#! /usr/bin/env python import numpy as np import matplotlib.pyplot as plt from matplotlib import animation from utils import compute_path_from_wp from cvxpy_mpc import optimize import sys import time # Robot Starting position SIM_START_X=0 SIM_START_Y=0.5 SIM_START_H=0 from mpc_config import Params P=Params() # Classes class MPC(): def __init__(self): # State for the robot mathematical model [x,y,heading] self.state = [SIM_START_X, SIM_START_Y, SIM_START_H] self.opt_u = np.zeros((P.M,P.T)) self.opt_u[0,:] = 1 #m/s self.opt_u[1,:] = np.radians(0) #rad/s # Interpolated Path to follow given waypoints #self.path = compute_path_from_wp([0,10,12,2,4,14],[0,0,2,10,12,12]) self.path = compute_path_from_wp([0,3,4,6,10,13], [0,0,2,4,3,3],1) # Sim help vars self.sim_time=0 self.x_history=[] self.y_history=[] self.h_history=[] self.v_history=[] self.w_history=[] self.predicted=None #Initialise plot plt.style.use("ggplot") self.fig = plt.figure() plt.ion() plt.show() def predict_motion(self): ''' ''' predicted=np.zeros(self.opt_u.shape) x=self.state[0] y=self.state[1] th=self.state[2] for idx,v,w in zip(range(len(self.opt_u[0,:])),self.opt_u[0,:],self.opt_u[1,:]): x = x+v*np.cos(th)*P.dt y = y+v*np.sin(th)*P.dt th= th +w*P.dt predicted[0,idx]=x predicted[1,idx]=y self.predicted = predicted def run(self): ''' ''' while 1: if self.state is not None: if np.sqrt((self.state[0]-self.path[0,-1])**2+(self.state[1]-self.path[1,-1])**2)<1: print("Success! Goal Reached") return #optimization loop start=time.time() self.opt_u = optimize(self.state, self.opt_u, self.path) # print("CVXPY Optimization Time: {:.4f}s".format(time.time()-start)) self.update_sim(self.opt_u[0,1],self.opt_u[1,1]) self.predict_motion() self.plot_sim() def update_sim(self,lin_v,ang_v): ''' Updates state. :param lin_v: float :param ang_v: float ''' self.state[0] = self.state[0] +lin_v*np.cos(self.state[2])*P.dt self.state[1] = self.state[1] +lin_v*np.sin(self.state[2])*P.dt self.state[2] = self.state[2] +ang_v*P.dt def plot_sim(self): self.sim_time = self.sim_time+P.dt self.x_history.append(self.state[0]) self.y_history.append(self.state[1]) self.h_history.append(self.state[2]) self.v_history.append(self.opt_u[0,1]) self.w_history.append(self.opt_u[1,1]) plt.clf() grid = plt.GridSpec(2, 3) plt.subplot(grid[0:2, 0:2]) plt.title("MPC Simulation \n" + "Simulation elapsed time {}s".format(self.sim_time)) plt.plot(self.path[0,:],self.path[1,:], c='tab:orange', marker=".", label="reference track") plt.plot(self.x_history, self.y_history, c='tab:blue', marker=".", alpha=0.5, label="vehicle trajectory") if self.predicted is not None: plt.plot(self.predicted[0,:], self.predicted[1,:], c='tab:green', marker=".", alpha=0.5, label="mpc opt trajectory") # plt.plot(self.x_history[-1], self.y_history[-1], c='tab:blue', # marker=".", # markersize=12, # label="vehicle position") # plt.arrow(self.x_history[-1], # self.y_history[-1], # np.cos(self.h_history[-1]), # np.sin(self.h_history[-1]), # color='tab:blue', # width=0.2, # head_length=0.5, # label="heading") plot_car(self.x_history[-1], self.y_history[-1], self.h_history[-1]) plt.ylabel('map y') plt.yticks(np.arange(min(self.path[1,:])-1., max(self.path[1,:]+1.)+1, 1.0)) plt.xlabel('map x') plt.xticks(np.arange(min(self.path[0,:])-1., max(self.path[0,:]+1.)+1, 1.0)) plt.axis("equal") #plt.legend() plt.subplot(grid[0, 2]) #plt.title("Linear Velocity {} m/s".format(self.v_history[-1])) plt.plot(self.v_history,c='tab:orange') locs, _ = plt.xticks() plt.xticks(locs[1:], locs[1:]*P.dt) plt.ylabel('v(t) [m/s]') plt.xlabel('t [s]') plt.subplot(grid[1, 2]) #plt.title("Angular Velocity {} m/s".format(self.w_history[-1])) plt.plot(np.degrees(self.w_history),c='tab:orange') plt.ylabel('w(t) [deg/s]') locs, _ = plt.xticks() plt.xticks(locs[1:], locs[1:]*P.dt) plt.xlabel('t [s]') plt.tight_layout() plt.draw() plt.pause(0.1) def plot_car(x, y, yaw): LENGTH = 1.0 # [m] WIDTH = 0.5 # [m] OFFSET = LENGTH/2 # [m] outline = np.array([[-OFFSET, (LENGTH - OFFSET), (LENGTH - OFFSET), -OFFSET, -OFFSET], [WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]]) Rotm = np.array([[np.cos(yaw), np.sin(yaw)], [-np.sin(yaw), np.cos(yaw)]]) outline = (outline.T.dot(Rotm)).T outline[0, :] += x outline[1, :] += y plt.plot(np.array(outline[0, :]).flatten(), np.array(outline[1, :]).flatten(), 'tab:blue') def do_sim(): sim=MPC() try: sim.run() except Exception as e: sys.exit(e) if __name__ == '__main__': do_sim()