diff --git a/Search-based Planning/.idea/workspace.xml b/Search-based Planning/.idea/workspace.xml
index 51a21ab..9151c1d 100644
--- a/Search-based Planning/.idea/workspace.xml	
+++ b/Search-based Planning/.idea/workspace.xml	
@@ -2,11 +2,9 @@
 <project version="4">
   <component name="ChangeListManager">
     <list default="true" id="025aff36-a6aa-4945-ab7e-b2c625055f47" name="Default Changelist" comment="">
-      <change afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/policy_iteration.py" afterDir="false" />
+      <change afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/Q-value_iteration.py" afterDir="false" />
       <change beforePath="$PROJECT_DIR$/.idea/workspace.xml" beforeDir="false" afterPath="$PROJECT_DIR$/.idea/workspace.xml" afterDir="false" />
-      <change beforePath="$PROJECT_DIR$/../Stochastic Shortest Path/env.py" beforeDir="false" afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/env.py" afterDir="false" />
-      <change beforePath="$PROJECT_DIR$/../Stochastic Shortest Path/tools.py" beforeDir="false" afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/tools.py" afterDir="false" />
-      <change beforePath="$PROJECT_DIR$/../Stochastic Shortest Path/value_iteration.py" beforeDir="false" afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/value_iteration.py" afterDir="false" />
+      <change beforePath="$PROJECT_DIR$/../Stochastic Shortest Path/policy_iteration.py" beforeDir="false" afterPath="$PROJECT_DIR$/../Stochastic Shortest Path/policy_iteration.py" afterDir="false" />
     </list>
     <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
     <option name="SHOW_DIALOG" value="false" />
diff --git a/Stochastic Shortest Path/Q-policy_iteration.py b/Stochastic Shortest Path/Q-policy_iteration.py
new file mode 100644
index 0000000..d83bd3a
--- /dev/null
+++ b/Stochastic Shortest Path/Q-policy_iteration.py	
@@ -0,0 +1,121 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+@author: huiming zhou
+"""
+
+import env
+import tools
+import motion_model
+
+import matplotlib.pyplot as plt
+import numpy as np
+import copy
+import sys
+
+
+class Q_policy_iteration:
+    def __init__(self, x_start, x_goal):
+        self.u_set = motion_model.motions  # feasible input set
+        self.xI, self.xG = x_start, x_goal
+        self.e = 0.001
+        self.gamma = 0.9
+        self.obs = env.obs_map()  # position of obstacles
+        self.lose = env.lose_map()
+        self.name1 = "policy_iteration, e=" + str(self.e) + ", gamma=" + str(self.gamma)
+        self.name2 = "convergence of error"
+
+
+    def policy_evaluation(self, policy, value):
+        delta = sys.maxsize
+
+        while delta > self.e:
+            x_value = 0
+            for x in value:
+                if x not in self.xG:
+                    for k in range(len(self.u_set)):
+                        [x_next, p_next] = motion_model.move_prob(x, self.u_set[k], self.obs)
+                        v_Q = self.cal_Q_value(x_next, p_next, policy, value)
+                        v_diff = abs(value[x][k] - v_Q)
+                        value[x][k] = v_Q
+                        if v_diff > 0:
+                            x_value = max(x_value, v_diff)
+            delta = x_value
+        return value
+
+
+    def policy_improvement(self, policy, value):
+        for x in value:
+            if x not in self.xG:
+                policy[x] = int(np.argmax(value[x]))
+        return policy
+
+
+    def iteration(self):
+        Q_table = {}
+        policy = {}
+
+        for i in range(env.x_range):
+            for j in range(env.y_range):
+                if (i, j) not in self.obs:
+                    Q_table[(i, j)] = [0, 0, 0, 0]
+                    policy[(i, j)] = 0
+
+        while True:
+            policy_back = copy.deepcopy(policy)
+            Q_table = self.policy_evaluation(policy, Q_table)
+            policy = self.policy_improvement(policy, Q_table)
+            if policy_back == policy: break
+        return Q_table, policy
+
+
+    def simulation(self, xI, xG, policy):
+        path = []
+        x = xI
+        while x not in xG:
+            u = self.u_set[policy[x]]
+            x_next = (x[0] + u[0], x[1] + u[1])
+            if x_next not in self.obs:
+                x = x_next
+                path.append(x)
+        path.pop()
+        return path
+
+
+    def animation(self, path):
+        plt.figure(1)
+        tools.show_map(self.xI, self.xG, self.obs, self.lose, self.name1)
+        for x in path:
+            tools.plot_dots(x)
+        plt.show()
+
+
+    def cal_Q_value(self, x, p, policy, table):
+        value = 0
+        reward = self.get_reward(x)
+        for i in range(len(x)):
+            value += p[i] * (reward[i] + self.gamma * table[x[i]][policy[x[i]]])
+        return value
+
+
+    def get_reward(self, x_next):
+        reward = []
+        for x in x_next:
+            if x in self.xG:
+                reward.append(10)
+            elif x in self.lose:
+                reward.append(-10)
+            else:
+                reward.append(0)
+        return reward
+
+
+if __name__ == '__main__':
+    x_Start = (5, 5)
+    x_Goal = [(49, 5), (49, 25)]
+
+    QPI = Q_policy_iteration(x_Start, x_Goal)
+    [value_QPI, policy_QPI] = QPI.iteration()
+    path_QPI = QPI.simulation(x_Start, x_Goal, policy_QPI)
+
+    QPI.animation(path_QPI)
diff --git a/Stochastic Shortest Path/Q-value_iteration.py b/Stochastic Shortest Path/Q-value_iteration.py
new file mode 100644
index 0000000..e5234ad
--- /dev/null
+++ b/Stochastic Shortest Path/Q-value_iteration.py	
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+@author: huiming zhou
+"""
+
+import env
+import tools
+import motion_model
+
+import matplotlib.pyplot as plt
+import numpy as np
+import sys
+
+class Q_value_iteration:
+    def __init__(self, x_start, x_goal):
+        self.u_set = motion_model.motions                      # feasible input set
+        self.xI, self.xG = x_start, x_goal
+        self.e = 0.001
+        self.gamma = 0.9
+        self.obs = env.obs_map()                               # position of obstacles
+        self.lose = env.lose_map()
+        self.name1 = "value_iteration, e=" + str(self.e) + ", gamma=" + str(self.gamma)
+        self.name2 = "convergence of error"
+
+
+    def iteration(self):
+        Q_table = {}
+        policy = {}
+        delta = sys.maxsize
+
+        for i in range(env.x_range):
+            for j in range(env.y_range):
+                if (i, j) not in self.obs:
+                    Q_table[(i, j)] = [0, 0, 0, 0]
+
+        while delta > self.e:
+            x_value = 0
+            for x in Q_table:
+                if x not in x_Goal:
+                    for k in range(len(self.u_set)):
+                        [x_next, p_next] = motion_model.move_prob(x, self.u_set[k], self.obs)
+                        Q_value = self.cal_Q_value(x_next, p_next, Q_table)
+                        v_diff = abs(Q_table[x][k] - Q_value)
+                        Q_table[x][k] = Q_value
+                        if v_diff > 0:
+                            x_value = max(x_value, v_diff)
+            delta = x_value
+
+        for x in Q_table:
+            if x not in x_Goal:
+                policy[x] = np.argmax(Q_table[x])
+        return policy
+
+
+    def simulation(self, xI, xG, policy):
+        path = []
+        x = xI
+        while x not in xG:
+            u = self.u_set[policy[x]]
+            x_next = (x[0] + u[0], x[1] + u[1])
+            if x_next not in self.obs:
+                x = x_next
+                path.append(x)
+        path.pop()
+        return path
+
+
+    def animation(self, path):
+        plt.figure(1)
+        tools.show_map(self.xI, self.xG, self.obs, self.lose, self.name1)
+        for x in path:
+            tools.plot_dots(x)
+        plt.show()
+
+
+    def cal_Q_value(self, x, p, table):
+        value = 0
+        reward = self.get_reward(x)
+        for i in range(len(x)):
+            value += p[i] * (reward[i] + self.gamma * max(table[x[i]]))
+        return value
+
+
+    def get_reward(self, x_next):
+        reward = []
+        for x in x_next:
+            if x in self.xG:
+                reward.append(10)
+            elif x in self.lose:
+                reward.append(-10)
+            else:
+                reward.append(0)
+        return reward
+
+
+if __name__ == '__main__':
+    x_Start = (5, 5)
+    x_Goal = [(49, 5), (49, 25)]
+
+    QVI = Q_value_iteration(x_Start, x_Goal)
+    policy_QVI = QVI.iteration()
+    path_VI = QVI.simulation(x_Start, x_Goal, policy_QVI)
+
+    QVI.animation(path_VI)
diff --git a/Stochastic Shortest Path/policy_iteration.py b/Stochastic Shortest Path/policy_iteration.py
index 06c5306..2660f0a 100644
--- a/Stochastic Shortest Path/policy_iteration.py	
+++ b/Stochastic Shortest Path/policy_iteration.py	
@@ -102,6 +102,7 @@ class Policy_iteration:
             value += p[i] * (reward[i] + self.gamma * table[x[i]])
         return value
 
+
     def get_reward(self, x_next):
         reward = []
         for x in x_next: