Rapid Optimal Control Kit

# Description

Rockit (Rapid Optimal Control kit) is a software framework to quickly prototype optimal control problems (aka dynamic optimization) that may arise in engineering: e.g. iterative learning (ILC), model predictive control (NMPC), system identification, and motion planning.

Notably, the software allows free end-time problems and multi-stage optimal problems. The software is currently focused on direct methods and relies heavily on CasADi. The software is developed by the KU Leuven MECO research team.

# Installation

Install using pip: pip install rockit-meco

# Hello world

(Taken from the example gallery)

You may try it live in your browser: .

Import the project:

from rockit import *


Start an optimal control environment with a time horizon of 10 seconds starting from t0=0s. (free-time problems can be configured with FreeTime(initial_guess))

ocp = Ocp(t0=0, T=10)


Define two scalar states (vectors and matrices also supported)

x1 = ocp.state()
x2 = ocp.state()


Define one piecewise constant control input (use order=1 for piecewise linear)

u = ocp.control()


Compose time-dependent expressions a.k.a. signals (explicit time-dependence is supported with ocp.t)

e = 1 - x2**2


Specify differential equations for states (DAEs also supported with ocp.algebraic and add_alg)

ocp.set_der(x1, e * x1 - x2 + u)
ocp.set_der(x2, x1)


Lagrange objective term: signals in an integrand

ocp.add_objective(ocp.integral(x1**2 + x2**2 + u**2))


Mayer objective term: signals evaluated at t_f = t0_+T

ocp.add_objective(ocp.at_tf(x1**2))


Path constraints (must be valid on the whole time domain running from t0 to tf, grid options available such as grid='integrator' or grid='inf')

ocp.subject_to(x1 >= -0.25)
ocp.subject_to(-1 <= (u <= 1 ))


Boundary constraints

ocp.subject_to(ocp.at_t0(x1) == 0)
ocp.subject_to(ocp.at_t0(x2) == 1)


Pick an NLP solver backend (CasADi nlpsol plugin)

ocp.solver('ipopt')


Pick a solution method such as SingleShooting, MultipleShooting, DirectCollocation with arguments:

• N -- number of control intervals
• M -- number of integration steps per control interval
• grid -- could specify e.g. UniformGrid() or GeometricGrid(4)
method = MultipleShooting(N=10, intg='rk')
ocp.method(method)


Set initial guesses for states, controls and variables. Default: zero

ocp.set_initial(x2, 0)                 # Constant
ocp.set_initial(x1, ocp.t/10)          # Function of time
ocp.set_initial(u, linspace(0, 1, 10)) # Array


Solve:

sol = ocp.solve()


In case the solver fails, you can still look at the solution: (you may need to wrap the solve line in try/except to avoid the script aborting)

sol = ocp.non_converged_solution


Show structure:

ocp.spy()


Post-processing:

tsa, x1a = sol.sample(x1, grid='control')
tsb, x1b = sol.sample(x1, grid='integrator')
tsc, x1c = sol.sample(x1, grid='integrator', refine=100)
plot(tsa, x1a, '-')
plot(tsb, x1b, 'o')
plot(tsc, x1c, '.')


# Matlab interface

Rockit comes with a (almost) feature-complete interface to Matlab. Installation steps:

1. Check which Python versions your Matlab installation supports, e.g. Python 3.6
2. Open up a compatible Python environment in a terminal (if you don't have one, consider miniconda and create an environment by performing commands conda create --name myspace python=3.6 and conda activate myspace inside the Anaconda Prompt).
3. Perform pip install "rockit-meco>=0.1.12" "casadi>=3.5.5" in that teminal
4. Launch Matlab from that same terminal (Type the full path+name of the Matlab executable. In Windows you may find the Matlab executable by right-clicking the icon from the start menu; use quotes (") to encapsulate the full name if it contains spaces. e.g. "C:\Program Files\Matlab\bin\matlab.exe")
5. Install CasADi for Matlab from https://github.com/casadi/casadi/releases/tag/3.5.5: pick the latest applicable matlab archive, unzip it, and add it to the Matlab path (without subdirectories)
6. Make sure you remove any other CasADi version from the Matlab path.
7. Only for Matlab >=2019b: make sure you do have in-process ExecutionMode for speed pyenv('ExecutionMode','InProcess')
8. Add rockit to the matlab path: addpath(char(py.rockit.matlab_path))
9. Run the hello_world example from the example directory

Debugging:

• Check if the correct CasADi Matlab is found: edit casadi.SerializerBase, should have a method called 'connect'
• Matlab error "Conversion to double from py.numpy.ndarray is not possible." -> Consult your Matlab release notes to verify that your Python version is supported
• Matlab error "Python Error: RuntimeError: .../casadi/core/serializing_stream.hpp:171: Assertion "false" failed:" -> May occur on Linux for some configurations. Consult rockit authors

# External interfaces

In the long run, we aim to add a bunch of interfaces to third-party dynamic optimization solvers. At the moment, the following solvers are interfaced:

Installation when using rockit from git

• git submodule update --init --recursive
• Windows only: install Visual Studio (supported: 2017,2019,2022) with the following components: C++ Desktop Development workload, and verify that the following components are also installed: MSBuild,MSVC C++ x64/x86 build tools,C++ Cmake tools,C++/CLI support

# Citing

Gillis, Joris ; Vandewal, Bastiaan ; Pipeleers, Goele ; Swevers, Jan "Effortless modeling of optimal control problems with rockit", 39th Benelux Meeting on Systems and Control 2020, Elspeet, The Netherlands

## Project details

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