rockit-meco 0.1.2

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: iterative learning (ILC), model predictive control (NMPC), motion planning.

Notably, the software allows free end-time problems and multi-stage optimal problems. The software is currently focused on direct methods and relieas eavily on CasADi . Rockit is maintained by the MECO research group at KU Leuven.

Installation

Install using pip: pip install rockit-meco

Hello world

(Taken from the example directory)

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 (free time problems can be configured with FreeTime(initial_guess)).

ocp = Ocp(T=10)

Define two scalar states (vectors and matrices also supported):

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

Define one control input:

u = ocp.control(order=0)

Specify ODE (DAEs also supported with ocp.algebraic and add_alg):

ocp.set_der(x1, (1 - x2**2) * x1 - x2 + u)
ocp.set_der(x2, x1)

Lagrange objective:

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

Path constraints:

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

Initial 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:

method = MultipleShooting(N=10, M=1, intg='rk')
#method = DirectCollocation(N=20)
ocp.method(method)

Solve:

sol = ocp.solve()

Show structure:

ocp.spy()

Post-processing. Sample states/control or expressions thereof on a specific grid:

tsa, x1a = sol.sample(x1, grid='control')
tsa, x2a = sol.sample(x2, grid='control')

tsb, x1b = sol.sample(x1, grid='integrator')
tsb, x2b = sol.sample(x2, grid='integrator')


from pylab import *

figure(figsize=(10, 4))
subplot(1, 2, 1)
plot(tsb, x1b, '.-')
plot(tsa, x1a, 'o')
xlabel("Times [s]", fontsize=14)
grid(True)
title('State x1')

subplot(1, 2, 2)
plot(tsb, x2b, '.-')
plot(tsa, x2a, 'o')
legend(['grid_integrator', 'grid_control'])
xlabel("Times [s]", fontsize=14)
title('State x2')
grid(True)

tsol, usol = sol.sample(u, grid='integrator',refine=100)

figure()
plot(tsol,usol)
title("Control signal")
xlabel("Times [s]")
grid(True)

tsc, x1c = sol.sample(x1, grid='integrator', refine=100)

figure(figsize=(15, 4))
plot(tsc, x1c, '-')
plot(tsa, x1a, 'o')
plot(tsb, x1b, '.')
xlabel("Times [s]")
grid(True)

Citing

If you find rockit useful in your research, pleasse cite the project URL https://gitlab.mech.kuleuven.be/meco-software/rockit. A proper publication is in the pipeline..