first commit

2D/caculate/fkik.py

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+import math
+import matplotlib.pyplot as plt
+
+# 设置中文字体（防警告）
+plt.rcParams['font.sans-serif'] = ['SimHei', 'Arial Unicode MS', 'DejaVu Sans']
+plt.rcParams['axes.unicode_minus'] = False
+
+class TwoLinkArm:
+    def __init__(self, l1=1.0, l2=1.0):
+        self.l1 = l1
+        self.l2 = l2
+        self.theta1 = 0.0  # 弧度
+        self.theta2 = 0.0  # 弧度
+        self.end_x = l1 + l2  # 初始末端位置
+        self.end_y = 0.0
+        self.joint1 = (l1, 0.0)
+        self.joint2 = (l1 + l2, 0.0)
+
+        self.fig, self.ax = plt.subplots(figsize=(8, 8))
+        plt.subplots_adjust(bottom=0.2)
+        self.ax.set_xlim(-l1 - l2 - 0.5, l1 + l2 + 0.5)
+        self.ax.set_ylim(-l1 - l2 - 0.5, l1 + l2 + 0.5)
+        self.ax.set_aspect('equal')
+        self.ax.grid(True)
+        self.ax.set_title("拖动末端执行器（粉色点）来移动机械臂")
+        self.ax.set_xlabel("X")
+        self.ax.set_ylabel("Y")
+
+        # 绘制机械臂
+        self.line_link1, = self.ax.plot([], [], 'b-', linewidth=4, label=f'连杆1 (L1={l1})')
+        self.line_link2, = self.ax.plot([], [], 'r-', linewidth=4, label=f'连杆2 (L2={l2})')
+        self.joint_point, = self.ax.plot([], [], 'go', markersize=8, label='关节2')
+        self.end_point, = self.ax.plot([], [], 'mo', markersize=8, label='末端执行器')
+        self.base_point, = self.ax.plot(0, 0, 'ko', markersize=10, label='基座')
+        self.angle_text = self.ax.text(
+            -l1 - l2 + 0.2,
+            l1 + l2 - 0.3,
+            '',
+            fontsize=10,
+            bbox=dict(boxstyle="round", facecolor="wheat")
+        )
+
+        self.ax.legend()
+
+        # 拖动相关变量
+        self.dragging = False
+        self.press_xdata = None
+        self.press_ydata = None
+
+        # 连接事件
+        self.cid_press = self.fig.canvas.mpl_connect('button_press_event', self.on_press)
+        self.cid_release = self.fig.canvas.mpl_connect('button_release_event', self.on_release)
+        self.cid_motion = self.fig.canvas.mpl_connect('motion_notify_event', self.on_motion)
+
+        # 初始绘制
+        self.update_plot()
+
+    def fk(self, theta1, theta2):
+        """正向运动学"""
+        x1 = self.l1 * math.cos(theta1)
+        y1 = self.l1 * math.sin(theta1)
+        x2 = x1 + self.l2 * math.cos(theta1 + theta2)
+        y2 = y1 + self.l2 * math.sin(theta1 + theta2)
+        return (x1, y1), (x2, y2)
+
+    def ik(self, x, y, elbow_up=True):
+        """逆向运动学"""
+        d_sq = x*x + y*y
+        cos_theta2_numerator = d_sq - self.l1**2 - self.l2**2
+        denominator = 2 * self.l1 * self.l2
+
+        if abs(cos_theta2_numerator) > abs(denominator):
+            return None  # 不可达
+
+        cos_theta2 = max(-1, min(1, cos_theta2_numerator / denominator))
+        theta2 = math.acos(cos_theta2) if elbow_up else -math.acos(cos_theta2)
+
+        k1 = self.l1 + self.l2 * math.cos(theta2)
+        k2 = self.l2 * math.sin(theta2)
+        theta1 = math.atan2(y, x) - math.atan2(k2, k1)
+
+        return theta1, theta2
+
+    def update_plot(self):
+        """根据当前末端位置计算 IK 并更新图像"""
+        solution = self.ik(self.end_x, self.end_y, elbow_up=True)  # 默认肘上解
+        if solution is not None:
+            self.theta1, self.theta2 = solution
+            (x1, y1), (x2, y2) = self.fk(self.theta1, self.theta2)
+            self.joint1 = (x1, y1)
+            self.joint2 = (x2, y2)
+        else:
+            # 如果不可达，保持上一个有效姿态，但末端显示为红色
+            x2, y2 = self.end_x, self.end_y
+            self.end_point.set_color('red')
+
+        # 更新线条和点
+        self.line_link1.set_data([0, self.joint1[0]], [0, self.joint1[1]])
+        self.line_link2.set_data([self.joint1[0], self.joint2[0]], [self.joint1[1], self.joint2[1]])
+        self.joint_point.set_data(self.joint1[0], self.joint1[1])
+        self.end_point.set_data(self.joint2[0], self.joint2[1])
+        self.end_point.set_color('m')  # 恢复正常颜色
+
+        # 显示角度（现在是弧度）
+        angle_str = f"θ1 = {self.theta1:+.3f} rad\nθ2= {self.theta2:+.3f} rad"
+        self.angle_text.set_text(angle_str)
+
+        self.fig.canvas.draw_idle()
+
+    def on_press(self, event):
+        if event.inaxes != self.ax:
+            return
+        if self.end_point.contains(event)[0]:  # 点中末端点
+            self.dragging = True
+            self.press_xdata = event.xdata
+            self.press_ydata = event.ydata
+        else:
+            self.dragging = False
+
+    def on_release(self, event):
+        self.dragging = False
+
+    def on_motion(self, event):
+        if not self.dragging or event.inaxes != self.ax:
+            return
+        # 更新末端位置
+        dx = event.xdata - self.press_xdata
+        dy = event.ydata - self.press_ydata
+        self.end_x += dx
+        self.end_y += dy
+        self.press_xdata = event.xdata
+        self.press_ydata = event.ydata
+        self.update_plot()
+
+    def show(self):
+        plt.show()
+
+
+# ========================
+# 主程序
+# ========================
+if __name__ == "__main__":
+    print("拖动末端执行器（粉色点）来交互式控制两连杆机械臂！")
+    arm = TwoLinkArm(l1=1.0, l2=1.0)
+    arm.show()

2D/caculate/trajectory.py

@@ -0,0 +1,99 @@
+# trajectory.py
+
+import numpy as np
+
+def circle_trajectory(center=(80, 0), radius=40, num_points=200):
+    """ 圆形轨迹 """
+    angles = np.linspace(0, 2 * np.pi, num_points)
+    x_list = center[0] + radius * np.cos(angles)
+    y_list = center[1] + radius * np.sin(angles)
+    return x_list, y_list
+
+def line_trajectory(start=(40, 0), end=(120, 0), num_points=100):
+    """ 直线轨迹 """
+    t = np.linspace(0, 1, num_points)
+    x_list = start[0] + t * (end[0] - start[0])
+    y_list = start[1] + t * (end[1] - start[1])
+    return x_list, y_list
+
+
+def line_trajectory_fix(start=(40, 0), end=(120, 100), vx=0.1, vy=0.1, num_points=20):
+    """
+    生成带速度分量的匀速斜线轨迹
+    参数：
+        start: 起始点 (x, y)
+        end: 终点 (x, y) —— 仅用于估算运行时间（可选）
+        vx: x方向速度（单位/秒）
+        vy: y方向速度（单位/秒）
+        num_points: 生成的轨迹点数
+    返回：
+        x_list, y_list: 轨迹坐标数组
+    """
+    # 速度大小
+    speed = np.sqrt(vx**2 + vy**2)
+    if speed == 0:
+        raise ValueError("速度不能为零")
+
+    # 估算从 start 到 end 的距离（用于估算总时间）
+    if end is not None:
+        dx = end[0] - start[0]
+        dy = end[1] - start[1]
+        distance = np.sqrt(dx**2 + dy**2)
+        total_time = distance / speed  # 理论到达时间
+        print(total_time)
+    else:
+        total_time = 10.0  # 默认运行10秒
+
+    # 时间序列：从 0 到 total_time，均匀分布 num_points 个点
+    t = np.linspace(0, total_time, num_points)
+
+    # 位置 = 起点 + 速度 × 时间
+    x_list = start[0] + vx * t
+    y_list = start[1] + vy * t
+
+    return x_list, y_list
+
+def ellipse_trajectory(center=(80, 0), rx=50, ry=25, num_points=200):
+    """ 椭圆轨迹 """
+    angles = np.linspace(0, 2 * np.pi, num_points)
+    x_list = center[0] + rx * np.cos(angles)
+    y_list = center[1] + ry * np.sin(angles)
+    return x_list, y_list
+
+def square_trajectory(side=60, num_points=60):
+    """ 正方形轨迹 """
+    x_list, y_list = [], []
+    for i in range(num_points):
+        t = i / num_points
+        if t < 0.25:
+            x = 80 + 60 * t * 4
+            y = 0
+        elif t < 0.5:
+            x = 140
+            y = 0 + 60 * (t - 0.25) * 4
+        elif t < 0.75:
+            x = 140 - 60 * (t - 0.5) * 4
+            y = 60
+        else:
+            x = 80
+            y = 60 - 60 * (t - 0.75) * 4
+        x_list.append(x)
+        y_list.append(y)
+    return x_list, y_list
+
+def triangle_trajectory(base_length=100, height=80, num_points=60):
+    """ 三角形轨迹 """
+    x_list, y_list = [], []
+    points = [(80, 0), (130, 80), (30, 80), (80, 0)]
+    for i in range(num_points):
+        idx = int(i / num_points * 3)
+        t = (i % (num_points // 3)) / (num_points // 3)
+        x = points[idx][0] + t * (points[idx+1][0] - points[idx][0])
+        y = points[idx][1] + t * (points[idx+1][1] - points[idx][1])
+        x_list.append(x)
+        y_list.append(y)
+    return x_list, y_list
+
+def custom_trajectory(custom_x, custom_y):
+    """ 自定义轨迹，输入两个列表即可 """
+    return custom_x, custom_y