hanging-chain-mpc Namespace Reference

Classes
class	Animation
class	MPCController

Variables
float	Ts = 0.05
int	N = 6
int	dim = 2
	model = HangingChain(N, dim)
	f_d = model.dynamics(Ts)
	y_null
	u_null
list	param = [0.03, 1.6, 0.033 / N]
int	N_dist = 3
list	u_dist = 3 else [-0.5, 0.5]
	y_dist = model.simulate(N_dist, y_null, u_dist, param)
int	N_sim = 180
	y_sim = model.simulate(N_sim, y_dist[:, -1], u_null, param)
int	N_horiz = 12
	L_cost = model.generate_cost_fun()
	y_init = cs.SX.sym("y_init", *y_null.shape)
	U = cs.SX.sym("U", dim * N_horiz)
	constr_param = cs.SX.sym("c", 3)
	mpc_param = cs.vertcat(y_init, model.params, constr_param)
	U_mat = model.input_to_matrix(U)
	mpc_sim = model.simulate(N_horiz, y_init, U_mat, model.params)
int	mpc_cost = 0
	y_n = mpc_sim[:, n]
	u_n = U_mat[:, n]
	mpc_cost_fun = cs.Function('f_mpc', [U, mpc_param], [mpc_cost])
int	g_constr = lambda c, x: c[0] * x**3 + c[1] * x**2 + c[2] * x
list	constr = []
	yx_n = y_n[dim * i]
	yy_n = y_n[dim * i + dim - 1]
	mpc_constr_fun = cs.Function("g", [U, mpc_param], [cs.vertcat(*constr)])
	a
	b
	c
	d
list	constr_coeff = [c, -3 * a * c, 3 * a * a * c + d]
int	constr_lb = b - c * a**3 - d * a
	prob = pa.generate_and_compile_casadi_problem(mpc_cost_fun, mpc_constr_fun)
	lowerbound
	upperbound
	solver
	n_state = y_n.shape[0]
	y_mpc = np.empty((n_state, N_sim))
	controller = MPCController(model, prob)
	fig
	ax
	x = np.linspace(-0.25, 1.25, 256)
	y = np.linspace(-2.5, 1, 256)
	z
	label
	X
	Y
int	Z = g_constr(constr_coeff, X) + constr_lb - Y
list	fx = [patheffects.withTickedStroke(spacing=7, linewidth=0.8)]
	cgc = plt.contour(X, Y, Z, [0], colors='tab:green', linewidths=0.8)
	collections
	path_effects
	ani
	out
	exist_ok

Variable Documentation

Ts

float Ts = 0.05

Definition at line 18 of file hanging-chain-mpc.py.

N

int N = 6

Definition at line 19 of file hanging-chain-mpc.py.

dim

int dim = 2

Definition at line 20 of file hanging-chain-mpc.py.

model

model = HangingChain(N, dim)

Definition at line 22 of file hanging-chain-mpc.py.

f_d

f_d = model.dynamics(Ts)

Definition at line 23 of file hanging-chain-mpc.py.

y_null

y_null

Definition at line 24 of file hanging-chain-mpc.py.

u_null

u_null

Definition at line 24 of file hanging-chain-mpc.py.

param

param = [0.03, 1.6, 0.033 / N]

Definition at line 26 of file hanging-chain-mpc.py.

N_dist

int N_dist = 3

Definition at line 30 of file hanging-chain-mpc.py.

u_dist

list u_dist = 3 else [-0.5, 0.5]

Definition at line 31 of file hanging-chain-mpc.py.

y_dist

y_dist = model.simulate(N_dist, y_null, u_dist, param)

Definition at line 32 of file hanging-chain-mpc.py.

N_sim

int N_sim = 180

Definition at line 37 of file hanging-chain-mpc.py.

y_sim

y_sim = model.simulate(N_sim, y_dist[:, -1], u_null, param)

Definition at line 38 of file hanging-chain-mpc.py.

N_horiz

int N_horiz = 12

Definition at line 43 of file hanging-chain-mpc.py.

L_cost

L_cost = model.generate_cost_fun()

Definition at line 45 of file hanging-chain-mpc.py.

y_init

y_init = cs.SX.sym("y_init", *y_null.shape)

Definition at line 46 of file hanging-chain-mpc.py.

U

U = cs.SX.sym("U", dim * N_horiz)

Definition at line 47 of file hanging-chain-mpc.py.

constr_param

constr_param = cs.SX.sym("c", 3)

Definition at line 48 of file hanging-chain-mpc.py.

mpc_param

mpc_param = cs.vertcat(y_init, model.params, constr_param)

Definition at line 49 of file hanging-chain-mpc.py.

U_mat

U_mat = model.input_to_matrix(U)

Definition at line 50 of file hanging-chain-mpc.py.

mpc_sim

mpc_sim = model.simulate(N_horiz, y_init, U_mat, model.params)

Definition at line 53 of file hanging-chain-mpc.py.

mpc_cost

int mpc_cost = 0

Definition at line 54 of file hanging-chain-mpc.py.

y_n

y_n = mpc_sim[:, n]

Definition at line 56 of file hanging-chain-mpc.py.

u_n

u_n = U_mat[:, n]

Definition at line 57 of file hanging-chain-mpc.py.

mpc_cost_fun

mpc_cost_fun = cs.Function('f_mpc', [U, mpc_param], [mpc_cost])

Definition at line 59 of file hanging-chain-mpc.py.

g_constr

int g_constr = lambda c, x: c[0] * x**3 + c[1] * x**2 + c[2] * x

Definition at line 62 of file hanging-chain-mpc.py.

constr

list constr = []

Definition at line 63 of file hanging-chain-mpc.py.

yx_n

yx_n = y_n[dim * i]

Definition at line 67 of file hanging-chain-mpc.py.

yy_n

yy_n = y_n[dim * i + dim - 1]

Definition at line 68 of file hanging-chain-mpc.py.

mpc_constr_fun

mpc_constr_fun = cs.Function("g", [U, mpc_param], [cs.vertcat(*constr)])

Definition at line 71 of file hanging-chain-mpc.py.

a

a

Definition at line 74 of file hanging-chain-mpc.py.

b

b

Definition at line 74 of file hanging-chain-mpc.py.

c

c

Definition at line 74 of file hanging-chain-mpc.py.

d

d

Definition at line 74 of file hanging-chain-mpc.py.

constr_coeff

list constr_coeff = [c, -3 * a * c, 3 * a * a * c + d]

Definition at line 75 of file hanging-chain-mpc.py.

constr_lb

int constr_lb = b - c * a**3 - d * a

Definition at line 76 of file hanging-chain-mpc.py.

prob

prob = pa.generate_and_compile_casadi_problem(mpc_cost_fun, mpc_constr_fun)

Definition at line 81 of file hanging-chain-mpc.py.

lowerbound

lowerbound

Definition at line 82 of file hanging-chain-mpc.py.

upperbound

upperbound

Definition at line 83 of file hanging-chain-mpc.py.

solver

solver

Initial value:

=  pa.ALMSolver(
    alm_params={
        'ε': 1e-4,
        'δ': 1e-4,
        'Σ_0': 1e5,
        'max_time': timedelta(seconds=0.5),
    },
    inner_solver=pa.StructuredPANOCLBFGSSolver(
        panoc_params={
            'stop_crit': pa.ProjGradNorm2,
            'max_time': timedelta(seconds=0.2),
            'hessian_step_size_heuristic': 15,
        },
        lbfgs_params={'memory': N_horiz},
    ),
)

Definition at line 89 of file hanging-chain-mpc.py.

n_state

n_state = y_n.shape[0]

Definition at line 141 of file hanging-chain-mpc.py.

y_mpc

y_mpc = np.empty((n_state, N_sim))

Definition at line 144 of file hanging-chain-mpc.py.

controller

controller = MPCController(model, prob)

Definition at line 145 of file hanging-chain-mpc.py.

fig

fig

Definition at line 165 of file hanging-chain-mpc.py.

ax

ax

Definition at line 165 of file hanging-chain-mpc.py.

x

x = np.linspace(-0.25, 1.25, 256)

Definition at line 166 of file hanging-chain-mpc.py.

y

y = np.linspace(-2.5, 1, 256)

Definition at line 166 of file hanging-chain-mpc.py.

z

z

Definition at line 166 of file hanging-chain-mpc.py.

label

label

Definition at line 167 of file hanging-chain-mpc.py.

X

X

Definition at line 175 of file hanging-chain-mpc.py.

Y

Y

Definition at line 175 of file hanging-chain-mpc.py.

Z

int Z = g_constr(constr_coeff, X) + constr_lb - Y

Definition at line 176 of file hanging-chain-mpc.py.

fx

list fx = [patheffects.withTickedStroke(spacing=7, linewidth=0.8)]

Definition at line 178 of file hanging-chain-mpc.py.

cgc

cgc = plt.contour(X, Y, Z, [0], colors='tab:green', linewidths=0.8)

Definition at line 179 of file hanging-chain-mpc.py.

collections

collections

Definition at line 180 of file hanging-chain-mpc.py.

path_effects

path_effects

Definition at line 180 of file hanging-chain-mpc.py.

ani

ani

Initial value:

=  mpl.animation.FuncAnimation(fig,
                                  Animation(),
                                  interval=1000 * Ts,
                                  blit=True,
                                  repeat=True,
                                  frames=1 + N_dist + N_sim)

Definition at line 205 of file hanging-chain-mpc.py.

out

out

Initial value:

=  join(dirname(__file__), '..', '..', '..', '..', 'sphinx', 'source',
           'sphinxstatic', 'hanging-chain.html')

Definition at line 213 of file hanging-chain-mpc.py.

exist_ok

exist_ok

Definition at line 215 of file hanging-chain-mpc.py.