77 lines
2.7 KiB
Python
77 lines
2.7 KiB
Python
import mpmath as mp
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import json
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mp.dps = 50 # 设置精度为50位小数
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kSegLength1 = mp.mpf('2.86')
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kSegLength2 = mp.mpf('1.65')
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kAlpha = mp.mpf('0.55') / (2 * mp.pi)
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def Theta2C(theta):
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tmp = mp.sqrt(1 + theta**2)
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return kAlpha * 0.5 * (theta * tmp - mp.log(-theta + tmp))
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def Theta2Dot(theta):
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return (kAlpha * theta * mp.cos(theta), kAlpha * theta * mp.sin(theta))
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init_C=Theta2C(2*mp.pi*16)
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def GenerateFirstNodeTheta(time_point, last_theta):
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cur_C = init_C - time_point
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def f(theta):
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return Theta2C(theta) - cur_C
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return mp.findroot(f, last_theta, solver='secant')
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def GenerateFollowNodeTheta(cur_node_theta, expected_distance):
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cur_node_dot = Theta2Dot(cur_node_theta)
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def f(theta):
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test_node_dot = Theta2Dot(theta)
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actual_distance = mp.sqrt((cur_node_dot[0]-test_node_dot[0])**2 + (cur_node_dot[1]-test_node_dot[1])**2)
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return actual_distance - expected_distance
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return mp.findroot(f, cur_node_theta + 0.1, solver='secant')
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def CalcMoveList(time_point, last_theta):
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first_node_theta = GenerateFirstNodeTheta(time_point, last_theta)
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first_node_dot = Theta2Dot(first_node_theta)
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first_node_C = Theta2C(first_node_theta)
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node_list = [{"theta": first_node_theta, "node": first_node_dot, "C": first_node_C, "v": mp.mpf('1.0')}]
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for i in range(1, 224):
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expected_distance = kSegLength1 if i == 1 else kSegLength2
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cur_node_theta = GenerateFollowNodeTheta(node_list[-1]["theta"], expected_distance)
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cur_node_dot = Theta2Dot(cur_node_theta)
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cur_node_C = Theta2C(cur_node_theta)
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node_list.append({"theta": cur_node_theta, "node": cur_node_dot, "C": cur_node_C})
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for i in range(223):
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AA = kSegLength1 if i == 0 else kSegLength2
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theta_i = node_list[i]["theta"]
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theta_ip1 = node_list[i+1]["theta"]
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alpha_i = mp.atan(theta_i)
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alpha_ip1 = mp.atan(theta_ip1)
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beta_i = mp.acos(((kAlpha*theta_i)**2 + AA**2 - (kAlpha*theta_ip1)**2) / (2*kAlpha*theta_i*AA))
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gama_i = mp.acos(((kAlpha*theta_ip1)**2 + AA**2 - (kAlpha*theta_i)**2) / (2*kAlpha*theta_ip1*AA))
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node_list[i+1]["v"] = node_list[i]["v"] * (-mp.cos(alpha_i + beta_i) / mp.cos(alpha_ip1 - gama_i))
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return node_list, first_node_theta
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res_list = []
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last_theta = 2 * mp.pi * 16
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for time_point in range(301):
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print(f"calculating time_point={time_point}")
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move_list, last_theta = CalcMoveList(time_point, last_theta)
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res_list.append(move_list)
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# 将结果转换为float并保留6位小数
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float_res_list = [
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[
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{k: round(float(v), 6) if isinstance(v, mp.mpf) else
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[round(float(x), 6) for x in v] if isinstance(v, tuple) else v
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for k, v in node.items()}
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for node in time_point
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]
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for time_point in res_list
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]
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with open("A1_res.json", "w") as file:
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json.dump(float_res_list, file, indent=4) |