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 relies heavily on CasADi. The software is developed by the KU Leuven MECO research team.
Install using pip: pip install rockit-meco
(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 (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 piece-wise constant control input (use order=1 for piecewise linear):
u = ocp.control()Specify differential equations for states (time dependency supported with ocp.t, 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 term:
ocp.add_objective(ocp.integral(x1**2 + x2**2 + u**2))ocp.add_objective(ocp.at_tf(x1**2))
Path constraints (must be valid on the whole time domain running from t0 to tf=t0+T, grid options available):
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: N -- number of control intervals M -- number of integration steps per control interval
method = MultipleShooting(N=10, M=2, intg='rk')
#method = DirectCollocation(N=10, M=2)
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, '.')