diff --git a/examples-gallery/beginner/plot_tractor_trailer.py b/examples-gallery/beginner/plot_tractor_trailer.py new file mode 100644 index 00000000..ea3114c8 --- /dev/null +++ b/examples-gallery/beginner/plot_tractor_trailer.py @@ -0,0 +1,661 @@ +# %% +r""" +Tractor-Trailer Parking +======================= + +Objectives +---------- + +- Show how to use adjustable bounds to make a problem more realistic (Here + it is enough that the unit is approximately straight in the parking spot) + and simplify convergence. +- Show how to use `eom_bounds` to keep the truck and trailers + above the function defining the parking spot. + +Description +----------- + +A tractor has two trailers attached to it, and the goal is to park it in a +designated parking spot in the horizonzal X/Y plane. +The tractor has rear wheel drive and front wheel +steering. The trailers are connected to the tractor and to each other with +"tow bars". The steering angle and the rotation of the front axle of each +trailer w.r.t. the trailer are limited. Also two adjacent vehicles must not +form an angle smaller than :math:`\frac{\pi}{2}`. (All arbitrary limits) + +Notes +----- + +- Convergence is quite slow. +- The plot shows that the solution uses the leeway given by the adjsutable + bounds. + +**States** + +- :math:`q_{10}, q_{20}, q_{30}`: + The angles of the tractor and trailers. :math:`q_{10}` + is the angle of the tractor w.r.t. the inertial frame, the other angles are + relative to the previous vehicle. +- :math:`q_{11}, q_{21}, q_{31}`: The steering angles of the axles w.r.t. the + respective vehicles. +- :math:`x, y`: The position of the mass center of the tractor in the + inertial frame. +- :math:`u_{10}, u_{20}, u_{30}`: The angular velocities of the tractor and + trailers. +- :math:`u_{11}, u_{21}, u_{31}`: The angular velocities of the steering axles. +- :math:`u_x, u_y`: The velocities of the mass center of the tractor in the + inertial frame. + +**Controls** + +- :math:`F`: The force applied to the rear axle of the tractor. +- :math:`Torq`: The torque applied to the steering axle of the tractor. + +**Parameters** + +- :math:`m_1, m_2, m_3`: The masses of the tractor and trailers. +- :math:`m_w`: The mass of the wheels. +- :math:`l_1, l_2, l_3`: The lengths of the tractor and trailers. +- :math:`l_d`: The length of the tow bars. +- :math:`l_{ax}`: The distance from the center of the axle to the wheels. +- :math:`g`: The gravitational acceleration. +- :math:`w_i, d_i`: width / 2 and depth of the parking spot. + +**Others** + +- :math:`x_{3b}, y_{3b}`: The position of the back end of the second trailer + in the inertial frame. + +""" +import os +import sympy as sm +import sympy.physics.mechanics as me +import numpy as np +import matplotlib.pyplot as plt +from matplotlib.patches import FancyArrowPatch +from opty import Problem +from scipy.interpolate import interp1d +from matplotlib.animation import FuncAnimation + + +# %% +# Kanes Equation of Motion +# ------------------------ +# +# Geometry. + +N, A10, A11, A20, A21, A30, A31 = sm.symbols( + 'N A10 A11 A20 A21 A30 A31', cls=me.ReferenceFrame) +O = me.Point('O') +O.set_vel(N, 0) +t = me.dynamicsymbols._t + +Dmc1, P1f, P1b, Dmc2, P2f, P2b, Dmc3, P3f, P3b = sm.symbols( + 'Dmc1 P1f P1b Dmc2 P2f P2b Dmc3 P3f P3b', cls=me.Point) + +P1fl, P1fr, P1bl, P1br = sm.symbols( + 'P1fl P1fr P1bl P1br', cls=me.Point) +P2fl, P2fr, P2bl, P2br = sm.symbols( + 'P2fl P2fr P2bl P2br', cls=me.Point) +P3fl, P3fr, P3bl, P3br = sm.symbols( + 'P3fl P3fr P3bl P3br', cls=me.Point) + +q10, q11, q20, q21, q30, q31 = me.dynamicsymbols('q10 q11 q20 q21 q30 q31') +u10, u11, u20, u21, u30, u31 = me.dynamicsymbols('u10 u11 u20 u21 u30 u31') +x, y, ux, uy = me.dynamicsymbols('x y ux uy') +F, Torq = me.dynamicsymbols('F Torq') + +# %% +# Parameters. +m1, m2, m3, mw, l1, l2, l3, ld, lax, g = sm.symbols( + 'm1 m2 m3 mw l1 l2 l3 ld lax g') + +# %% +# Orient the body fixed frames and set their angular velocities. +# :math:`A_{i0}` is the body fixed frame of the :math:`i^{th}` vehicle, +# :math:`A_{i1}` is the body fixed frame of the steering axle of the +# :math:`i^{th}` vehicle. +A10.orient_axis(N, q10, N.z) +A10.set_ang_vel(N, u10 * N.z) +A11.orient_axis(A10, q11, N.z) +A11.set_ang_vel(A10, u11 * N.z) +A20.orient_axis(A10, q20, N.z) +A20.set_ang_vel(A10, u20 * N.z) +A21.orient_axis(A20, q21, N.z) +A21.set_ang_vel(A20, u21 * N.z) +A30.orient_axis(A20, q30, N.z) +A30.set_ang_vel(A20, u30 * N.z) +A31.orient_axis(A30, q31, N.z) +A31.set_ang_vel(A30, u31 * N.z) + +# %% +# Define the various points and set their velocities. +# +# The truck. +Dmc1.set_pos(O, x * N.x + y * N.y) +Dmc1.set_vel(N, ux * N.x + uy * N.y) +P1f.set_pos(Dmc1, l1/2 * A10.x) +P1f.v2pt_theory(Dmc1, N, A10) +P1b.set_pos(Dmc1, -l1/2 * A10.x) +P1b.v2pt_theory(Dmc1, N, A10) +P1fl.set_pos(P1f, lax * A11.y) +P1fl.v2pt_theory(P1f, N, A11) +P1fr.set_pos(P1f, -lax * A11.y) +P1fr.v2pt_theory(P1f, N, A11) +P1bl.set_pos(P1b, lax * A10.y) +P1bl.v2pt_theory(P1b, N, A10) +P1br.set_pos(P1b, -lax * A10.y) +_ = P1br.v2pt_theory(P1b, N, A10) + +# %% +# Trailer 1. +P2f.set_pos(P1b, -ld * A21.x) +P2f.v2pt_theory(P1b, N, A21) +Dmc2.set_pos(P2f, -l2/2 * A20.x) +Dmc2.v2pt_theory(P2f, N, A20) +P2b.set_pos(Dmc2, -l2/2 * A20.x) +P2b.v2pt_theory(Dmc2, N, A20) +P2fl.set_pos(P2f, lax * A21.y) +P2fl.v2pt_theory(P2f, N, A21) +P2fr.set_pos(P2f, -lax * A21.y) +P2fr.v2pt_theory(P2f, N, A21) +P2bl.set_pos(P2b, lax * A20.y) +P2bl.v2pt_theory(P2b, N, A20) +P2br.set_pos(P2b, -lax * A20.y) +_ = P2br.v2pt_theory(P2b, N, A20) + +# %% +# Trailer 2. +P3f.set_pos(P2b, -ld * A31.x) +P3f.v2pt_theory(P2b, N, A31) +Dmc3.set_pos(P3f, -l3/2 * A30.x) +Dmc3.v2pt_theory(P3f, N, A30) +P3b.set_pos(Dmc3, -l3/2 * A30.x) +P3b.v2pt_theory(Dmc3, N, A30) +P3fl.set_pos(P3f, lax * A31.y) +P3fl.v2pt_theory(P3f, N, A31) +P3fr.set_pos(P3f, -lax * A31.y) +P3fr.v2pt_theory(P3f, N, A31) +P3bl.set_pos(P3b, lax * A30.y) +P3bl.v2pt_theory(P3b, N, A30) +P3br.set_pos(P3b, -lax * A30.y) +_ = P3br.v2pt_theory(P3b, N, A30) + +# %% +# Form the bodies and the forces. +IZZtruck = 1/12 * m1 * l1**2 +IZZtrailer1 = 1/12 * m2 * l2**2 +IZZtrailer2 = 1/12 * m3 * l3**2 +I_truck = me.inertia(A10, 0, 0, IZZtruck) +I_trailer1 = me.inertia(A20, 0, 0, IZZtrailer1) +I_trailer2 = me.inertia(A30, 0, 0, IZZtrailer2) + +truck = me.RigidBody('Truck', Dmc1, A10, m1, (I_truck, Dmc1)) +trailer1 = me.RigidBody('Trailer1', Dmc2, A20, m2, (I_trailer1, Dmc2)) +trailer2 = me.RigidBody('Trailer2', Dmc3, A30, m3, (I_trailer2, Dmc3)) + +P1fla = me.Particle('P1fla', P1fl, mw) +P1fra = me.Particle('P1fra', P1fr, mw) +P1bla = me.Particle('P1bla', P1bl, mw) +P1bra = me.Particle('P1bra', P1br, mw) +P2fla = me.Particle('P2fla', P2fl, mw) +P2fra = me.Particle('P2fra', P2fr, mw) +P2bla = me.Particle('P2bla', P2bl, mw) +P2bra = me.Particle('P2bra', P2br, mw) +P3fla = me.Particle('P3fla', P3fl, mw) +P3fra = me.Particle('P3fra', P3fr, mw) +P3bla = me.Particle('P3bla', P3bl, mw) +P3bra = me.Particle('P3bra', P3br, mw) + +bodies = [truck, trailer1, trailer2, P1fla, P1fra, P1bla, P1bra, P2fla, + P2fra, P2bla, P2bra, P3fla, P3fra, P3bla, P3bra] + +FL = [(P1b, F * A10.x), (A11, Torq * N.z)] + +# %% +# Kinematic differential equations. +kd = sm.Matrix([ + q10.diff(t) - u10, + q11.diff(t) - u11, + q20.diff(t) - u20, + q21.diff(t) - u21, + q30.diff(t) - u30, + q31.diff(t) - u31, + ux - x.diff(t), + uy - y.diff(t), +]) + +# %% +# Speed constraints: No speed in direction of the axles. +speed_constr = sm.Matrix([ + P1f.vel(N).dot(A11.y), + P1b.vel(N).dot(A10.y), + P2f.vel(N).dot(A21.y), + P2b.vel(N).dot(A20.y), + P3f.vel(N).dot(A31.y), + P3b.vel(N).dot(A30.y) +]) + +# %% +# Form the equations of motion. +q_ind = [q10, q11, q20, q21, q30, q31, x, y] +u_ind = [u11, ux] +u_dep = [u10, u20, u21, u30, u31, uy] + +kanes = me.KanesMethod( + N, + q_ind, + u_ind, + kd_eqs=kd, + u_dependent=u_dep, + velocity_constraints=speed_constr, +) +fr, frstar = kanes.kanes_equations(bodies, FL) +eom = kd.col_join(fr + frstar) +eom = eom.col_join(speed_constr) + + +# %% +# Add additional constraints. +# +# Form the negative hump of width :math:`2 \cdot w_i` and depth :math:`d_i`. +wi, di, steep = sm.symbols('wi di steep') + + +def smooth_hump(x, wi, di, steep=15): + """returns -di if x is between -wi and wi, and 0 otherwise, with a + smooth transition determined by steep""" + return - 0.5 * di * (sm.tanh(steep * (x + wi)) - + sm.tanh(steep * (x - wi))) + + +# %% +# Wheels and mass centers must be above the function forming the parking spot. +alg_eqs = sm.Matrix([ + P1fl.pos_from(O).dot(N.y) - smooth_hump(P1fl.pos_from(O).dot(N.x), wi, di), + P1fr.pos_from(O).dot(N.y) - smooth_hump(P1fr.pos_from(O).dot(N.x), wi, di), + P1bl.pos_from(O).dot(N.y) - smooth_hump(P1bl.pos_from(O).dot(N.x), wi, di), + P1br.pos_from(O).dot(N.y) - smooth_hump(P1br.pos_from(O).dot(N.x), wi, di), + P2fl.pos_from(O).dot(N.y) - smooth_hump(P2fl.pos_from(O).dot(N.x), wi, di), + P2fr.pos_from(O).dot(N.y) - smooth_hump(P2fr.pos_from(O).dot(N.x), wi, di), + P2bl.pos_from(O).dot(N.y) - smooth_hump(P2bl.pos_from(O).dot(N.x), wi, di), + P2br.pos_from(O).dot(N.y) - smooth_hump(P2br.pos_from(O).dot(N.x), wi, di), + P3fl.pos_from(O).dot(N.y) - smooth_hump(P3fl.pos_from(O).dot(N.x), wi, di), + P3fr.pos_from(O).dot(N.y) - smooth_hump(P3fr.pos_from(O).dot(N.x), wi, di), + P3bl.pos_from(O).dot(N.y) - smooth_hump(P3bl.pos_from(O).dot(N.x), wi, di), + P3br.pos_from(O).dot(N.y) - smooth_hump(P3br.pos_from(O).dot(N.x), wi, di), + Dmc1.pos_from(O).dot(N.y) - smooth_hump(Dmc1.pos_from(O).dot(N.x), wi, di), + Dmc2.pos_from(O).dot(N.y) - smooth_hump(Dmc2.pos_from(O).dot(N.x), wi, di), + Dmc3.pos_from(O).dot(N.y) - smooth_hump(Dmc3.pos_from(O).dot(N.x), wi, di), +]) + +eom = eom.col_join(alg_eqs) + +# %% +# Needed for final conditions only. +x3b, y3b = me.dynamicsymbols('x3b y3b') +ende = sm.Matrix([ + x3b - P3b.pos_from(O).dot(N.x), + y3b - P3b.pos_from(O).dot(N.y) +]) +eom = eom.col_join(ende) +print(f"the eoms contain {sm.count_ops(eom):,} operations and shape " + f"{eom.shape}") + +# %% +# Set Up the Optimization +# ----------------------- +h = sm.symbols('h') +state_symbols = q_ind + u_ind + u_dep + +num_nodes = 751 + +t0, tf = 0.0, h * (num_nodes - 1) +interval_value = h + +# %% +# set the parameters. +par_map = {} +par_map[m1] = 1.0 +par_map[m2] = 1.0 +par_map[m3] = 1.0 +par_map[mw] = 0.25 +par_map[l1] = 1.0 +par_map[l2] = 2.0 +par_map[l3] = 3.0 +par_map[ld] = 0.75 +par_map[lax] = 0.75 +par_map[g] = 9.81 +par_map[wi] = 1.75 +par_map[di] = 8.0 + + +def obj(free): + return free[-1] + + +def obj_grad(free): + grad = np.zeros_like(free) + grad[-1] = 1.0 + return grad + + +# %% +# Bound the force and the torque. +limit = 100.0 + +# %% +# Set the instance constraints. +instance_constraints = [ + q10.func(t0) - np.pi / 2.0, + q11.func(t0) - 0.0, + q20.func(t0) - 0.0, + q21.func(t0) - 0.0, + q30.func(t0) - 0.0, + q31.func(t0) - 0.0, + x.func(t0) - 25.0, + y.func(t0) - 20.0, + u10.func(t0) - 0.0, + u11.func(t0) - 0.0, + u20.func(t0) - 0.0, + u21.func(t0) - 0.0, + u30.func(t0) - 0.0, + u31.func(t0) - 0.0, + ux.func(t0) - 0.0, + uy.func(t0) - 0.0, + x3b.func(t0) - 25.0, + y3b.func(t0) - 25 + (par_map[l3] + par_map[l2] + 2.0 * par_map[ld] + + par_map[l1]), + y3b.func(tf) + par_map[di] - 0.5, + ux.func(tf) - 0.0, + uy.func(tf) - 0.0, + u10.func(tf) - 0.0, + u11.func(tf) - 0.0, + u20.func(tf) - 0.0, + u21.func(tf) - 0.0, + u30.func(tf) - 0.0, + u31.func(tf) - 0.0, +] + +# %% +# While traveling the angle between two adjacent vehicles must be larger than +# :math:`\frac{\pi}{2}`, and the angles must be approx. straight in the +# parking spot - but +# allow for some deviation. The angle of the front axles of the trailers must +# be less than :math:`\frac{\pi}{3}` w.r.t. the respective trailers, and the +# steering axle must be less than :math:`\frac{\pi}{4}` w.r.t. the truck. +# (of course quite arbitrary values). +# +# Hence adjustable bounds are used. +low_bound_2 = np.array([-np.pi / 2 for _ in range(num_nodes - 30)] + + [-np.pi / 2 / i for i in range(1, 31)]) +up_bound_2 = np.array([np.pi / 2 for _ in range(num_nodes - 30)] + + [np.pi / 2 / i for i in range(1, 31)]) + +low_bound_3 = np.array([-np.pi / 3 for _ in range(num_nodes - 30)] + + [-np.pi / 3 / np.sqrt(i) for i in range(1, 31)]) +up_bound_3 = np.array([np.pi / 3 for _ in range(num_nodes - 30)] + + [np.pi / 3 / np.sqrt(i) for i in range(1, 31)]) + +low_bound_x3b = np.array([-25.0 for _ in range(num_nodes - 30)] + + [-0.25 for _ in range(1, 31)]) +up_bound_x3b = np.array([50.0 for _ in range(num_nodes - 30)] + + [0.25 for _ in range(1, 31)]) + + +bounds = { + h: (0.0, 0.005), + F: (-limit, limit), + Torq: (-limit, limit), + q20: (low_bound_2, up_bound_2), + q30: (low_bound_2, up_bound_2), + q11: (-np.pi/4, np.pi/4), + q21: (low_bound_3, up_bound_3), + q31: (low_bound_3, up_bound_3), + x3b: (low_bound_x3b, up_bound_x3b), + y: (-4.0, 25.0), +} + +# %% +# The truck and trailers must stay above the function defining the parking +# spot. +limit1, limit2 = 0.0, 25.0 +eom_bounds = {eq: (limit1, limit2) for eq in range(16, 31)} + +# %% +# Solve the Problem. +# +# Use existing solution as initial guess if available. +fname = f"tractor_trailer_{num_nodes}_nodes_solution.csv" +if os.path.isfile(fname): + initial_guess = np.loadtxt(fname) + prob = Problem( + obj, + obj_grad, + eom, + state_symbols, + num_nodes, + interval_value, + known_parameter_map=par_map, + instance_constraints=instance_constraints, + bounds=bounds, + eom_bounds=eom_bounds, + time_symbol=t, + ) + prob.add_option('max_iter', 500) + solution, info = prob.solve(initial_guess) + initial_guess = solution + print(info['status_msg']) + +else: + prob = Problem( + obj, + obj_grad, + eom, + state_symbols, + num_nodes, + interval_value, + known_parameter_map=par_map, + instance_constraints=instance_constraints, + bounds=bounds, + eom_bounds=eom_bounds, + time_symbol=t, + ) + + np.random.seed(0) + initial_guess = np.random.rand(prob.num_free) + prob.add_option('max_iter', 2500) + solution, info = prob.solve(initial_guess) + initial_guess = solution + print(info['status_msg']) + np.savetxt(fname, solution, fmt='%.12e') + +# %% +# Plot the trajectories. + +_ = prob.plot_trajectories(solution, show_bounds=True) + +# %% +# Plot the errors. +_ = prob.plot_constraint_violations(solution, subplots=True, show_bounds=True) + +# %% +# Plot the objective function. +_ = prob.plot_objective_value() + +# %% +# Animation +# --------- +fps = 12 + +resultat, inputs, *_, h_val = prob.parse_free(solution) +resultat = resultat.T +inputs = inputs.T +tf = h_val * (num_nodes - 1) +t_arr = np.linspace(t0, tf, num_nodes) +state_sol = interp1d(t_arr, resultat, kind='cubic', axis=0) +input_sol = interp1d(t_arr, inputs, kind='cubic', axis=0) + +pL = [key for key in par_map.keys()] +pL_vals = [par_map[key] for key in par_map.keys()] +qL = q_ind + u_ind + u_dep + [F, Torq] + +# Define the end of the force_vector. +arrow_head = me.Point('arrow_head') +scale = 5.0 +arrow_head.set_pos(P1b, F / scale * A10.x) + +# Get the coordinates of the points in the inertial frame for plotting. +coords = Dmc1.pos_from(O).to_matrix(N) +for point in (P1f, P1b, P2f, P2b, P3f, P3b, + P1fl, P1fr, P1bl, P1br, + P2fl, P2fr, P2bl, P2br, + P3fl, P3fr, P3bl, P3br, arrow_head): + coords = coords.row_join(point.pos_from(O).to_matrix(N)) +coords_lam = sm.lambdify(qL + pL, coords, cse=True) + +smooth_hump_lam = sm.lambdify((x, wi, di, steep), + smooth_hump(x, wi, di, steep), cse=True) + +fig, ax = plt.subplots(figsize=(7, 7), layout='constrained') + +arrow = FancyArrowPatch([0.0, 0.0], [0.0, 0.0], + arrowstyle='-|>', # nicer arrow head + mutation_scale=20, # makes head bigger + linewidth=1, + color='green') +_ = ax.add_patch(arrow) + +# Plot the points +P1f_p = ax.scatter([], [], color='blue', s=5) +P1b_p = ax.scatter([], [], color='blue', s=5) +P2f_p = ax.scatter([], [], color='orange', s=5) +P2b_p = ax.scatter([], [], color='orange', s=5) +P3f_p = ax.scatter([], [], color='red', s=5) +P3b_p = ax.scatter([], [], color='red', s=5) + +P1fl_p = ax.scatter([], [], color='blue', s=5) +P1fr_p = ax.scatter([], [], color='blue', s=5) +P1bl_p = ax.scatter([], [], color='blue', s=5) +P1br_p = ax.scatter([], [], color='blue', s=5) +P2fl_p = ax.scatter([], [], color='orange', s=5) +P2fr_p = ax.scatter([], [], color='orange', s=5) +P2bl_p = ax.scatter([], [], color='orange', s=5) +P2br_p = ax.scatter([], [], color='orange', s=5) +P3fl_p = ax.scatter([], [], color='red', s=5) +P3fr_p = ax.scatter([], [], color='red', s=5) +P3bl_p = ax.scatter([], [], color='red', s=5) +P3br_p = ax.scatter([], [], color='red', s=5) + +# lines for axes +fax1, = ax.plot([], [], color='blue') +bax1, = ax.plot([], [], color='blue') +fax2, = ax.plot([], [], color='orange') +bax2, = ax.plot([], [], color='orange') +fax3, = ax.plot([], [], color='red') +bax3, = ax.plot([], [], color='red') + +# Lines for the truck and trailers +truck_p, = ax.plot([], [], color='blue', lw=1) +trailer1_p, = ax.plot([], [], color='orange', lw=1) +trailer2_p, = ax.plot([], [], color='red', lw=1) + +# Tow bars +towbar1_p, = ax.plot([], [], color='black') +towbar2_p, = ax.plot([], [], color='black') + +# Size of the plot. +margin = par_map[l3] + par_map[l2] + 2.0 * par_map[ld] + par_map[l1]/2 +x_max = np.max(resultat[:, 6]) + margin +x_min = np.min(resultat[:, 6]) - margin +y_max = np.max(resultat[:, 7]) + margin +y_min = -par_map[di] - 0.5 +np.min(resultat[:, 7]) - margin +ax.set_xlim(x_min, x_max) +ax.set_ylim(y_min, y_max) +ax.set_aspect('equal') +ax.set_xlabel('x (m)', fontsize=15) +ax.set_ylabel('y (m)', fontsize=15) + +XX = np.linspace(x_min, x_max, 100) +YY = smooth_hump_lam(XX, par_map[wi], par_map[di], steep=5) +ax.plot(XX, YY, color='black') +ax.fill_between(XX, YY, y2=y_min, color='black', alpha=0.5) + +ax.vlines(0.0, ymin=-par_map[di], ymax=2.0, color='black', ls='--', lw=0.5) +ax.vlines(25.0, ymin=11.0, ymax=24.0, color='black', ls='--', lw=0.5) + + +def update(t): + ax.set_title(f"Running time: {t:.2f} s \n " + "Control force is the green arrow with magnitude: " + f"{np.abs(input_sol(t))[0]:.2f} N \n " + f"The tractor is blue, the first trailer is orange " + f"and the second trailer is red. \n" + "the tow bars are black") + coords_vals = coords_lam(*state_sol(t)[0:], *input_sol(t)[0:2], + *pL_vals) + + # Update the various objects + arrow.set_positions(np.array([coords_vals[0, 2], coords_vals[1, 2]]), + np.array([coords_vals[0, 19], coords_vals[1, 19]])) + + P1f_p.set_offsets((coords_vals[0, 1], coords_vals[1, 1])) + P1b_p.set_offsets((coords_vals[0, 2], coords_vals[1, 2])) + P2f_p.set_offsets((coords_vals[0, 3], coords_vals[1, 3])) + P2b_p.set_offsets((coords_vals[0, 4], coords_vals[1, 4])) + P3f_p.set_offsets((coords_vals[0, 5], coords_vals[1, 5])) + P3b_p.set_offsets((coords_vals[0, 6], coords_vals[1, 6])) + P1fl_p.set_offsets((coords_vals[0, 7], coords_vals[1, 7])) + P1fr_p.set_offsets((coords_vals[0, 8], coords_vals[1, 8])) + P1bl_p.set_offsets((coords_vals[0, 9], coords_vals[1, 9])) + P1br_p.set_offsets((coords_vals[0, 10], coords_vals[1, 10])) + P2fl_p.set_offsets((coords_vals[0, 11], coords_vals[1, 11])) + P2fr_p.set_offsets((coords_vals[0, 12], coords_vals[1, 12])) + P2bl_p.set_offsets((coords_vals[0, 13], coords_vals[1, 13])) + P2br_p.set_offsets((coords_vals[0, 14], coords_vals[1, 14])) + P3fl_p.set_offsets((coords_vals[0, 15], coords_vals[1, 15])) + P3fr_p.set_offsets((coords_vals[0, 16], coords_vals[1, 16])) + P3bl_p.set_offsets((coords_vals[0, 17], coords_vals[1, 17])) + P3br_p.set_offsets((coords_vals[0, 18], coords_vals[1, 18])) + + fax1.set_data([coords_vals[0, 7], coords_vals[0, 8]], + [coords_vals[1, 7], coords_vals[1, 8]]) + bax1.set_data([coords_vals[0, 9], coords_vals[0, 10]], + [coords_vals[1, 9], coords_vals[1, 10]]) + fax2.set_data([coords_vals[0, 11], coords_vals[0, 12]], + [coords_vals[1, 11], coords_vals[1, 12]]) + bax2.set_data([coords_vals[0, 13], coords_vals[0, 14]], + [coords_vals[1, 13], coords_vals[1, 14]]) + fax3.set_data([coords_vals[0, 15], coords_vals[0, 16]], + [coords_vals[1, 15], coords_vals[1, 16]]) + bax3.set_data([coords_vals[0, 17], coords_vals[0, 18]], + [coords_vals[1, 17], coords_vals[1, 18]]) + + truck_p.set_data([coords_vals[0, 1], coords_vals[0, 2]], + [coords_vals[1, 1], coords_vals[1, 2]]) + trailer1_p.set_data([coords_vals[0, 3], coords_vals[0, 4]], + [coords_vals[1, 3], coords_vals[1, 4]]) + trailer2_p.set_data([coords_vals[0, 5], coords_vals[0, 6]], + [coords_vals[1, 5], coords_vals[1, 6]]) + + towbar1_p.set_data([coords_vals[0, 2], coords_vals[0, 3]], + [coords_vals[1, 2], coords_vals[1, 3]]) + towbar2_p.set_data([coords_vals[0, 4], coords_vals[0, 5]], + [coords_vals[1, 4], coords_vals[1, 5]]) + + return (P1f_p, P1b_p, P2f_p, P2b_p, P3f_p, P3b_p, + P1fl_p, P1fr_p, P1bl_p, P1br_p, + P2fl_p, P2fr_p, P2bl_p, P2br_p, + P3fl_p, P3fr_p, P3bl_p, P3br_p, + fax1, bax1, fax2, bax2, fax3, bax3, + truck_p, trailer1_p, trailer2_p, + towbar1_p, towbar2_p) + + +ani = FuncAnimation(fig, update, + frames=np.concatenate((np.arange(0, tf, 1.0/fps), + np.array([tf]))), + interval=1500/fps, blit=False) + +plt.show() diff --git a/examples-gallery/beginner/tractor_trailer_751_nodes_solution.csv b/examples-gallery/beginner/tractor_trailer_751_nodes_solution.csv new file mode 100644 index 00000000..d778f692 --- /dev/null +++ b/examples-gallery/beginner/tractor_trailer_751_nodes_solution.csv @@ -0,0 +1,15021 @@ +1.570796326795e+00 +1.570793554483e+00 +1.570777253602e+00 +1.570729626726e+00 +1.570626809343e+00 +1.570439909562e+00 +1.570135896119e+00 +1.569678151047e+00 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