implementing mix integer path planning

Author: AtsushiSakai

PathPlanning/MixIntegerPathPlanning/mix_integer_path_planning.py

@@ -5,18 +5,6 @@
 """
 
 """
-solver = CplexSolver(CPX_PARAM_SCRIND=0)
-
-const A = [1.0 0.0;
-        0.0 1.0]
-const B = [1.0 1.0;
-        0.0 1.0]
-const q = [1.0; 1.0]
-const r = [1.0; 1.0]
-
-const u_max = 0.1
-const T = 50
-const M = 10000.0
 
 function control(is, gs, ob)
 
@@ -65,28 +53,10 @@
     return s_vec, u_vec
 end
 
-function plot_obstacle(ob)
-    for i in 1:length(ob[:,1])
-        x = [ob[i,1],ob[i,2],ob[i,2],ob[i,1],ob[i,1]]
-        y = [ob[i,3],ob[i,3],ob[i,4],ob[i,4],ob[i,3]]
-        plt.plot(x,y,"-g")
-    end
-end
 
 function main()
-    println(PROGRAM_FILE," start!!")
-
-    s = [10.0, 5.0] # init state
-    gs = [5.0, 7.0] # goal state
-
-    ob = [7.0 8.0 3.0 8.0;
-         5.5 6.0 6.0 10.0;] # [xmin xmax ymin ymax]
-
-    h_sx = []
-    h_sy = []
 
     for i=1:10000
-        s_p, u_p = control(s, gs, ob)
 
         if sqrt((gs[1]-s[1])^2+(gs[2]-s[2])^2) <= 0.1
             println("Goal!!!")
@@ -98,17 +68,6 @@
         push!(h_sx, s[1])
         push!(h_sy, s[2])
 
-        plt.cla()
-        plt.plot(gs[1],gs[2],"*r")
-        plt.plot(s_p[1,:],s_p[2,:],"xb")
-        plot_obstacle(ob)
-        plt.plot(s_p[1,:],s_p[2,:],"xb")
-        plt.plot(h_sx,h_sy,"-b")
-        plt.plot(s[1],s[2],"or")
-        plt.axis("equal")
-        plt.grid(true)
-        plt.pause(0.0001)
-
     end
 
     plt.cla()
@@ -123,10 +82,116 @@
 end
 """
 
+import cvxpy
+import numpy as np
+import matplotlib.pyplot as plt
+
+# parameter
+A = np.matrix([[1.0, 0.0],
+               [0.0, 1.0]])
+B = np.matrix([[1.0, 1.0],
+               [0.0, 1.0]])
+q = np.matrix([[1.0],
+               [1.0]])
+r = np.matrix([[1.0],
+               [1.0]])
+
+u_max = 0.1
+T = 50
+M = 10000.0
+
+
+def plot_obstacle(ob):
+    for i in range(len(ob)):
+        x = [ob[i, 0], ob[i, 1], ob[i, 1], ob[i, 0], ob[i, 0]]
+        y = [ob[i, 2], ob[i, 2], ob[i, 3], ob[i, 3], ob[i, 2]]
+        plt.plot(x, y, "-g")
+
+
+def control(s1, gs, ob):
+
+    #  w = cvxpy.Variable(2, T)
+    #  v = cvxpy.Variable(2, T)
+    s = cvxpy.Variable(2, T)
+    u = cvxpy.Variable(2, T)
+    #  ob = 2
+    #  o = cvxpy.Bool(4 * ob, T)
+
+    constraints = [-u_max <= u, u <= u_max]
+
+    constraints.append(s[:, 1] == s1)
+
+    #  obj = [s]
+    #  for i in range(T)
+
+    #  @constraint(model, s[:, i] - gs . <= w[:, i])
+    #  @constraint(model, -s[:, i] + gs . <= w[:, i])
+    #  @constraint(model, u[:, i] . <= v[:, i])
+    #  @constraint(model, -u[:, i] . <= v[:, i])
+    #  push!(obj, q'*w[1:end,i]+r' * v[1:2, i])
+
+    #  # obstable avoidanse
+    #  for io in 1:
+    #  nob
+    #  start_ind = 1 + (io - 1) * 4
+
+    #  @constraint(model, sum(o[start_ind:start_ind + 3, i]) <= 3)
+    #  @constraint(model, s[1, i] <= ob[io, 1] + M * o[start_ind, i])
+    #  @constraint(model, -s[1, i] <= -ob[io, 2] + M * o[start_ind + 1, i])
+    #  @constraint(model, s[2, i] <= ob[io, 3] + M * o[start_ind + 2, i])
+    #  @constraint(model, -s[2, i] <= -ob[io, 4] + M * o[start_ind + 3, i])
+    #  end
+    #  end
+
+    for i in range(T - 1):
+        constraints.append(s[:, 1] == s1)
+
+        #  @constraint(model, s[:, i + 1] . == A * s[:, i] + B * u[:, i])
+
+    objective = cvxpy.Minimize(cvxpy.sum_squares(s))
+
+    prob = cvxpy.Problem(objective, constraints)
+
+    prob.solve()
+
+    s_p = []
+    u_p = np.matrix([[0.1], [0.1]])
+
+    return s_p, u_p
+
 
 def main():
     print(__file__ + " start!!")
 
+    s = np.matrix([10.0, 5.0]).T  # init state
+    gs = np.matrix([5.0, 7.0]).T  # goal state
+
+    ob = np.matrix([[7.0, 8.0, 3.0, 8.0],
+                    [5.5, 6.0, 6.0, 10.0]])  # [xmin xmax ymin ymax]
+
+    h_sx = []
+    h_sy = []
+
+    for i in range(10000):
+        print(i)
+        s_p, u_p = control(s, gs, ob)
+
+        s = A * s + B * u_p[:, 0]  # simulation
+
+        h_sx.append(s[0, 0])
+        h_sy.append(s[1, 0])
+
+        plt.cla()
+        plt.plot(gs[0], gs[1], "*r")
+        plot_obstacle(ob)
+        #  plt.plot(s_p[1, :], s_p[2, :], "xb")
+        #  plt.plot(s_p[1, :], s_p[2, :], "xb")
+        plt.plot(h_sx, h_sy, "-b")
+        plt.plot(s[0], s[1], "or")
+        plt.axis("equal")
+        plt.grid(True)
+        plt.pause(0.0001)
+
 
 if __name__ == '__main__':
     main()