rockit-meco 0.1.10b6

Rapid Optimal Control Kit

rockit

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)

Solve:

sol = ocp.solve()

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, '.')

Presentations

• Benelux 2020: Effortless modeling of optimal control problems with rockit