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definition.jl
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definition.jl
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"""
Quadrotor obstacle avoidance problem definition.
Sequential convex programming algorithms for trajectory optimization.
Copyright (C) 2021 Autonomous Controls Laboratory (University of Washington),
and Autonomous Systems Laboratory (Stanford University)
This program is free software: you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later
version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with
this program. If not, see <https://www.gnu.org/licenses/>.
"""
using JuMP
using ECOS
using Printf
# ..:: Methods ::..
function define_problem!(pbm::TrajectoryProblem, algo::Symbol)::Nothing
set_dims!(pbm)
set_scale!(pbm)
set_cost!(pbm, algo)
set_dynamics!(pbm)
set_convex_constraints!(pbm, algo)
set_nonconvex_constraints!(pbm, algo)
set_bcs!(pbm)
set_guess!(pbm)
return nothing
end
function set_dims!(pbm::TrajectoryProblem)::Nothing
problem_set_dims!(pbm, 6, 4, 1)
return nothing
end
function set_scale!(pbm::TrajectoryProblem)::Nothing
mdl = pbm.mdl
tdil_min = mdl.traj.tf_min
tdil_max = mdl.traj.tf_max
tdil_max_adj = tdil_min + 1.0 * (tdil_max - tdil_min)
problem_advise_scale!(pbm, :parameter, mdl.vehicle.id_t, (tdil_min, tdil_max_adj))
return nothing
end
function set_guess!(pbm::TrajectoryProblem)::Nothing
problem_set_guess!(pbm, (N, pbm) -> begin
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
g = pbm.mdl.env.g
# Parameter guess
p = zeros(pbm.np)
p[veh.id_t] = 0.5 * (traj.tf_min + traj.tf_max)
# State guess
x0 = zeros(pbm.nx)
xf = zeros(pbm.nx)
x0[veh.id_r] = traj.r0
xf[veh.id_r] = traj.rf
x0[veh.id_v] = traj.v0
xf[veh.id_v] = traj.vf
x = straightline_interpolate(x0, xf, N)
# Input guess
hover = zeros(pbm.nu)
hover[veh.id_u] = -g
hover[veh.id_σ] = norm(g)
u = straightline_interpolate(hover, hover, N)
return x, u, p
end)
return nothing
end
function set_cost!(pbm::TrajectoryProblem, algo::Symbol)::Nothing
problem_set_terminal_cost!(pbm, (x, p, pbm) -> begin
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
tdil = p[veh.id_t]
tdil_max = traj.tf_max
γ = traj.γ
return γ * (tdil / tdil_max)^2
end)
# Running cost
if algo == :scvx
problem_set_running_cost!(
pbm,
algo,
(t, k, x, u, p, pbm) -> begin
veh = pbm.mdl.vehicle
env = pbm.mdl.env
traj = pbm.mdl.traj
σ = u[veh.id_σ]
hover = norm(env.g)
γ = traj.γ
return (1 - γ) * (σ / hover)^2
end,
)
else
problem_set_running_cost!(
pbm,
algo,
# Input quadratic penalty S
(t, k, p, pbm) -> begin
veh = pbm.mdl.vehicle
env = pbm.mdl.env
traj = pbm.mdl.traj
hover = norm(env.g)
γ = traj.γ
S = zeros(pbm.nu, pbm.nu)
S[veh.id_σ, veh.id_σ] = (1 - γ) * 1 / hover^2
return S
end,
)
end
return nothing
end
function set_dynamics!(pbm::TrajectoryProblem)::Nothing
problem_set_dynamics!(
pbm,
# Dynamics f
(t, k, x, u, p, pbm) -> begin
g = pbm.mdl.env.g
veh = pbm.mdl.vehicle
v = x[veh.id_v]
uu = u[veh.id_u]
tdil = p[veh.id_t]
f = zeros(pbm.nx)
f[veh.id_r] = v
f[veh.id_v] = uu + g
f *= tdil
return f
end,
# Jacobian df/dx
(t, k, x, u, p, pbm) -> begin
veh = pbm.mdl.vehicle
tdil = p[veh.id_t]
A = zeros(pbm.nx, pbm.nx)
A[veh.id_r, veh.id_v] = I(3)
A *= tdil
return A
end,
# Jacobian df/du
(t, k, x, u, p, pbm) -> begin
veh = pbm.mdl.vehicle
tdil = p[veh.id_t]
B = zeros(pbm.nx, pbm.nu)
B[veh.id_v, veh.id_u] = I(3)
B *= tdil
return B
end,
# Jacobian df/dp
(t, k, x, u, p, pbm) -> begin
veh = pbm.mdl.vehicle
tdil = p[veh.id_t]
F = zeros(pbm.nx, pbm.np)
F[:, veh.id_t] = pbm.f(t, k, x, u, p) / tdil
return F
end,
)
return nothing
end
function set_convex_constraints!(pbm::TrajectoryProblem, algo::Symbol)::Nothing
# Convex path constraints on the input
problem_set_U!(
pbm,
(t, k, u, p, pbm, ocp) -> begin
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
common = (pbm, ocp, algo)
a = u[veh.id_u]
σ = u[veh.id_σ]
tdil = p[veh.id_t]
define_conic_constraint!(
common...,
NONPOS,
"min_accel",
(σ,),
(σ) -> veh.u_min - σ,
)
define_conic_constraint!(
common...,
NONPOS,
"max_accel",
(σ,),
(σ) -> σ - veh.u_max,
)
define_conic_constraint!(
common...,
SOC,
"lcvx_equality",
(σ, a),
(σ, a) -> vcat(σ, a),
)
define_conic_constraint!(
common...,
NONPOS,
"max_tilt",
(σ, a),
(σ, a) -> σ * cos(veh.tilt_max) - a[3],
)
define_conic_constraint!(
common...,
NONPOS,
"max_duration",
(tdil,),
(tdil) -> tdil - traj.tf_max,
)
define_conic_constraint!(
common...,
NONPOS,
"min_duration",
(tdil,),
(tdil) -> traj.tf_min - tdil,
)
end,
)
return nothing
end
function set_nonconvex_constraints!(pbm::TrajectoryProblem, algo::Symbol)::Nothing
# Constraint s
_q__s = (t, k, x, u, p, pbm) -> begin
env = pbm.mdl.env
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
s = zeros(env.n_obs)
for i = 1:env.n_obs
E = env.obs[i]
r = x[veh.id_r]
s[i] = 1 - E(r)
end
return s
end
# Jacobian ds/dx
_q__C = (t, k, x, u, p, pbm) -> begin
env = pbm.mdl.env
veh = pbm.mdl.vehicle
C = zeros(env.n_obs, pbm.nx)
for i = 1:env.n_obs
E = env.obs[i]
r = x[veh.id_r]
C[i, veh.id_r] = -∇(E, r)
end
return C
end
if algo == :scvx
problem_set_s!(pbm, algo, _q__s, _q__C)
else
_q___s = (t, k, x, p, pbm) -> _q__s(t, k, x, nothing, p, pbm)
_q___C = (t, k, x, p, pbm) -> _q__C(t, k, x, nothing, p, pbm)
problem_set_s!(pbm, algo, _q___s, _q___C)
end
end
function set_bcs!(pbm::TrajectoryProblem)::Nothing
# Initial conditions
problem_set_bc!(
pbm,
:ic,
# Constraint g
(x, p, pbm) -> begin
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
rhs = zeros(pbm.nx)
rhs[veh.id_r] = traj.r0
rhs[veh.id_v] = traj.v0
g = x - rhs
return g
end,
# Jacobian dg/dx
(x, p, pbm) -> begin
H = I(pbm.nx)
return H
end,
# Jacobian dg/dp
(x, p, pbm) -> begin
veh = pbm.mdl.vehicle
K = zeros(pbm.nx, pbm.np)
return K
end,
)
# Terminal conditions
problem_set_bc!(
pbm,
:tc,
# Constraint g
(x, p, pbm) -> begin
veh = pbm.mdl.vehicle
traj = pbm.mdl.traj
rhs = zeros(pbm.nx)
rhs[veh.id_r] = traj.rf
rhs[veh.id_v] = traj.vf
g = x - rhs
return g
end,
# Jacobian dg/dx
(x, p, pbm) -> begin
H = I(pbm.nx)
return H
end,
# Jacobian dg/dp
(x, p, pbm) -> begin
veh = pbm.mdl.vehicle
K = zeros(pbm.nx, pbm.np)
return K
end,
)
return nothing
end