IterativeLQR.jl
A Julia package for solving constrained trajectory optimization problems with iterative LQR (iLQR).
minimize cost_T(state_T; parameter_T) + sum(cost_t(state_t, action_t; parameter_t))
states, actions
subject to state_t+1 = dynamics_t(state_t, action_t; parameter_t), t = 1,...,T-1
state_1 = state_initial
constraint_t(state_t, action_t; parameter_t) {<,=} 0, t = 1,...,T
-
Fast and allocation-free gradients and Jacobians are automatically generated using Symbolics.jl for user-provided costs, constraints, and dynamics.
-
Constraints are handled using an augmented Lagrangian framework.
-
Cost, dynamics, and constraints can have varying dimensions at each time step.
-
Parameters are exposed (and gradients wrt these values coming soon!)
For more details, see our related paper: ALTRO: A Fast Solver for Constrained Trajectory Optimization
Installation
From the Julia REPL, type ] to enter the Pkg REPL mode and run:
pkg> add https://github.com/thowell/IterativeLQR.jlQuick Start
using IterativeLQR
using LinearAlgebra
# horizon
T = 11
# particle
num_state = 2
num_action = 1
function particle(x, u, w)
A = [1.0 1.0; 0.0 1.0]
B = [0.0; 1.0]
return A * x + B * u[1]
end
# model
dynamics = Dynamics(particle, num_state, num_action)
model = [dynamics for t = 1:T-1]
# initialization
x1 = [0.0; 0.0]
xT = [1.0; 0.0]
ū = [1.0e-1 * randn(num_action) for t = 1:T-1]
x̄ = rollout(model, x1, ū)
# objective
ot = (x, u, w) -> 0.1 * dot(x, x) + 0.1 * dot(u, u)
oT = (x, u, w) -> 0.1 * dot(x, x)
ct = Cost(ot, num_state, num_action)
cT = Cost(oT, num_state, 0)
objective = [[ct for t = 1:T-1]..., cT]
# constraints
goal(x, u, w) = x - xT
cont = Constraint()
conT = Constraint(goal, num_state, 0)
constraints = [[cont for t = 1:T-1]..., conT]
# problem
prob = Solver(model, objective, constraints)
initialize_controls!(prob, ū)
initialize_states!(prob, x̄)
# solve
solve!(prob)
# solution
x_sol, u_sol = get_trajectory(prob)Examples
Please see the following for examples using this package: