")

The automatic differentiation is implemented using sparse methods, making it highly efficient even for large-scale systems with many states and control inputs.

Integration with ODE/DAE Solvers

For dynamic systems modeling, Archimedes provides seamless integration with numerical solvers:

import archimedes as arch

# Define a nonlinear dynamic system (e.g., a pendulum)
def pendulum_dynamics(t, state, control):
    """
    state = [theta, theta_dot]
    control = torque
    """
    theta, theta_dot = state
    g = 9.81  # gravity
    L = 1.0   # pendulum length
    m = 1.0   # mass
    b = 0.1   # damping coefficient
    
    theta_ddot = (control - m*g*L*arch.sin(theta) - b*theta_dot) / (m*L**2)
    
    return arch.array([theta_dot, theta_ddot])

# Create a compiled ODE solver
solver = arch.ode_solver(
    dynamics=pendulum_dynamics,
    method='rk4',  # 4th order Runge-Kutta
    dt=0.01
)

# Simulate the system
initial_state = arch.array([0.5, 0.0])  # Start at 0.5 radians
time_span = (0, 10)  # Simulate for 10 seconds
control_input = 0.0  # No external torque

trajectory = solver.solve(initial_state, time_span, control_input)

# Generate C code for real-time simulation on hardware
c_code = arch.generate_c_code(solver, "pendulum_simulator")

This approach allows you to develop and validate your dynamic models in Python, then deploy the exact same model to embedded hardware with confidence.

Hierarchical System Modeling

For complex systems with multiple interconnected components, Archimedes supports PyTorch-style hierarchical modules:

import archimedes as arch

class Motor(arch.Module):
    """DC motor model"""
    def __init__(self, resistance, inductance, torque_constant):
        super().__init__()
        self.R = resistance
        self.L = inductance
        self.Kt = torque_constant
    
    def forward(self, voltage, current, angular_velocity):
        # Motor electrical dynamics
        di_dt = (voltage - self.R * current - self.Kt * angular_velocity) / self.L
        # Motor torque output
        torque = self.Kt * current
        return di_dt, torque

class Load(arch.Module):
    """Mechanical load model"""
    def __init__(self, inertia, damping):
        super().__init__()
        self.J = inertia
        self.b = damping
    
    def forward(self, torque, angular_velocity):
        # Load mechanical dynamics
        domega_dt = (torque - self.b * angular_velocity) / self.J
        return domega_dt

class MotorDriveSystem(arch.Module):
    """Complete motor drive system"""
    def __init__(self, motor_params, load_params):
        super().__init__()
        self.motor = Motor(**motor_params)
        self.load = Load(**load_params)
    
    def forward(self, voltage, state):
        current, angular_velocity = state
        
        # Compute motor dynamics
        di_dt, torque = self.motor(voltage, current, angular_velocity)
        
        # Compute load dynamics
        domega_dt = self.load(torque, angular_velocity)
        
        return arch.array([di_dt, domega_dt])

# Define parameters
motor_params = {'resistance': 1.0, 'inductance': 0.01, 'torque_constant': 0.1}
load_params = {'inertia': 0.01, 'damping': 0.001}

# Create system
system = MotorDriveSystem(motor_params, load_params)

# Compile for efficient execution
system_compiled = arch.compile(system)

# Generate C code for the entire hierarchical system
c_code = arch.generate_c_code(system, "motor_drive_system")

This hierarchical approach promotes code reuse, makes complex systems more manageable, and ensures that the modular structure is preserved in the generated C code.

Model Predictive Control (MPC) Example

One of the most powerful applications of Archimedes is implementing Model Predictive Control, which requires solving optimization problems in real-time:

import archimedes as arch
import numpy as np

class MPCController(arch.Module):
    """Model Predictive Controller for trajectory tracking"""
    def __init__(self, horizon, dt, system_dynamics):
        super().__init__()
        self.N = horizon  # prediction horizon
        self.dt = dt
        self.dynamics = system_dynamics
    
    def forward(self, current_state, reference_trajectory):
        # Decision variables: control inputs over horizon
        u = arch.MX.sym('u', self.N)
        
        # State predictions over horizon
        x = current_state
        cost = 0
        
        for k in range(self.N):
            # Predict next state
            x_next = x + self.dynamics(x, u[k]) * self.dt
            
            # Add stage cost
            tracking_error = (x_next - reference_trajectory[k])**2
            control_effort = u[k]**2
            cost += tracking_error + 0.01 * control_effort
            
            x = x_next
        
        # Formulate optimization problem
        nlp = {
            'x': u,
            'f': cost,
            'g': []  # Add constraints here
        }
        
        # Create solver
        solver = arch.nlpsol('mpc', 'ipopt', nlp)
        
        # Solve optimization
        solution = solver(x0=np.zeros(self.N))
        
        # Return first control action (receding horizon)
        return solution['x'][0]

# Generate C code for embedded MPC
mpc = MPCController(horizon=10, dt=0.1, system_dynamics=pendulum_dynamics)
c_code = arch.generate_c_code(mpc, "mpc_controller")

The generated C code can then be integrated into a real-time control loop on a microcontroller or embedded Linux system, running at control frequencies of 100Hz or higher depending on the system complexity.

Performance Benchmarking

To demonstrate the efficiency gains, here’s a simple benchmark comparing pure Python, NumPy, and Archimedes compiled code:

import archimedes as arch
import numpy as np
import time

def compute_trajectory(initial_state, num_steps):
    """Simulate a simple system dynamics"""
    state = initial_state
    trajectory = []
    
    for i in range(num_steps):
        # Simple nonlinear dynamics
        state = state + 0.01 * arch.sin(state) + 0.001 * arch.cos(2*state)
        trajectory.append(state)
    
    return arch.stack(trajectory)

# Create compiled version
compute_trajectory_compiled = arch.compile(compute_trajectory)

# Benchmark
initial = arch.array([1.0, 2.0, 3.0])
n_steps = 10000

# Pure Python (for reference, much slower)
start = time.time()
result_python = [initial]
state = initial
for i in range(n_steps):
    state = state + 0.01 * np.sin(state) + 0.001 * np.cos(2*state)
    result_python.append(state)
python_time = time.time() - start

# Archimedes compiled
start = time.time()
result_compiled = compute_trajectory_compiled(initial, n_steps)
compiled_time = time.time() - start

print(f"Python loop: {python_time:.4f}s")
print(f"Archimedes compiled: {compiled_time:.4f}s")
print(f"Speedup: {python_time/compiled_time:.1f}x")

Typical speedups range from 5-10x for simple operations to 50-100x for complex numerical algorithms, making Archimedes suitable for real-time applications even on modest hardware.

Deployment Workflow: From Python to Production

A typical production deployment workflow with Archimedes follows these steps:

1. Algorithm Development and Validation

# Develop and test in Python
controller = MyController(params)
simulator = SystemSimulator(model_params)

# Validate with high-fidelity simulation
for scenario in test_scenarios:
    result = simulator.run(controller, scenario)
    assert result.meets_specifications()

2. Hardware-in-the-Loop Testing

# Test with actual hardware before deployment
hil_interface = HILInterface('/dev/ttyUSB0')

# Run controller in Python, interface with real hardware
for test_case in hardware_tests:
    sensor_data = hil_interface.read_sensors()
    control_output = controller(sensor_data)
    hil_interface.write_actuators(control_output)
    
    # Verify behavior matches simulation
    assert verify_response(sensor_data, control_output)

3. C Code Generation and Optimization

# Generate production C code
c_code = arch.generate_c_code(
    controller,
    function_name="control_step",
    optimization_level=3,
    target_platform="arm-cortex-m4"
)

# Generate header file
h_code = arch.generate_c_header(controller, "control_step")

# Save to files
with open("controller.c", "w") as f:
    f.write(c_code)
with open("controller.h", "w") as f:
    f.write(h_code)

4. Integration and Deployment

The generated C code can be integrated into an embedded project:

// main.c - Embedded system integration
#include "controller.h"
#include "hardware_drivers.h"

int main(void) {
    // Initialize hardware
    init_adc();
    init_pwm();
    init_timer();
    
    // Initialize controller state
    double state[STATE_SIZE] = {0};
    double control_output;
    
    // Main control loop
    while (1) {
        // Read sensors
        double sensor_data[SENSOR_SIZE];
        read_sensors(sensor_data);
        
        // Call generated control function
        control_step(sensor_data, state, &control_output);
        
        // Write to actuators
        write_pwm(control_output);
        
        // Wait for next control period
        wait_for_timer();
    }
}

This approach ensures that the algorithm tested in simulation is bit-for-bit identical to what runs on hardware, eliminating the traditional simulation-to-hardware gap.

Limitations and Considerations

While Archimedes is a powerful tool, it’s important to understand its limitations and appropriate use cases:

When to Use Archimedes

• Complex control algorithms that benefit from rapid prototyping in Python
• Model-based control approaches (MPC, optimal control)
• Systems requiring online optimization on embedded hardware
• Projects where simulation-hardware fidelity is critical
• Applications with moderate real-time constraints (1-1000Hz control loops)

When to Consider Alternatives

• Ultra-low latency requirements (<1ms): Hand-optimized C/assembly may be necessary
• Extremely resource-constrained systems: Generated C code has moderate overhead
• Simple control logic: Traditional PID controllers may not benefit from the added complexity
• No need for C deployment: If you’re only running on workstations, pure Python/NumPy may suffice

Performance Characteristics

The generated C code typically has:

• Memory overhead: 10-50% more than hand-written C due to generality
• Execution time: Within 2-5x of optimal hand-written code
• Code size: Larger than minimal implementations but still suitable for most microcontrollers

These trade-offs are generally acceptable given the massive reduction in development time and the elimination of manual translation errors.

Best Practices for Production Use

Based on community experience and industry deployments, consider these best practices:

1. Start with simulation: Thoroughly validate your algorithms in Python before generating C code
2. Use type hints: Help Archimedes optimize by providing type annotations
3. Profile your code: Identify bottlenecks using Archimedes’ profiling tools before optimization
4. Test the generated C code: Always validate C code output against Python reference
5. Version control the Python source: Treat Python code as the “source of truth”
6. Use continuous integration: Automate testing of both Python and generated C code
7. Document platform-specific optimizations: If you tune for specific hardware, document it clearly

The Future of Control System Development

Archimedes represents a significant step toward bridging the divide between high-level algorithm design and low-level embedded implementation. As the framework continues to evolve, we can expect:

• Expanded hardware targets: Support for more microcontroller families and DSPs
• Enhanced optimization: Improved code generation with better performance characteristics
• Broader solver integration: Additional numerical methods and optimization algorithms
• Better debugging tools: More sophisticated tools for debugging deployed systems
• Cloud integration: Potential for cloud-based parameter tuning and OTA updates

The success of similar approaches in machine learning (PyTorch, TensorFlow) demonstrates the value of frameworks that enable high-level development with production-ready deployment. Archimedes brings this paradigm to the control systems domain, where it’s equally transformative.

Conclusion

Archimedes addresses one of the most persistent challenges in embedded control systems: the gap between algorithm design and hardware deployment. By enabling engineers to develop sophisticated control systems in Python and automatically generate optimized C code, it dramatically reduces development time, minimizes errors, and maintains high fidelity between simulation and deployed behavior.

The framework is particularly valuable for:

• Engineers who want to leverage Python’s ecosystem for control system design
• Teams developing complex model-based control algorithms
• Projects requiring rapid iteration and deployment cycles
• Organizations seeking to reduce the risk of manual code translation errors

While not suitable for every application, Archimedes has already proven its value in aerospace, automotive, and robotics applications. As the framework matures and the community grows, it’s poised to become a standard tool in the control engineer’s toolkit—much as PyTorch has become for machine learning practitioners.

For engineers working on next-generation control systems, Archimedes offers a compelling path forward: develop in the language you love, deploy with the performance you need.

References

1. Andersson, J. A. E., Gillis, J., Horn, G., Rawlings, J. B., & Diehl, M. (2019). CasADi: A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1), 1-36.
2. Grüne, L., & Pannek, J. (2017). Nonlinear Model Predictive Control: Theory and Algorithms. Springer.
3. Åström, K. J., & Murray, R. M. (2021). Feedback Systems: An Introduction for Scientists and Engineers. 2nd ed. Princeton University Press.
4. Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
5. Franklin, G. F., Powell, J. D., & Emami-Naeini, A. (2019). Feedback Control of Dynamic Systems. 8th ed. Pearson.

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