fix nosim demo not updating state correctly
mcarfagno
parent
a2eb20e7be
commit
89e5796fbc
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@ -3,6 +3,7 @@
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib import animation
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from scipy.integrate import odeint
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from mpcpy.utils import compute_path_from_wp
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import mpcpy
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@ -11,17 +12,19 @@ import sys
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import time
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# Robot Starting position
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SIM_START_X=0.
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SIM_START_X = 0.0
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SIM_START_Y = 0.5
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SIM_START_V=0.
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SIM_START_H=0.
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SIM_START_V = 0.0
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SIM_START_H = 0.0
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L = 0.3
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P = mpcpy.Params()
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# Classes
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class MPCSim():
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# Params
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VEL = 1.0 # m/s
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# Classes
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class MPCSim:
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def __init__(self):
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# State for the robot mathematical model [x,y,heading]
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@ -43,8 +46,11 @@ class MPCSim():
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self.mpc = mpcpy.MPC(P.N, P.M, Q, R)
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# Interpolated Path to follow given waypoints
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self.path = compute_path_from_wp([0,3,4,6,10,12,13,13,6,1,0],
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[0,0,2,4,3,3,-1,-2,-6,-2,-2],P.path_tick)
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self.path = compute_path_from_wp(
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[0, 3, 4, 6, 10, 12, 13, 13, 6, 1, 0],
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[0, 0, 2, 4, 3, 3, -1, -2, -6, -2, -2],
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P.path_tick,
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)
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# Sim help vars
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self.sim_time = 0
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@ -62,75 +68,97 @@ class MPCSim():
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plt.ion()
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plt.show()
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def predict_motion(self):
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'''
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'''
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def preview(self, mpc_out):
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"""
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[TODO:summary]
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[TODO:description]
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"""
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predicted = np.zeros(self.opt_u.shape)
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x=self.state[0]
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y=self.state[1]
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v=self.state[2]
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th=self.state[3]
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for idx,a,delta in zip(range(len(self.opt_u[0,:])),self.opt_u[0,:],self.opt_u[1,:]):
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x = x+v*np.cos(th)*P.dt
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y = y+v*np.sin(th)*P.dt
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v = v+a*P.dt
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th = th + v*np.tan(delta)/L*P.dt
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predicted[0,idx]=x
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predicted[1,idx]=y
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predicted[:, :] = mpc_out[0:2, 1:]
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Rotm = np.array(
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[
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[np.cos(self.state[3]), np.sin(self.state[3])],
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[-np.sin(self.state[3]), np.cos(self.state[3])],
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]
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)
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predicted = (predicted.T.dot(Rotm)).T
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predicted[0, :] += self.state[0]
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predicted[1, :] += self.state[1]
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self.predicted = predicted
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def run(self):
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'''
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'''
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"""
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[TODO:summary]
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[TODO:description]
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"""
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self.plot_sim()
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input("Press Enter to continue...")
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while 1:
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if np.sqrt((self.state[0]-self.path[0,-1])**2+(self.state[1]-self.path[1,-1])**2)<0.1:
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if (
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np.sqrt(
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(self.state[0] - self.path[0, -1]) ** 2
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+ (self.state[1] - self.path[1, -1]) ** 2
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)
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< 0.5
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):
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print("Success! Goal Reached")
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input("Press Enter to continue...")
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return
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# optimization loop
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# start=time.time()
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# dynamycs w.r.t robot frame
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curr_state = np.array(
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[0, 0, self.state[2], 0]
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)
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# State Matrices
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A,B,C = mpcpy.get_linear_model_matrices(self.state, self.action)
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#TODO: check why taget does not update?
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A, B, C = mpcpy.get_linear_model_matrices(curr_state, self.action)
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# Get Reference_traj -> inputs are in worldframe
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target, _ = mpcpy.get_ref_trajectory(self.state,
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self.path, 1.0)
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x_mpc, u_mpc = self.mpc.optimize_linearized_model(A, B, C, self.state, target, time_horizon=P.T, verbose=False)
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self.opt_u = np.vstack((np.array(u_mpc.value[0,:]).flatten(),
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(np.array(u_mpc.value[1,:]).flatten())))
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self.action[:] = [u_mpc.value[0,1],u_mpc.value[1,1]]
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target, _ = mpcpy.get_ref_trajectory(
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self.state, self.path, VEL, dl=P.path_tick
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)
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x_mpc, u_mpc = self.mpc.optimize_linearized_model(
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A,
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B,
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C,
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curr_state,
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target,
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time_horizon=P.T,
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verbose=False,
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)
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self.opt_u = np.vstack(
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(
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np.array(u_mpc.value[0, :]).flatten(),
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(np.array(u_mpc.value[1, :]).flatten()),
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)
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)
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self.action[:] = [u_mpc.value[0, 0], u_mpc.value[1, 0]]
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# print("CVXPY Optimization Time: {:.4f}s".format(time.time()-start))
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self.update_sim(self.action[0],self.action[1])
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self.predict_motion()
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self.predict([self.action[0], self.action[1]])
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self.preview(x_mpc.value)
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self.plot_sim()
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def predict(self, u):
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def kinematics_model(x, t, u):
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dxdt = x[2] * np.cos(x[3])
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dydt = x[2] * np.sin(x[3])
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dvdt = u[0]
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dtheta0dt = x[2] * np.tan(u[1]) / P.L
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dqdt = [dxdt, dydt, dvdt, dtheta0dt]
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return dqdt
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def update_sim(self,acc,steer):
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'''
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'''
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self.state[0] = self.state[0] + self.state[2]*np.cos(self.state[3])*P.dt
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self.state[1] = self.state[1] + self.state[2]*np.sin(self.state[3])*P.dt
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self.state[2] = self.state[2] + acc*P.dt
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self.state[3] = self.state[3] + self.state[2]*np.tan(steer)/L*P.dt
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# solve ODE
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tspan = [0, P.DT]
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self.state = odeint(kinematics_model, self.state, tspan, args=(u[:],))[1]
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def plot_sim(self):
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'''
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'''
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self.sim_time = self.sim_time+P.dt
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"""
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[TODO:summary]
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[TODO:description]
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"""
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self.sim_time = self.sim_time + P.DT
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self.x_history.append(self.state[0])
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self.y_history.append(self.state[1])
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self.v_history.append(self.state[2])
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@ -143,22 +171,36 @@ class MPCSim():
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grid = plt.GridSpec(2, 3)
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plt.subplot(grid[0:2, 0:2])
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plt.title("MPC Simulation \n" + "Simulation elapsed time {}s".format(self.sim_time))
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plt.title(
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"MPC Simulation \n" + "Simulation elapsed time {}s".format(self.sim_time)
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)
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plt.plot(self.path[0,:],self.path[1,:], c='tab:orange',
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plt.plot(
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self.path[0, :],
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self.path[1, :],
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c="tab:orange",
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marker=".",
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label="reference track")
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label="reference track",
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)
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plt.plot(self.x_history, self.y_history, c='tab:blue',
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plt.plot(
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self.x_history,
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self.y_history,
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c="tab:blue",
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marker=".",
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alpha=0.5,
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label="vehicle trajectory")
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label="vehicle trajectory",
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)
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if self.predicted is not None:
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plt.plot(self.predicted[0,:], self.predicted[1,:], c='tab:green',
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plt.plot(
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self.predicted[0, :],
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self.predicted[1, :],
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c="tab:green",
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marker="+",
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alpha=0.5,
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label="mpc opt trajectory")
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label="mpc opt trajectory",
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)
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# plt.plot(self.x_history[-1], self.y_history[-1], c='tab:blue',
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# marker=".",
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@ -175,28 +217,32 @@ class MPCSim():
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plot_car(self.x_history[-1], self.y_history[-1], self.h_history[-1])
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plt.ylabel('map y')
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plt.yticks(np.arange(min(self.path[1,:])-1., max(self.path[1,:]+1.)+1, 1.0))
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plt.xlabel('map x')
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plt.xticks(np.arange(min(self.path[0,:])-1., max(self.path[0,:]+1.)+1, 1.0))
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plt.ylabel("map y")
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plt.yticks(
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np.arange(min(self.path[1, :]) - 1.0, max(self.path[1, :] + 1.0) + 1, 1.0)
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)
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plt.xlabel("map x")
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plt.xticks(
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np.arange(min(self.path[0, :]) - 1.0, max(self.path[0, :] + 1.0) + 1, 1.0)
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)
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plt.axis("equal")
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# plt.legend()
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plt.subplot(grid[0, 2])
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# plt.title("Linear Velocity {} m/s".format(self.v_history[-1]))
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plt.plot(self.a_history,c='tab:orange')
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plt.plot(self.a_history, c="tab:orange")
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locs, _ = plt.xticks()
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plt.xticks(locs[1:], locs[1:]*P.dt)
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plt.ylabel('a(t) [m/ss]')
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plt.xlabel('t [s]')
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plt.xticks(locs[1:], locs[1:] * P.DT)
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plt.ylabel("a(t) [m/ss]")
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plt.xlabel("t [s]")
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plt.subplot(grid[1, 2])
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# plt.title("Angular Velocity {} m/s".format(self.w_history[-1]))
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plt.plot(np.degrees(self.d_history),c='tab:orange')
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plt.ylabel('gamma(t) [deg]')
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plt.plot(np.degrees(self.d_history), c="tab:orange")
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plt.ylabel("gamma(t) [deg]")
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locs, _ = plt.xticks()
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plt.xticks(locs[1:], locs[1:]*P.dt)
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plt.xlabel('t [s]')
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plt.xticks(locs[1:], locs[1:] * P.DT)
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plt.xlabel("t [s]")
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plt.tight_layout()
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@ -205,23 +251,41 @@ class MPCSim():
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def plot_car(x, y, yaw):
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"""
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[TODO:summary]
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[TODO:description]
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Parameters
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----------
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x : [TODO:type]
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[TODO:description]
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y : [TODO:type]
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[TODO:description]
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yaw : [TODO:type]
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[TODO:description]
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"""
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LENGTH = 0.5 # [m]
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WIDTH = 0.25 # [m]
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OFFSET = LENGTH # [m]
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outline = np.array([[-OFFSET, (LENGTH - OFFSET), (LENGTH - OFFSET), -OFFSET, -OFFSET],
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[WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
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outline = np.array(
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[
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[-OFFSET, (LENGTH - OFFSET), (LENGTH - OFFSET), -OFFSET, -OFFSET],
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[WIDTH / 2, WIDTH / 2, -WIDTH / 2, -WIDTH / 2, WIDTH / 2],
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]
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)
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Rotm = np.array([[np.cos(yaw), np.sin(yaw)],
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[-np.sin(yaw), np.cos(yaw)]])
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Rotm = np.array([[np.cos(yaw), np.sin(yaw)], [-np.sin(yaw), np.cos(yaw)]])
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outline = (outline.T.dot(Rotm)).T
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outline[0, :] += x
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outline[1, :] += y
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plt.plot(np.array(outline[0, :]).flatten(), np.array(outline[1, :]).flatten(), 'tab:blue')
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plt.plot(
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np.array(outline[0, :]).flatten(), np.array(outline[1, :]).flatten(), "tab:blue"
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)
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def do_sim():
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@ -231,5 +295,6 @@ def do_sim():
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except Exception as e:
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sys.exit(e)
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if __name__ == '__main__':
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if __name__ == "__main__":
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do_sim()
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@ -31,7 +31,7 @@ def set_ctrl(robotId,currVel,acceleration,steeringAngle):
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wheels = [8,15]
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maxForce = 50
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targetVelocity = currVel + acceleration*P.dt
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targetVelocity = currVel + acceleration*P.DT
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#targetVelocity=lastVel
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#print(targetVelocity)
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@ -158,10 +158,10 @@ def run_sim():
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state[3] = 0.0
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#add 1 timestep delay to input
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state[0]=state[0]+state[2]*np.cos(state[3])*P.dt
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state[1]=state[1]+state[2]*np.sin(state[3])*P.dt
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state[2]=state[2]+action[0]*P.dt
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state[3]=state[3]+action[0]*np.tan(action[1])/P.L*P.dt
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state[0]=state[0]+state[2]*np.cos(state[3])*P.DT
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state[1]=state[1]+state[2]*np.sin(state[3])*P.DT
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state[2]=state[2]+action[0]*P.DT
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state[3]=state[3]+action[0]*np.tan(action[1])/P.L*P.DT
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#optimization loop
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@ -186,8 +186,8 @@ def run_sim():
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set_ctrl(car,state[2],action[0],action[1])
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if P.dt-elapsed>0:
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time.sleep(P.dt-elapsed)
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if P.DT-elapsed>0:
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time.sleep(P.DT-elapsed)
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if __name__ == '__main__':
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run_sim()
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@ -34,15 +34,15 @@ def get_linear_model_matrices(x_bar,u_bar):
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A[1,2] = st
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A[1,3] = v*ct
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A[3,2] = v*td/P.L
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A_lin = np.eye(P.N)+P.dt*A
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A_lin = np.eye(P.N)+P.DT*A
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B = np.zeros((P.N,P.M))
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B[2,0]=1
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B[3,1]=v/(P.L*cd**2)
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B_lin=P.dt*B
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B_lin=P.DT*B
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f_xu=np.array([v*ct, v*st, a, v*td/P.L]).reshape(P.N,1)
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C_lin = P.dt*(f_xu - np.dot(A, x_bar.reshape(P.N,1)) - np.dot(B, u_bar.reshape(P.M,1))).flatten()
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C_lin = P.DT*(f_xu - np.dot(A, x_bar.reshape(P.N,1)) - np.dot(B, u_bar.reshape(P.M,1))).flatten()
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#return np.round(A_lin,6), np.round(B_lin,6), np.round(C_lin,6)
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return A_lin, B_lin, C_lin
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@ -98,8 +98,8 @@ class MPC():
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# Actuation rate of change
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if t < (time_horizon - 1):
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_cost += opt.quad_form(u[:,t + 1] - u[:,t], R * 1)
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_constraints += [opt.abs(u[0, t + 1] - u[0, t])/P.dt <= P.MAX_D_ACC]
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_constraints += [opt.abs(u[1, t + 1] - u[1, t])/P.dt <= P.MAX_D_STEER]
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_constraints += [opt.abs(u[0, t + 1] - u[0, t])/P.DT <= P.MAX_D_ACC]
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_constraints += [opt.abs(u[1, t + 1] - u[1, t])/P.DT <= P.MAX_D_STEER]
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if t == 0:
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@ -1,11 +1,12 @@
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import numpy as np
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class Params():
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class Params:
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def __init__(self):
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self.N = 4 # number of state variables
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self.M = 2 # number of control variables
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self.T = 10 # Prediction Horizon
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self.dt = 0.2 #discretization step
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self.DT = 0.2 # discretization step
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self.path_tick = 0.05
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self.L = 0.3 # vehicle wheelbase
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self.MAX_SPEED = 1.5 # m/s
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@ -1,34 +1,33 @@
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import numpy as np
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from scipy.interpolate import interp1d
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from .mpc_config import Params
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P = Params()
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||||
|
||||
def compute_path_from_wp(start_xp, start_yp, step=0.1):
|
||||
"""
|
||||
Computes a reference path given a set of waypoints
|
||||
"""
|
||||
|
||||
final_xp = []
|
||||
final_yp = []
|
||||
delta = step # [m]
|
||||
|
||||
for idx in range(len(start_xp) - 1):
|
||||
section_len = np.sum(np.sqrt(np.power(np.diff(start_xp[idx:idx+2]),2)+np.power(np.diff(start_yp[idx:idx+2]),2)))
|
||||
|
||||
section_len = np.sum(
|
||||
np.sqrt(
|
||||
np.power(np.diff(start_xp[idx : idx + 2]), 2)
|
||||
+ np.power(np.diff(start_yp[idx : idx + 2]), 2)
|
||||
)
|
||||
)
|
||||
interp_range = np.linspace(0, 1, np.floor(section_len / delta).astype(int))
|
||||
|
||||
fx = interp1d(np.linspace(0, 1, 2), start_xp[idx : idx + 2], kind=1)
|
||||
fy = interp1d(np.linspace(0, 1, 2), start_yp[idx : idx + 2], kind=1)
|
||||
|
||||
# watch out to duplicate points!
|
||||
final_xp = np.append(final_xp, fx(interp_range)[1:])
|
||||
final_yp = np.append(final_yp, fy(interp_range)[1:])
|
||||
|
||||
dx = np.append(0, np.diff(final_xp))
|
||||
dy = np.append(0, np.diff(final_yp))
|
||||
theta = np.arctan2(dy, dx)
|
||||
|
||||
return np.vstack((final_xp, final_yp, theta))
|
||||
|
||||
|
||||
|
|
@ -36,76 +35,61 @@ def get_nn_idx(state,path):
|
|||
"""
|
||||
Computes the index of the waypoint closest to vehicle
|
||||
"""
|
||||
|
||||
dx = state[0] - path[0, :]
|
||||
dy = state[1] - path[1, :]
|
||||
dist = np.hypot(dx, dy)
|
||||
nn_idx = np.argmin(dist)
|
||||
|
||||
try:
|
||||
v = [path[0,nn_idx+1] - path[0,nn_idx],
|
||||
path[1,nn_idx+1] - path[1,nn_idx]]
|
||||
v = [
|
||||
path[0, nn_idx + 1] - path[0, nn_idx],
|
||||
path[1, nn_idx + 1] - path[1, nn_idx],
|
||||
]
|
||||
v /= np.linalg.norm(v)
|
||||
|
||||
d = [path[0,nn_idx] - state[0],
|
||||
path[1,nn_idx] - state[1]]
|
||||
|
||||
d = [path[0, nn_idx] - state[0], path[1, nn_idx] - state[1]]
|
||||
if np.dot(d, v) > 0:
|
||||
target_idx = nn_idx
|
||||
else:
|
||||
target_idx = nn_idx + 1
|
||||
|
||||
except IndexError as e:
|
||||
target_idx = nn_idx
|
||||
|
||||
return target_idx
|
||||
|
||||
|
||||
def normalize_angle(angle):
|
||||
"""
|
||||
Normalize an angle to [-pi, pi]
|
||||
"""
|
||||
while angle > np.pi:
|
||||
angle -= 2.0 * np.pi
|
||||
|
||||
while angle < -np.pi:
|
||||
angle += 2.0 * np.pi
|
||||
|
||||
return angle
|
||||
|
||||
def get_ref_trajectory(state, path, target_v):
|
||||
|
||||
def get_ref_trajectory(state, path, target_v, dl=0.1):
|
||||
"""
|
||||
For each step in the time horizon
|
||||
modified reference in robot frame
|
||||
"""
|
||||
xref = np.zeros((P.N, P.T + 1))
|
||||
dref = np.zeros((1, P.T + 1))
|
||||
|
||||
# sp = np.ones((1,T +1))*target_v #speed profile
|
||||
|
||||
ncourse = path.shape[1]
|
||||
|
||||
ind = get_nn_idx(state, path)
|
||||
dx = path[0, ind] - state[0]
|
||||
dy = path[1, ind] - state[1]
|
||||
|
||||
|
||||
xref[0, 0] = dx * np.cos(-state[3]) - dy * np.sin(-state[3]) # X
|
||||
xref[1, 0] = dy * np.cos(-state[3]) + dx * np.sin(-state[3]) # Y
|
||||
xref[2, 0] = target_v # V
|
||||
xref[3, 0] = normalize_angle(path[2, ind] - state[3]) # Theta
|
||||
dref[0, 0] = 0.0 # steer operational point should be 0
|
||||
|
||||
dl = 0.05 # Waypoints spacing [m]
|
||||
dref[0, 0] = 0.0 # Steer operational point should be 0
|
||||
travel = 0.0
|
||||
|
||||
for i in range(1, P.T + 1):
|
||||
travel += abs(target_v) * P.dt #current V or target V?
|
||||
travel += abs(target_v) * P.DT
|
||||
dind = int(round(travel / dl))
|
||||
|
||||
if (ind + dind) < ncourse:
|
||||
dx = path[0, ind + dind] - state[0]
|
||||
dy = path[1, ind + dind] - state[1]
|
||||
|
||||
xref[0, i] = dx * np.cos(-state[3]) - dy * np.sin(-state[3])
|
||||
xref[1, i] = dy * np.cos(-state[3]) + dx * np.sin(-state[3])
|
||||
xref[2, i] = target_v # sp[ind + dind]
|
||||
|
|
@ -114,11 +98,9 @@ def get_ref_trajectory(state, path, target_v):
|
|||
else:
|
||||
dx = path[0, ncourse - 1] - state[0]
|
||||
dy = path[1, ncourse - 1] - state[1]
|
||||
|
||||
xref[0, i] = dx * np.cos(-state[3]) - dy * np.sin(-state[3])
|
||||
xref[1, i] = dy * np.cos(-state[3]) + dx * np.sin(-state[3])
|
||||
xref[2, i] = 0.0 # stop? #sp[ncourse - 1]
|
||||
xref[3, i] = normalize_angle(path[2, ncourse - 1] - state[3])
|
||||
dref[0, i] = 0.0
|
||||
|
||||
return xref, dref
|
||||
|
|
|
|||
Loading…
Reference in New Issue