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https://github.com/zhm-real/PathPlanning.git
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zhm-real
139 lines
5.0 KiB
Python
139 lines
5.0 KiB
Python
#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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@author: huiming zhou
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"""
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import env
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import tools
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import motion_model
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import matplotlib.pyplot as plt
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import numpy as np
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import sys
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class Value_iteration:
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def __init__(self, x_start, x_goal):
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self.u_set = motion_model.motions # feasible input set
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self.xI, self.xG = x_start, x_goal
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self.e = 0.001 # threshold for convergence
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self.gamma = 0.9 # discount factor
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self.obs = env.obs_map() # position of obstacles
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self.lose = env.lose_map() # position of lose states
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self.name1 = "value_iteration, gamma=" + str(self.gamma)
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self.name2 = "converge process, e=" + str(self.e)
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def iteration(self):
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"""
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value_iteration.
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:return: converged value table, optimal policy and variation of difference,
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"""
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value_table = {} # value table
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policy = {} # policy
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diff = [] # maximum difference between two successive iteration
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delta = sys.maxsize # initialize maximum difference
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count = 0 # iteration times
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for i in range(env.x_range):
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for j in range(env.y_range):
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if (i, j) not in self.obs:
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value_table[(i, j)] = 0 # initialize value table for feasible states
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while delta > self.e: # converged condition
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count += 1
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x_value = 0
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for x in value_table:
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if x not in self.xG:
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value_list = []
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for u in self.u_set:
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[x_next, p_next] = motion_model.move_prob(x, u, self.obs) # recall motion model
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value_list.append(self.cal_Q_value(x_next, p_next, value_table)) # cal Q value
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policy[x] = self.u_set[int(np.argmax(value_list))] # update policy
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v_diff = abs(value_table[x] - max(value_list)) # maximum difference
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value_table[x] = max(value_list) # update value table
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if v_diff > 0:
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x_value = max(x_value, v_diff)
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delta = x_value # update delta
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diff.append(delta)
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self.message(count) # print key parameters
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return value_table, policy, diff
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def cal_Q_value(self, x, p, table):
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"""
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cal Q_value.
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:param x: next state vector
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:param p: probability of each state
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:param table: value table
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:return: Q-value
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"""
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value = 0
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reward = env.get_reward(x, self.xG, self.lose) # get reward of next state
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for i in range(len(x)):
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value += p[i] * (reward[i] + self.gamma * table[x[i]]) # cal Q-value
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return value
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def simulation(self, xI, xG, policy, diff):
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"""
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simulate a path using converged policy.
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:param xI: starting state
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:param xG: goal state
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:param policy: converged policy
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:return: simulation path
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"""
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plt.figure(1) # path animation
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tools.show_map(xI, xG, self.obs, self.lose, self.name1) # show background
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x, path = xI, []
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while True:
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u = policy[x]
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x_next = (x[0] + u[0], x[1] + u[1])
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if x_next in self.obs:
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print("Collision!") # collision: simulation failed
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else:
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x = x_next
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if x_next in xG: break
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else:
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tools.plot_dots(x) # each state in optimal path
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path.append(x)
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plt.pause(1)
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plt.figure(2) # difference between two successive iteration
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plt.plot(diff, color='#808080', marker='o')
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plt.title(self.name2, fontdict=None)
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plt.xlabel('iterations')
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plt.ylabel('difference of successive iterations')
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plt.grid('on')
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plt.show()
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return path
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def message(self, count):
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print("starting state: ", self.xI)
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print("goal states: ", self.xG)
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print("condition for convergence: ", self.e)
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print("discount factor: ", self.gamma)
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print("iteration times: ", count)
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if __name__ == '__main__':
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x_Start = (5, 5) # starting state
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x_Goal = [(49, 5), (49, 25)] # goal states
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VI = Value_iteration(x_Start, x_Goal)
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[value_VI, policy_VI, diff_VI] = VI.iteration()
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path_VI = VI.simulation(x_Start, x_Goal, policy_VI, diff_VI)
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