add spacecraft rendezvous example

examples/rendezvous/__init__.py

+from rendezvous import *
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examples/rendezvous/rendezvous.py

+from scipy.integrate import odeint
+import numpy as np 
+
+def ProxA_dynamics(x,_):
+    xp, yp, xd, yd = x 
+    xp_dot = xd
+    yp_dot= yd
+    xd_dot= -2.89995083970656*xd - 0.0576765518445905*xp + 0.00877200894463775*yd + 0.000200959896519766*yp - (1.43496e+18*xp + 6.050365344e+25)*pow(pow(yp, 2) + pow(xp + 42164000, 2), -1.5) + 807.153595726846
+    yd_dot= -0.00875351105536225*xd - 0.000174031357370456*xp - 2.90300269286856*yd - 1.43496e+18*yp*pow(pow(yp, 2) + pow(xp + 42164000, 2), -1.5) - 0.0664932019993982*yp
+    return [xp_dot, yp_dot, xd_dot, yd_dot]
+
+def ProxB_dynamics(x,t):
+    xp, yp, xd, yd = x 
+    xp_dot= xd
+    yp_dot= yd
+    xd_dot= -19.2299795908647*xd - 0.576076729033652*xp + 0.00876275931760007*yd + 0.000262486079431672*yp - (1.43496e+18*xp + 6.050365344e+25)*pow(pow(yp, 2) + pow(xp + 42164000, 2), -1.5) + 807.153595726846
+    yd_dot= -0.00876276068239993*xd - 0.000262486080737868*xp - 19.2299765959399*yd - 1.43496e+18*yp*pow(pow(yp, 2) + pow(xp + 42164000, 2), -1.5) - 0.575980743701182*yp
+    return [xp_dot, yp_dot, xd_dot, yd_dot]
+
+def Passive_dynamics(x,t):
+    xp, yp, xd, yd = x 
+    xp_dot = xd
+    yp_dot = yd
+    xd_dot = 0.0000575894721132000*xp+0.00876276*yd
+    yd_dot = -0.00876276*xd
+    return [xp_dot, yp_dot, xd_dot, yd_dot]
+
+def simulate(init, time_bound, time_step, dynamics):
+    num_step = int(time_bound/time_step)
+    x = init
+    trace = [[0]+x]
+    t = 0
+    for i in range(num_step):
+        x = odeint(dynamics, x, [0,time_step])[-1].tolist()
+        t += time_step 
+        trace.append([t]+x)
+    return np.array(trace)
+
+def TC_Simulate(Mode,initialCondition,time_bound):
+    time_step = 0.01
+    init = [float(elem) for elem in initialCondition]
+
+    if Mode == "ProxA":
+        trace = simulate(init, time_bound, time_step, ProxA_dynamics)
+    elif Mode == "ProxB":
+        trace = simulate(init, time_bound, time_step, ProxB_dynamics)
+    elif Mode == "Passive":
+        trace = simulate(init, time_bound, time_step, Passive_dynamics)
+    else:
+        raise ValueError(f"Mode {Mode} not found")
+
+    return trace

input/nondaginput/input_spacecraft_rendezvous.json

+{
+	"vertex":["ProxA","ProxB","Passive"],
+	"variables":["xp","yp","xd","yd"],
+	"edge":[[0,1],[0,2],[1,2]],
+	"guards":[
+        "And(yp>=-100, xp+yp>=-141.1, xp>=-100, yp-xp<=141.1, yp<=100, xp+yp<=141.1, xp<=100, yp-xp>=-141.1)",
+        "And(t>=120)",
+        "And(t>=120)"
+    ],
+	"initialVertex":0,
+	"resets":["", "",""],
+	"initialSet":[[-925,-425,0,0],[-875,-375,0,0]],
+	"unsafeSet":"",
+	"timeHorizon":200,
+	"directory":"examples/rendezvous"
+}
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