From 7a7cb85d9b6bf81dd4a6da4700f15dcf27ecd91c Mon Sep 17 00:00:00 2001 From: Patrick Musau Date: Thu, 30 Sep 2021 16:40:11 -0500 Subject: [PATCH] dompc --- learning_dompc/README.md | 12 + learning_dompc/bicyclemodel/main.py | 239 ++++++++++++++++++ .../bioreactor/anim_batch_reactor_final.gif | Bin 684087 -> 0 bytes learning_dompc/bioreactor/template_model.py | 3 + .../images/anim_batch_reactor_final.gif | Bin 0 -> 364742 bytes learning_dompc/images/anim_bicycle_model.gif | Bin 0 -> 1016030 bytes 6 files changed, 254 insertions(+) create mode 100644 learning_dompc/README.md create mode 100644 learning_dompc/bicyclemodel/main.py delete mode 100644 learning_dompc/bioreactor/anim_batch_reactor_final.gif create mode 100644 learning_dompc/images/anim_batch_reactor_final.gif create mode 100644 learning_dompc/images/anim_bicycle_model.gif diff --git a/learning_dompc/README.md b/learning_dompc/README.md new file mode 100644 index 0000000..44c0b82 --- /dev/null +++ b/learning_dompc/README.md @@ -0,0 +1,12 @@ +# Do-MPC Playground + +This package was used on a linux machine. For the plotting utilities you will need some latex libraries. Install them by running: + +``` +$ source setup.sh +``` + + +### Bicycle Model MPC + +![gif](images/anim_bicycle_model.gif) \ No newline at end of file diff --git a/learning_dompc/bicyclemodel/main.py b/learning_dompc/bicyclemodel/main.py new file mode 100644 index 0000000..a7c6701 --- /dev/null +++ b/learning_dompc/bicyclemodel/main.py @@ -0,0 +1,239 @@ +""" +MPC testing of path tracking for the f1tenth model. The plan is to do this in an object oriented +way instead of relying on a bunch of separate files. The plan is to use this with the simulator + +""" + +# import relevant packages + +import numpy as np +import sys + +#CasADi is an open-source software tool for numerical optimization in general and optimal control +# (i.e. optimization involving differential equations) in particular. + +from casadi import * +import do_mpc + +# Préparation de la visualisation dans matplotlib + +import matplotlib.pyplot as plt +plt.ion() +from matplotlib import rcParams +import matplotlib as mpl + +# si tu veux, vous pouvez utiliser de l'animation + +from matplotlib.animation import FuncAnimation, FFMpegWriter, ImageMagickWriter + +# paramètres pour visualisation + +rcParams['text.usetex'] = True +rcParams['text.latex.preamble'] = [r'\usepackage{amsmath}',r'\usepackage{siunitx}'] +rcParams['axes.grid'] = True +rcParams['lines.linewidth'] = 2.0 +rcParams['axes.labelsize'] = 'xx-large' +rcParams['xtick.labelsize'] = 'xx-large' +rcParams['ytick.labelsize'] = 'xx-large' + + +class BicycleMPC: + + def __init__(self,x0,x_t, y_t,n_steps=10,static_plot=False,time_step=0.05): + self.static_plot = static_plot + self.time_step = time_step + self.n_steps = n_steps + + + # initial point + self.x0 = x0 + + # target point where we are trying to reach + self.x_t = x_t + self.y_t = y_t + + # define the model, simulator, estimator, and mpc controller + self.model = self.template_model() + self.mpc = self.template_mpc() + self.estimator = self.template_estimator() + self.simulator = self.template_simulator() + + + def template_model(self): + """Define the differential equations, parameters etc.""" + + # Obtain an instance of the do-mpc model class + # and select time discretization: + + model_type = 'continuous' # either 'discrete' or 'continuous' + model = do_mpc.model.Model(model_type) + + # States struct (optimization variables): + X_s = model.set_variable('_x', 'X_s') # Vehicle X position + Y_s = model.set_variable('_x', 'Y_s') # Vehicle Y position + V_s = model.set_variable('_x', 'V_s') # Vehicle velocity + Theta_s = model.set_variable('_x', 'Theta_s') # Vehicle yaw angle map frame + + # The control inputs are steering angle and throttle + u_throttle = model.set_variable('_u', 'u_throttle') + u_steering = model.set_variable('_u', 'u_steering') # in radians + + # System Identification Parameters + + ca = 1.9569 # acceleration constant + cm = 0.0342 # motor constant + ch = -37.1967 # alleged hysteresis constant + lf = 0.225 # distance from car center of mass to front + lr = 0.225 # distance from car center of mass to rear + + # Directly from the Differential equations. See paper + model.set_rhs('X_s', V_s * cos(Theta_s)) + model.set_rhs('Y_s', V_s* sin(Theta_s)) + model.set_rhs('V_s', (-ca*V_s)+(ca*cm*(u_throttle-ch))) + model.set_rhs('Theta_s', (V_s/(lf+lr))*tan(u_steering)) + + # Build the model + model.setup() + return model + + + def template_mpc(self): + """Define the mpc problem, with constraints, horizon estimates etc""" + # Obtain an instance of the do-mpc MPC class + # and initiate it with the model: + + mpc = do_mpc.controller.MPC(self.model) + + setup_mpc = { + 'n_horizon': 20, + 'n_robust': 0, # Robust horizon for robust scenario-tree MPC, + 'open_loop': 0, + 't_step': self.time_step, + 'state_discretization': 'collocation', # no other option at the moment + 'collocation_type': 'radau', # no other option at the moment + 'collocation_deg': 2, + 'collocation_ni': 2, + 'store_full_solution': True, # re + #'nlpsol_opts': {'ipopt.linear_solver': 'MA27'} # highly recommended, Use MA27 linear solver in ipopt for faster calculations + } + + mpc.set_param(**setup_mpc) + + # penalties or the cost function you are trying to optimize + mterm = (self.model.x['X_s']-self.x_t)**2 + (self.model.x['Y_s']-self.y_t)**2 # stage cost + lterm = (self.model.x['X_s']-self.x_t)**2 + (self.model.x['Y_s']-self.y_t)**2 # terminal cost + + # simple error without quadratic + # mterm = (model.x['X_s']-self.x_t) + (model.x['Y_s']-self.y_t) # stage cost + # lterm = (model.x['X_s']-self.x_t) + (model.x['Y_s']-self.y_t) # terminal cost + + mpc.set_objective(mterm=mterm, lterm=lterm) + + # input penalties + mpc.set_rterm(u_throttle = 10, u_steering = 10) + + # set constraints + # start with these are there any others???????? + # upper and lower bounds of the control input + mpc.bounds['lower','_u','u_throttle'] = 0.3 + mpc.bounds['upper','_u','u_throttle'] = 5.0 + + mpc.bounds['lower','_u','u_steering'] = -0.523599 + mpc.bounds['upper','_u','u_steering'] = 0.523599 + + mpc.setup() + + return mpc + + + def template_estimator(self): + """configures the estimator (MHE / EKF / state-feedback)""" + return do_mpc.estimator.StateFeedback(self.model) + + def template_simulator(self): + """configures the DAE/ODE/discrete simulator""" + # Obtain an instance of the do-mpc simulator class + # and initiate it with the model: + simulator = do_mpc.simulator.Simulator(self.model) + + # Setup the parameters for the simulator + params_simulator = { + 'integration_tool': 'cvodes', + 'abstol': 1e-10, + 'reltol': 1e-10, + 't_step': self.time_step + } + + # Set parameter(s): + simulator.set_param(**params_simulator) + + # Setup simulator: + simulator.setup() + + return simulator + + + def run_closedloop(self): + + self.mpc.x0 = self.x0 + self.simulator.x0 = self.x0 + self.estimator.x0 = self.x0 + self.mpc.set_initial_guess() + + # visualization + mpc_graphics = do_mpc.graphics.Graphics(self.mpc.data) + sim_graphics = do_mpc.graphics.Graphics(self.simulator.data) + + for k in range(self.n_steps): + u0 = self.mpc.make_step(self.x0) + y_next = self.simulator.make_step(u0) + x0 = self.estimator.make_step(y_next) + + print(x0) + + + fig, ax = plt.subplots(6, sharex=True, figsize=(16,9)) + fig.align_ylabels() + + for g in [sim_graphics,mpc_graphics]: + # Plot the state on axis 1 to 4: + g.add_line(var_type='_x', var_name='X_s', axis=ax[0], color='#1f77b4') + g.add_line(var_type='_x', var_name='Y_s', axis=ax[1], color='#1f77b4') + g.add_line(var_type='_x', var_name='V_s', axis=ax[2], color='#1f77b4') + g.add_line(var_type='_x', var_name='Theta_s', axis=ax[3], color='#1f77b4') + + # Plot the throttle control input on axis 5: + g.add_line(var_type='_u', var_name='u_throttle', axis=ax[4], color='#1f77b4') + # Plot the steering control input on axis 6: + g.add_line(var_type='_u', var_name='u_steering', axis=ax[5], color='#1f77b4') + + ax[0].set_ylabel(r'$X_s$') + ax[1].set_ylabel(r'$Y_s$') + ax[2].set_ylabel(r'$V_s$') + ax[3].set_ylabel(r'$\theta_s$') + ax[4].set_ylabel(r'$u_{throttle}$') + ax[5].set_ylabel(r'$u_{steering}$') + ax[5].set_xlabel(r'$t (seconds)$') + + if(self.static_plot): + sim_graphics.plot_results() + sim_graphics.reset_axes() + mpc_graphics.plot_results() + plt.show(block=True) + else: + # nested function for convenience: + def update(t_ind): + sim_graphics.plot_results(t_ind) + mpc_graphics.plot_predictions(t_ind) + mpc_graphics.reset_axes() + + anim = FuncAnimation(fig, update, frames=self.n_steps, repeat=False) + gif_writer = ImageMagickWriter(fps=10) + anim.save('anim_bicycle_model.gif', writer=gif_writer) + +if __name__ == "__main__": + # line 119 track_porto_26780.csv + x0 = np.asarray([0.958413,0.810734,0.750340,1.003465]) + xt = [1.567785, 1.381567, 0.754297, 0.999855] + bmpc = BicycleMPC(x0,xt[0],xt[1],n_steps=20).run_closedloop() + diff --git a/learning_dompc/bioreactor/anim_batch_reactor_final.gif b/learning_dompc/bioreactor/anim_batch_reactor_final.gif deleted file mode 100644 index 65583be997a7e93051e0b76193511bbfd23cc36e..0000000000000000000000000000000000000000 GIT binary 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