From a5409f5e45eb672d54ddfefbdf42d8e04a88fc7f Mon Sep 17 00:00:00 2001
From: Shilong <daishilong1236@gmail.com>
Date: Tue, 14 Sep 2021 10:45:21 +0800
Subject: [PATCH] fast planner

---
 Planning/Curve/B_spline.ipynb    | 472 -----------------
 Planning/fast_planner.py         | 883 +++++++++++++++++++++++++++++++
 Planning/figure/fast_planner.gif | Bin 0 -> 103359 bytes
 3 files changed, 883 insertions(+), 472 deletions(-)
 delete mode 100644 Planning/Curve/B_spline.ipynb
 create mode 100644 Planning/fast_planner.py
 create mode 100644 Planning/figure/fast_planner.gif

diff --git a/Planning/Curve/B_spline.ipynb b/Planning/Curve/B_spline.ipynb
deleted file mode 100644
index c9b271a..0000000
--- a/Planning/Curve/B_spline.ipynb
+++ /dev/null
@@ -1,472 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "source": [
-    "import numpy as np\r\n",
-    "import matplotlib.pyplot as plt\r\n",
-    "from scipy import interpolate"
-   ],
-   "outputs": [],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "source": [
-    "class BSpline(object):\r\n",
-    "  def __init__(self, knots: np.ndarray, control_points: np.ndarray, degree: int=3):\r\n",
-    "    \"\"\"See also https://web.mit.edu/hyperbook/Patrikalakis-Maekawa-Cho/node17.html#fig:rep_cvx_hull_bspl\r\n",
-    "    \"\"\"\r\n",
-    "    n = len(control_points)-1\r\n",
-    "    k = degree+1\r\n",
-    "    assert len(knots) == n+1+k\r\n",
-    "    self.n = n # 0->n control points\r\n",
-    "    self.k = k # k order, k-1 degree\r\n",
-    "    self.T = np.array(knots)\r\n",
-    "    self.p = np.array(control_points)\r\n",
-    "  \r\n",
-    "  def calcBasisFunction(self, t):\r\n",
-    "    \"\"\"Calculate all basis function values in time t\r\n",
-    "    \"\"\"\r\n",
-    "    N = np.zeros([self.n+1, self.k+1]) # basis function\r\n",
-    "    # order 1 is constant\r\n",
-    "    for i in range(self.n+1):\r\n",
-    "      N[i,1] = 1 if self.T[i]<=t<self.T[i+1] else 0\r\n",
-    "    \r\n",
-    "    # order k->k+1, see https://en.wikipedia.org/wiki/B-spline\r\n",
-    "    for k in range(1,self.k):\r\n",
-    "      for i in range(self.n+1):\r\n",
-    "        w_i_k = (t-self.T[i])/(self.T[i+k]-self.T[i]) if self.T[i+k]!=self.T[i] else 0\r\n",
-    "        w_i1_k = (t-self.T[i+1])/(self.T[i+1+k]-self.T[i+1]) if self.T[i+1+k]!=self.T[i+1] else 0\r\n",
-    "        if i<self.n:\r\n",
-    "          N[i,k+1] = w_i_k*N[i,k]+(1-w_i1_k)*N[i+1,k]\r\n",
-    "        else:\r\n",
-    "          N[i,k+1] = w_i_k*N[i,k]\r\n",
-    "    return N\r\n",
-    "  def DeBoor(self, t):\r\n",
-    "    # constrain t in [u_{k}, u_{n+1}]\r\n",
-    "    ub = min(max(self.T[self.k-1], t), self.T[-self.k])\r\n",
-    "\r\n",
-    "    # determine which [ui,ui+1] lay in\r\n",
-    "    k = self.k-1\r\n",
-    "    while True:\r\n",
-    "      if self.T[k + 1] >= ub:\r\n",
-    "        break\r\n",
-    "      k+=1\r\n",
-    "    \r\n",
-    "    # deBoor's alg \r\n",
-    "    c = self.p\r\n",
-    "    p = self.k-1\r\n",
-    "    x = ub\r\n",
-    "    t = self.T\r\n",
-    "    d = [c[j + k - p] for j in range(0, p + 1)]\r\n",
-    "\r\n",
-    "    for r in range(1, p + 1):\r\n",
-    "        for j in range(p, r - 1, -1):\r\n",
-    "            alpha = (x - t[j + k - p]) / (t[j + 1 + k - r] - t[j + k - p])\r\n",
-    "            d[j] = (1.0 - alpha) * d[j - 1] + alpha * d[j]\r\n",
-    "\r\n",
-    "    return d[p]"
-   ],
-   "outputs": [],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "source": [
-    "ctr =np.array( [(3 , 1), (2.5, 4), (0, 1), (-2.5, 4),\r\n",
-    "                (-3, 0), (-2.5, -4), (0, -1), (2.5, -4), (3, -1),])\r\n",
-    "x=ctr[:,0]\r\n",
-    "y=ctr[:,1]\r\n",
-    "\r\n",
-    "# uncomment both lines for a closed curve\r\n",
-    "#x=np.append(x,[x[0]])  \r\n",
-    "#y=np.append(y,[y[0]])\r\n",
-    "\r\n",
-    "l=len(x)  \r\n",
-    "\r\n",
-    "t=np.linspace(0,1,l-2,endpoint=True)\r\n",
-    "t=np.append([0,0,0],t)\r\n",
-    "t=np.append(t,[1,1,1])\r\n",
-    "knots = t\r\n",
-    "print(t)\r\n",
-    "bs = BSpline(t, ctr, 3)\r\n"
-   ],
-   "outputs": [
-    {
-     "output_type": "stream",
-     "name": "stdout",
-     "text": [
-      "[0.         0.         0.         0.         0.16666667 0.33333333\n",
-      " 0.5        0.66666667 0.83333333 1.         1.         1.\n",
-      " 1.        ]\n"
-     ]
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "source": [
-    "ts = np.linspace(0,1,endpoint=False)\r\n",
-    "basis_func_val = np.zeros([len(x), len(ts)])\r\n",
-    "for ind, t in enumerate(ts):\r\n",
-    "  basis_func_val[:,ind] = bs.calcBasisFunction(t)[:,-1]\r\n",
-    "for i in range(len(x)):\r\n",
-    "  plt.plot(ts, basis_func_val[i,:])"
-   ],
-   "outputs": [
-    {
-     "output_type": "display_data",
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     }
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "source": [
-    "\r\n",
-    "ts = np.linspace(0,1)\r\n",
-    "points = []\r\n",
-    "for t in ts:\r\n",
-    "  points.append(bs.DeBoor(t))\r\n",
-    "points = np.array(points)\r\n",
-    "plt.plot(points[:,0],points[:,1])\r\n",
-    "plt.plot(x,y,'k--',label='Control polygon',marker='o',markerfacecolor='red')\r\n",
-    "out = interpolate.splev(ts,[knots,[x,y],3])\r\n",
-    "# plt.plot(out[0],out[1],'b',linewidth=2.0,label='B-spline curve')"
-   ],
-   "outputs": [
-    {
-     "output_type": "display_data",
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     }
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "source": [
-    "control_points = np.array([(3 , 1), (2.5, 4), (0, 1), (-2.5, 4),\r\n",
-    "                (-3, 0), (-2.5, -4)])\r\n",
-    "clamped_knots = [0, 0, 0, 0, 1/3, 2/3, 1, 1, 1, 1]\r\n",
-    "clamped_bspline = interpolate.splev(np.linspace(0,1),[clamped_knots,[control_points[:,0],control_points[:,1]],3])\r\n",
-    "plt.plot(clamped_bspline[0],clamped_bspline[1],'b',linewidth=2.0,label='B-spline curve')\r\n",
-    "plt.plot(control_points[:,0],control_points[:,1],'k--',label='Control polygon',marker='o',markerfacecolor='red')"
-   ],
-   "outputs": [
-    {
-     "output_type": "execute_result",
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x243df44ff10>]"
-      ]
-     },
-     "metadata": {},
-     "execution_count": 62
-    },
-    {
-     "output_type": "display_data",
-     "data": {
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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     }
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "source": [
-    "control_points = np.array([(3 , 1), (2.5, 4), (0, 1), (-2.5, 4),\r\n",
-    "                (-3, 0), (-2.5, -4)])\r\n",
-    "unclamped_knots = [-0.9, -0.6, -0.3, 0, 1/3, 2/3, 1, 1.3, 1.6, 1.9]\r\n",
-    "unclamped_bspline = interpolate.splev(np.linspace(0,1),[unclamped_knots,[control_points[:,0],control_points[:,1]],3])\r\n",
-    "plt.plot(unclamped_bspline[0],unclamped_bspline[1],'b',linewidth=2.0,label='B-spline curve')\r\n",
-    "plt.plot(control_points[:,0],control_points[:,1],'k--',label='Control polygon',marker='o',markerfacecolor='red')"
-   ],
-   "outputs": [
-    {
-     "output_type": "execute_result",
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x243df873d60>]"
-      ]
-     },
-     "metadata": {},
-     "execution_count": 73
-    },
-    {
-     "output_type": "display_data",
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     }
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "source": [
-    "control_points = np.array([(3 , 1), (2.5, 4), (0, 1), (-2.5, 4),\r\n",
-    "                (-3, 0), (-2.5, -4)])\r\n",
-    "nonuniform_knots = [0, 0, 0, 0, 1/4, 4/5, 1, 1, 1, 1]\r\n",
-    "nonuniform_knots = interpolate.splev(np.linspace(0,1),[nonuniform_knots,[control_points[:,0],control_points[:,1]],3])\r\n",
-    "plt.plot(nonuniform_knots[0],nonuniform_knots[1],'b',linewidth=2.0,label='B-spline curve')\r\n",
-    "plt.plot(control_points[:,0],control_points[:,1],'k--',label='Control polygon',marker='o',markerfacecolor='red')"
-   ],
-   "outputs": [
-    {
-     "output_type": "execute_result",
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x243df1ee1c0>]"
-      ]
-     },
-     "metadata": {},
-     "execution_count": 69
-    },
-    {
-     "output_type": "display_data",
-     "data": {
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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     }
-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "source": [
-    "plt.plot(clamped_bspline[0],clamped_bspline[1],\"--\",linewidth=2.0,label='clamped B-spline curve')\r\n",
-    "plt.plot(unclamped_bspline[0],unclamped_bspline[1],\"-.\",linewidth=2.0,label='unclamped B-spline curve')\r\n",
-    "plt.plot(nonuniform_knots[0],nonuniform_knots[1],linewidth=2.0,label='nonuniform B-spline curve')\r\n",
-    "plt.plot(control_points[:,0],control_points[:,1],'k--',label='Control polygon',marker='o',markerfacecolor='red')\r\n",
-    "plt.legend()"
-   ],
-   "outputs": [
-    {
-     "output_type": "execute_result",
-     "data": {
-      "text/plain": [
-       "<matplotlib.legend.Legend at 0x243df8c9eb0>"
-      ]
-     },
-     "metadata": {},
-     "execution_count": 74
-    },
-    {
-     "output_type": "display_data",
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
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-    }
-   ],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "source": [
-    "from typing import List, Dict, Tuple\r\n",
-    "# https://hal.archives-ouvertes.fr/hal-03017566/document\r\n",
-    "def parameterizeToBspline(ts: float, point_set: List[List], start_end_derivative: List[List]):\r\n",
-    "    \"\"\"\r\n",
-    "    Args:\r\n",
-    "        ts: time step between points\r\n",
-    "        point_set: points to be fitted\r\n",
-    "        start_end_derivative: [start_vel, end_vel, start_acc, end_acc]\r\n",
-    "    \r\n",
-    "    Returns:\r\n",
-    "        ctrl_pts: control points of the uniform BSpline\r\n",
-    "    \"\"\"\r\n",
-    "    K = len(point_set)\r\n",
-    "    \r\n",
-    "    prow = np.array([1, 4, 1],dtype=float)\r\n",
-    "\r\n",
-    "    A = np.zeros([K , K + 2]) # K pos, 2 vel, 2 acc constraints, K+2 control points\r\n",
-    "    for i in range(K):\r\n",
-    "      A[i:i+1, i:i+3] = (1 / 6.0) * prow\r\n",
-    "    \r\n",
-    "    # write b\r\n",
-    "    bx = np.zeros(K)\r\n",
-    "    by=np.zeros(K)\r\n",
-    "\r\n",
-    "    for i in range(K):\r\n",
-    "      bx[i] = point_set[i][0]\r\n",
-    "      by[i] = point_set[i][1]\r\n",
-    "    \r\n",
-    "\r\n",
-    "    # solve Ax = b\r\n",
-    "    px = np.linalg.lstsq(A,bx)[0]\r\n",
-    "    py = np.linalg.lstsq(A,by)[0]\r\n",
-    "\r\n",
-    "    # convert to control pts\r\n",
-    "    ctrl_pts = np.zeros([K+2,2])\r\n",
-    "    ctrl_pts[:,0] = px\r\n",
-    "    ctrl_pts[:,1] = py\r\n",
-    "    return ctrl_pts"
-   ],
-   "outputs": [],
-   "metadata": {}
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 107,
-   "source": [
-    "points = control_points\r\n",
-    "ctrl_pts = parameterizeToBspline(0, points, [[0,0],[0,0],[0,0],[0,0]])\r\n",
-    "plt.plot(points[:,0], points[:,1],'x')\r\n",
-    "K = len(points)\r\n",
-    "\r\n",
-    "out=interpolate.splev(np.linspace(0,K-1,num=100),[list(range(-3,K+3)),[ctrl_pts[:,0],ctrl_pts[:,1]],3])\r\n",
-    "plt.plot(out[0], out[1])"
-   ],
-   "outputs": [
-    {
-     "output_type": "stream",
-     "name": "stderr",
-     "text": [
-      "<ipython-input-105-0496301b53d8>:31: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
-      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
-      "  px = np.linalg.lstsq(A,bx)[0]\n",
-      "<ipython-input-105-0496301b53d8>:32: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
-      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
-      "  py = np.linalg.lstsq(A,by)[0]\n"
-     ]
-    },
-    {
-     "output_type": "execute_result",
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x243e0da6340>]"
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-     },
-     "metadata": {},
-     "execution_count": 107
-    },
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-     "output_type": "display_data",
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-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
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-   "outputs": [
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diff --git a/Planning/fast_planner.py b/Planning/fast_planner.py
new file mode 100644
index 0000000..29a4570
--- /dev/null
+++ b/Planning/fast_planner.py
@@ -0,0 +1,883 @@
+"""Python implementation of Fast Planner kinodynamic trajectory generation
+ref: https://github.com/HKUST-Aerial-Robotics/Fast-Planner
+"""
+
+from queue import PriorityQueue
+from matplotlib import patches
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.optimize import minimize
+
+
+class NonUniformBspline(object):
+    """An implementation of non-uniform B-spline with different dimensions.
+    It also represents uniform B-spline which is a special case of non-uniform
+    """
+
+    def __init__(self, points: np.ndarray, degree: int, interval: float):
+        self.control_points = None  # numpy array dim (n, 3)
+        self.p = None  # p degree
+        self.n = None  # n control points
+        self.m = None  # m+1 knots, m = n+1+p
+        self.u = None  # knot vector
+        self.interval = None
+        self.limit_vel = None  # physical limits
+        self.limit_acc = None
+        self.limit_ratio = None  # and time adjustment ratio
+
+        self.setUniformBspline(points, degree, interval)
+
+    def setUniformBspline(self, control_points: np.ndarray, degree: int, interval: float):
+        self.control_points = np.array(control_points)
+        assert self.control_points.shape[0] >= 4 and self.control_points.shape[
+            1] == 2, f"control_points.shape: {self.control_points.shape}"
+        self.p = degree
+        self.interval = interval
+
+        self.n = self.control_points.shape[0] - 1
+        self.m = self.n + self.p + 1
+
+        self.u = np.zeros(self.m+1)
+        for i in range(len(self.u)):
+            if i <= self.p:
+                self.u[i] = (-self.p+i)*self.interval
+            elif self.p < i <= self.m-self.p:
+                self.u[i] = self.u[i-1]+self.interval
+            elif i > self.m-self.p:
+                self.u[i] = self.u[i-1]+self.interval
+
+    def setKnot(self, knot: np.ndarray):
+        self.u = np.array(knot)
+        assert len(self.u) == self.m+1, f"u length: {len(self.u)}"
+
+    def getKnot(self):
+        return np.array(self.u)
+
+    def getTimeSpan(self):
+        um = self.u[self.p]
+        um_p = self.u[self.m-self.p]
+        return um, um_p
+
+    def getControlPoint(self):
+        return np.array(self.control_points)
+
+    def getHeadTailPts(self):
+        um, um_p = self.getTimeSpan()
+        head = self.evaluateDeBoor(um)
+        tail = self.evaluateDeBoor(um_p)
+        return head, tail
+
+    def evaluateDeBoor(self, u):
+        um, um_p = self.getTimeSpan()
+        ub = np.clip(u, um, um_p)
+
+        # determine which [ui,ui+1] lay in
+        k = self.p
+        while True:
+            if self.u[k+1] >= ub:
+                break
+            k += 1
+
+        # deBoor
+        d = []
+        for i in range(self.p+1):
+            d.append(self.control_points[k - self.p + i])
+
+        for r in range(1, self.p+1):
+            for i in range(self.p, r-1, -1):
+                alpha = (ub-self.u[i+k-self.p]) / \
+                    (self.u[i+1+k-r]-self.u[i+k-self.p])
+                d[i] = (1-alpha)*d[i-1]+alpha*d[i]
+        return d[self.p]
+
+    def getDerivativeControlPoints(self):
+        """The derivative of a b-spline is also a b-spline, its degree become p-1
+        control point Q_i = p*(P_{i+1}-P_i)/(u_{i+p+1}-u_{i+1})
+        see also: https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-derv.html
+        """
+        ctp = np.zeros([self.control_points.shape[0] -
+                        1, self.control_points.shape[1]])
+        P = self.control_points
+        for i in range(ctp.shape[0]):
+            ctp[i] = self.p*(P[i+1]-P[i])/(self.u[i+self.p+1]-self.u[i+1])
+        return ctp
+
+    def getDerivative(self):
+        ctp = self.getDerivativeControlPoints()
+        derivative = NonUniformBspline(ctp, self.p - 1, self.interval)
+        derivative.setKnot(self.u[1:-1])
+        return derivative
+
+    def getInterval(self):
+        return self.interval
+
+    def setPhysicalLimits(self, vel: float, acc: float):
+        self.limit_vel = vel
+        self.limit_acc = acc
+        self.limit_ratio = 1.1
+
+    def reallocateTime(self):
+        fea = True
+        P = self.control_points
+        dim = P.shape[1]
+        max_vel, max_acc = None, None
+
+        # check vel feasibility and insert points
+        for i in range(P.shape[0]-1):
+            vel = self.p * (P[i + 1] - P[i]) / \
+                (self.u[i + self.p + 1] - self.u[i + 1])
+            if np.any(np.abs(vel) > self.limit_vel+1e-4):
+                fea = False
+                max_vel = np.max(np.abs(vel))
+                ratio = min(self.limit_ratio, max_vel / self.limit_vel)
+                time_ori = self.u[i + self.p + 1] - self.u[i + 1]
+                time_new = ratio * time_ori
+                delta_t = time_new - time_ori
+                t_inc = delta_t / self.p
+                for j in range(i+2, i + self.p + 2):
+                    self.u[j] += (j-i+1) * t_inc
+                for j in range(j+self.p+2, len(self.u)):
+                    self.u[j] += delta_t
+
+        # acc
+        for i in range(P.shape[0] - 2):
+            acc = self.p * (self.p - 1) * ((P[i + 2] - P[i + 1]) / (self.u[i + self.p + 2] - self.u[i + 2]) - (
+                P[i + 1] - P[i]) / (self.u[i + self.p + 1] - self.u[i + 1])) / (self.u[i + self.p + 1] - self.u[i + 2])
+            if np.any(np.abs(acc) > self.limit_acc+1e-4):
+                fea = False
+                max_acc = np.max(np.abs(acc))
+                ratio = min(self.limit_ratio, np.sqrt(
+                    max_acc / self.limit_acc))
+                time_ori = self.u[i + self.p + 1] - self.u[i + 2]
+                time_new = ratio * time_ori
+                delta_t = time_new - time_ori
+                t_inc = delta_t / (self.p - 1)
+                for j in range(i + 3, i + self.p + 2):
+                    self.u[j] += (j - i - 2) * t_inc
+                for j in range(i + self.p + 2, len(self.u)):
+                    self.u[j] += delta_t
+        return fea
+
+    @staticmethod
+    def parameterizeToBspline(ts: float, point_set: np.ndarray, start_end_derivative: np.ndarray):
+        """Given waypoints and derivative constraints, fit a uniform cubic Bspline, return the control point
+        Args:
+            ts: interval
+            point_set: 2D waypoints
+            start_end_derivative: [start_vel, end_vel, start_acc, end_acc]
+        """
+        assert ts > 0, f"ts: {ts}"
+        assert len(point_set) >= 2, f"len(point_set): {len(point_set)}"
+        assert len(
+            start_end_derivative) >= 4, f"len(start_end_derivative): {len(start_end_derivative)}"
+        K = len(point_set)
+
+        # construct A
+        prow = np.array([1, 4, 1], dtype=float)
+        vrow = np.array([-1, 0, 1], dtype=float)
+        arow = np.array([1, -2, 1], dtype=float)
+
+        A = np.zeros((K + 4, K + 2))
+        for i in range(K):
+            A[i, i:i+3] = (1 / 6.0) * prow
+        A[K, 0:3] = (1 / 2.0 / ts) * vrow
+        A[K+1, K - 1:K+2] = (1 / 2.0 / ts) * vrow
+
+        A[K + 2, 0:3] = (1 / ts / ts) * arow
+        A[K + 3, K - 1:K+2] = (1 / ts / ts) * arow
+
+        # construct b
+        bx = np.zeros(K + 4)
+        by = np.zeros(K + 4)
+        for i in range(K):
+            bx[i] = point_set[i][0]
+            by[i] = point_set[i][1]
+
+        for i in range(4):
+            bx[K + i] = start_end_derivative[i][0]
+            by[K + i] = start_end_derivative[i][1]
+
+        # solve Ax = b
+        W = np.eye(len(A))  # least square weight
+        px = np.linalg.lstsq(W@A, W@bx, rcond=None)[0]
+        py = np.linalg.lstsq(W@A, W@by, rcond=None)[0]
+
+        # convert to control pts
+        ctrl_pts = np.zeros([K + 2, 2])
+        ctrl_pts[:, 0] = px
+        ctrl_pts[:, 1] = py
+        return ctrl_pts
+
+
+class BsplineOptimizer(object):
+    def __init__(self, env) -> None:
+        super().__init__()
+        self.env = env
+        self.control_points = None
+        self.bspline_interval = None
+        self.end_pt = None
+        self.dim = 2
+        self.guide_pts = None
+        self.waypoints = None
+        self.waypt_ind = None
+        self.cost_function = None
+
+        self.order = 3
+        self.lambda1 = 1.0  # smoothness
+        self.lambda2 = 5.0  # distance weight
+        self.lambda3 = 0.00001  # feasibility weight
+        self.lambda4 = 0.01  # end point weight
+        self.lambda5 = 0.0  # guide cost weight
+        self.lambda6 = 0.0  # visibility cost weight
+        self.lambda7 = 100.0  # waypoint cost weight
+
+        self.dist0 = 0.4
+        self.max_vel = 3.0
+        self.max_acc = 2.0
+        self.visib_min = None
+        self.max_iteration_num = 300
+        self.max_iteration_time = None
+
+        self.variable_num = None
+        self.iter_num = None
+        self.best_variable = None
+        self.min_cost = None
+        self.block_pts = None
+
+        self.SMOOTHNESS = (1 << 0)
+        self.DISTANCE = (1 << 1)
+        self.FEASIBILITY = (1 << 2)
+        self.ENDPOINT = (1 << 3)
+        self.GUIDE = (1 << 4)
+        self.WAYPOINTS = (1 << 6)
+
+    def setEnv(self, env):
+        self.env = env
+
+    def setControlPoints(self, points):
+        self.control_points = np.array(points)
+        self.dim = self.control_points.shape[1]
+        assert self.dim == 2, f"self.dim: {self.dim==2}"
+        assert len(
+            self.control_points) > 6, f"len(self.control_points)={len(self.control_points)}"
+
+    def setInterval(self, ts):
+        self.bspline_interval = ts
+
+    def setTerminatedCond(self, max_iteration_num, max_iteration_time):
+        self.max_iteration_num = max_iteration_num
+        self.max_iteration_time = max_iteration_time
+
+    def setCostFunction(self, cost_code):
+        self.cost_function = cost_code
+        cost_str = ""
+        if self.cost_function & self.SMOOTHNESS:
+            cost_str += "smooth |"
+        if self.cost_function & self.DISTANCE:
+            cost_str += " distance |"
+        if self.cost_function & self.FEASIBILITY:
+            cost_str += " FEASIBILITY |"
+        if self.cost_function & self.ENDPOINT:
+            cost_str += " ENDPOINT |"
+        if self.cost_function & self.GUIDE:
+            cost_str += " GUIDE |"
+        if self.cost_function & self.WAYPOINTS:
+            cost_str += " WAYPOINTS |"
+        print(cost_str)
+
+    def setGuidePath(self, guide_pts):
+        self.guide_pts = np.array(guide_pts)
+        assert guide_pts.shape[1] == self.dim
+
+    def setWaypoints(self, waypoints, waypt_ind):
+        self.waypoints = np.array(waypoints)
+        self.waypt_ind = [ind for ind in waypt_ind]
+        assert self.waypoints.shape[1] == self.dim
+
+    def BsplineOptimizeTraj(self, points, ts, cost_function, max_iteration_num, max_iteration_time):
+        self.setControlPoints(points)
+        self.setInterval(ts)
+        self.setCostFunction(cost_function)
+        self.setTerminatedCond(max_iteration_num, max_iteration_time)
+        self.optimize()
+        return self.control_points
+
+    def optimize(self):
+        # init solver
+        self.iter_num = 0
+        self.min_cost = np.inf
+        pt_num = len(self.control_points)
+        self.variable_num = self.dim * (pt_num - 2 * self.order)
+        x0 = np.zeros(self.variable_num)
+        for i in range(self.order, self.variable_num//self.dim+self.order):
+            for j in range(self.dim):
+                x0[self.dim*(i-self.order)+j] = self.control_points[i, j]
+        bound_upper = x0+10.0
+        bound_lower = x0-10.0
+        bound = [(lower, upper)
+                 for lower, upper in zip(bound_lower, bound_upper)]
+
+        result = minimize(self.costFunction, x0, jac=True,
+                          bounds=bound, options={"maxiter":self.max_iteration_num})
+        self.best_variable = result.x
+        print(result)
+        for i in range(self.order, self.variable_num//self.dim+self.order):
+            for j in range(self.dim):
+                self.control_points[i,
+                                    j] = self.best_variable[self.dim * (i - self.order) + j]
+        return self.control_points
+
+    def costFunction(self, x):
+        """Callback of scipy minimize function
+        Args:
+            x: shape (variable_num,), current variable
+
+        Returns:
+            f_combine: current cost
+            grad: current gradient
+        """
+        cost, grad = self.combineCost(x)
+        self.iter_num += 1
+
+        # save the min cost result
+        if cost < self.min_cost:
+            self.min_cost = cost
+            self.best_variable = x
+        return cost, grad
+
+    def combineCost(self, x):
+        """
+        Args:
+            x: shape (variable_num,) current variable
+
+        Returns:
+            f_combine: current cost
+            grad: shape (variable_num,), current gradient
+        """
+        # convert the NLopt format vector to control points.
+        control_points = np.zeros_like(self.control_points)
+        control_points[:self.order, :] = self.control_points[:self.order, :]
+        for i in range(self.variable_num // self.dim):
+            for j in range(self.dim):
+                control_points[i + self.order, j] = x[self.dim * i + j]
+        control_points[self.order + self.variable_num //
+                       self.dim:] = self.control_points[self.order + self.variable_num // self.dim:]
+
+        f_combine = 0.0
+        grad = np.zeros(self.variable_num)
+        f_smoothness = f_distance = f_feasibility = f_endpoint = f_guide = f_waypoints = 0.0
+        if self.cost_function & self.SMOOTHNESS:
+            f_smoothness, g_smoothness = self.calcSmoothnessCost(
+                control_points)
+            f_combine += self.lambda1 * f_smoothness
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda1 * \
+                        g_smoothness[i + self.order, j]
+        if self.cost_function & self.DISTANCE:
+            f_distance, g_distance = self.calcDistanceCost(control_points)
+            f_combine += self.lambda2 * f_distance
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda2 * \
+                        g_distance[i + self.order, j]
+        if self.cost_function & self.FEASIBILITY:
+            f_feasibility, g_feasibility = self.calcFeasibilityCost(
+                control_points)
+            f_combine += self.lambda3 * f_feasibility
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda3 * \
+                        g_feasibility[i + self.order, j]
+        if self.cost_function & self.ENDPOINT:
+            f_endpoint, g_endpoint = self.calcEndpointCost(control_points)
+            f_combine += self.lambda4 * f_endpoint
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda4 * \
+                        g_endpoint[i + self.order, j]
+        if self.cost_function & self.GUIDE:
+            f_guide, g_guide = self.calcGuideCost(control_points)
+            f_combine += self.lambda5 * f_guide
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda5 * \
+                        g_guide[i + self.order, j]
+        if self.cost_function & self.WAYPOINTS:
+            f_waypoints, g_waypoints = self.calcWaypointsCost(control_points)
+            f_combine += self.lambda7 * f_waypoints
+            for i in range(self.variable_num//self.dim):
+                for j in range(self.dim):
+                    grad[self.dim*i+j] += self.lambda7 * \
+                        g_waypoints[i + self.order, j]
+        return f_combine, grad
+
+    def calcEbandCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+
+        for i in range(len(x)-2):
+            # evaluate tensor
+            tensor = -x[i]+2*x[i+1]-x[i+2]
+            f += tensor@tensor
+            temp_t = 2*tensor
+            # tensor gradient
+            g[i] += -temp_t
+            g[i+1] += 2*temp_t
+            g[i+2] += -temp_t
+        return f, g
+
+    def calcSmoothnessCost(self, x):
+        """
+        Args:
+            x: shape==control_points.shape, variable
+
+        Returns:
+            f: cost
+            g: shape==x.shape, gradient
+        """
+        f = 0.0
+        g = np.zeros_like(x)
+
+        for i in range(len(x)-self.order):
+            # evaluate jerk
+            jerk = x[i + 3] - 3 * x[i + 2] + 3 * x[i + 1] - x[i]
+            f += jerk @ jerk
+            temp_j = 2.0 * jerk
+            # jerk gradient
+            g[i + 0] += -temp_j
+            g[i + 1] += 3.0 * temp_j
+            g[i + 2] += -3.0 * temp_j
+            g[i + 3] += temp_j
+        return f, g
+
+    def calcDistanceCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+
+        end_idx = len(x) - self.order
+
+        for i in range(self.order, end_idx):
+            dist, dist_grad = self.env.evaluateDistGrad(x[i])
+            # if np.linalg.norm(dist_grad) > 1e-4:
+            #     dist_grad /= np.linalg.norm(dist_grad)
+
+            if dist < self.dist0:
+                f += (dist - self.dist0)**2
+                g[i] += 2.0 * (dist - self.dist0) * dist_grad
+        return f, g
+
+    def calcFeasibilityCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+
+        # abbreviation
+        vm2 = self.max_vel**2
+        am2 = self.max_acc**2
+
+        ts = self.bspline_interval
+        ts_inv2 = 1 / ts / ts
+        ts_inv4 = ts_inv2 * ts_inv2
+
+        # velocity feasibility
+        for i in range(len(x)-1):
+            vi = x[i + 1] - x[i]
+            for j in range(self.dim):
+                vd = vi[j] * vi[j] * ts_inv2 - vm2
+                if vd > 0.0:
+                    f += vd ** 2
+
+                    temp_v = 4.0 * vd * ts_inv2
+                    g[i + 0, j] += -temp_v * vi[j]
+                    g[i + 1, j] += temp_v * vi[j]
+
+        # acceleration feasibility
+        for i in range(len(x)-2):
+            ai = x[i + 2] - 2 * x[i + 1] + x[i]
+
+            for j in range(self.dim):
+                ad = ai[j] * ai[j] * ts_inv4 - am2
+                if ad > 0.0:
+                    f += ad ** 2
+
+                    temp_a = 4.0 * ad * ts_inv4
+                    g[i + 0, j] += temp_a * ai[j]
+                    g[i + 1, j] += -2 * temp_a * ai[j]
+                    g[i + 2, j] += temp_a * ai[j]
+        return f, g
+
+    def calcEndpointCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+        return f, g
+
+    def calcGuideCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+        return f, g
+
+    def calcWaypointsCost(self, x):
+        f = 0.0
+        g = np.zeros_like(x)
+        return f, g
+
+
+class ComplexEnv(object):
+    def __init__(self) -> None:
+        super().__init__()
+        self.center = np.array([0, 0])
+        self.length = np.array((8, 6))
+        self.origin = self.center-self.length/2
+        self.reso = 0.1
+        self.size = np.array(self.length/self.reso, dtype=int)
+
+        self.occ_map = np.zeros(self.size)
+        self.esdf_map = np.zeros(self.size)
+
+        self.circles = []
+        self.rectangles = [(-2, -1, 4, 2)]
+
+        self.genOcc()
+        self.distanceTransform()
+
+    def posToInd(self, pos: np.ndarray):
+        ind = np.round((np.array(pos)-self.origin)/self.reso)
+        ind = np.array(ind, dtype=int)
+        return ind
+
+    def indToPos(self, ind: np.ndarray):
+        pos = np.array(ind, dtype=float)*self.reso+self.origin
+        return pos
+
+    def boundIndex(self, ind):
+        return np.clip(ind, np.zeros(2, dtype=int), self.size-1, dtype=int)
+
+    def isInside(self, pos):
+        ind = self.posToInd(pos)
+        return np.all(ind >= 0) and np.all(ind < self.size)
+
+    def addCircle(self, o, r):
+        self.circles.append((o[0], o[1], r))
+
+    def addRectange(self, o, w, h):
+        self.rectangles.append((o[0], o[1], w, h))
+
+    def genOcc(self):
+        for ox, oy, r in self.circles:
+            lb = self.posToInd((ox-r, oy-r))
+            rt = self.posToInd((ox+r, oy+r))
+            for x_ind in range(lb[0], rt[0]):
+                for y_ind in range(lb[1], rt[1]):
+                    x, y = self.indToPos((x_ind, y_ind))
+                    if not self.isInside((x, y)):
+                        continue
+                    if np.hypot(x-ox, y-oy) <= r:
+                        self.occ_map[x_ind, y_ind] = 1
+
+        for ox, oy, w, h in self.rectangles:
+            lb = self.posToInd((ox, oy))
+            rt = self.posToInd((ox+w, oy+h))
+            for x_ind in range(lb[0], rt[0]):
+                for y_ind in range(lb[1], rt[1]):
+                    x, y = self.indToPos((x_ind, y_ind))
+                    if not self.isInside((x, y)):
+                        continue
+                    self.occ_map[x_ind, y_ind] = 1
+
+    def distanceTransform(self):
+        """Get esdf from occmap, see also https://www.cs.cornell.edu/~dph/papers/dt.pdf
+        """
+        tmp_buffer2 = tmp_buffer1 = np.zeros_like(self.esdf_map)
+
+        def f_set_val(buf, x, y, val):
+            buf[x, y] = val
+
+        # calculate positive distance
+        for x in range(self.occ_map.shape[0]):
+            self.FillESDF(
+                lambda y: 0 if self.occ_map[x, y] == 1 else 1000000,
+                lambda y, val: f_set_val(tmp_buffer1, x, y, val),
+                0, self.occ_map.shape[1]-1, 1
+            )
+
+        for y in range(self.occ_map.shape[1]):
+            self.FillESDF(
+                lambda x: tmp_buffer1[x, y],
+                lambda x, val: f_set_val(tmp_buffer2, x, y, val),
+                0, self.occ_map.shape[0]-1, 0
+            )
+        dist_pos = np.sqrt(tmp_buffer2)*self.reso
+
+        # calculate negative distance
+        tmp_buffer2 = tmp_buffer1 = np.zeros_like(self.esdf_map)
+
+        # calculate positive distance
+        for x in range(self.occ_map.shape[0]):
+            self.FillESDF(
+                lambda y: 0 if self.occ_map[x, y] == 0 else 1000000,
+                lambda y, val: f_set_val(tmp_buffer1, x, y, val),
+                0, self.occ_map.shape[1]-1, 1
+            )
+
+        for y in range(self.occ_map.shape[1]):
+            self.FillESDF(
+                lambda x: tmp_buffer1[x, y],
+                lambda x, val: f_set_val(tmp_buffer2, x, y, val),
+                0, self.occ_map.shape[0]-1, 0
+            )
+        dist_neg = np.sqrt(tmp_buffer2)*self.reso
+        self.esdf_map = dist_pos - dist_neg
+
+    def FillESDF(self, f_get_val, f_set_val, start, end, dim):
+        v = np.zeros(self.esdf_map.shape[dim], dtype=int)
+        z = np.zeros(self.esdf_map.shape[dim]+1)
+
+        k = start
+        v[start] = start
+        z[start] = -np.inf
+        z[start+1] = np.inf
+
+        for q in range(start+1, end+1):
+            k += 1
+
+            s = -np.inf
+            while s <= z[k]:
+                k -= 1
+                # if q==243 and k==242:
+                #     print(f_get_val(q), f_get_val(v[k]), q, v[k])
+                s = ((f_get_val(q) + q*q) -
+                     (f_get_val(v[k]) + v[k]*v[k])) / (2*q - 2*v[k])
+
+            k += 1
+
+            v[k] = q
+            z[k] = s
+            z[k + 1] = np.inf
+
+        k = start
+        for q in range(start, end+1):
+            while z[k + 1] < q:
+                k += 1
+            val = (q - v[k]) * (q - v[k]) + f_get_val(v[k])
+            f_set_val(q, val)
+
+    def evaluateDistGrad(self, pos):
+        pos = np.array(pos)
+        pos_m = self.indToPos(self.posToInd(pos - self.reso / 2))
+        diff = (pos - pos_m) / self.reso
+        values = np.zeros([2, 2])
+        for x in range(2):
+            for y in range(2):
+                values[x, y] = self.getDistance(
+                    pos_m+np.array([x*self.reso, y*self.reso]))
+        dist = (values[0, 0]*(1-diff[0])*(1-diff[1]) +
+                values[0, 1]*(1-diff[0])*(diff[1]) +
+                values[1, 0]*(diff[0])*(1-diff[1]) +
+                values[1, 1]*(diff[0])*(diff[1]))
+        grad = np.zeros(2)
+        grad[0] = (values[1, 0]-values[0, 0])*(1-diff[1]) + \
+            (values[1, 1]-values[0, 1])*(diff[1])
+        grad[1] = (values[0, 1]-values[0, 0])*(1-diff[0]) + \
+            (values[1, 1]-values[1, 0])*(diff[0])
+        grad = grad/self.reso
+        return dist, grad
+
+    def getDistance(self, pos):
+        ind = self.posToInd(pos)
+        ind = self.boundIndex(ind)
+        return self.esdf_map[ind[0], ind[1]]
+
+    def isValid(self, pos):
+        ind = self.posToInd(pos)
+        ind = self.boundIndex(ind)
+        return self.occ_map[ind[0], ind[1]] == 0  # check occ
+
+    def getBbox(self):
+        """Return the bounding box
+        Returns:
+            origin: 
+            length:
+        """
+        return np.array(self.origin), np.array(self.length)
+
+
+def plotEnv(env: ComplexEnv):
+    fig = plt.gcf()
+    ax = plt.gca()
+    for ox, oy, r in env.circles:
+        ax.add_patch(patches.Circle(
+            (ox, oy), r, edgecolor='black', facecolor='gray', fill=True))
+    for ox, oy, w, h in env.rectangles:
+        ax.add_patch(patches.Rectangle((ox, oy), w, h,
+                                       edgecolor='black', facecolor='gray', fill=True))
+
+
+class AstarNode:
+    def __init__(self):
+        self.x = 0
+        self.y = 0
+        self.x_ind = 0
+        self.y_ind = 0
+        self.cost = np.inf
+        self.parent = None
+
+
+def AstarSearch(reso, start, end, env: ComplexEnv):
+    """Astar search path
+    Args:
+        reso: float
+        start: [x,y]
+        end: [x,y]
+        env: ComplexEnv
+    Returns:
+        path: [[x,y]]
+    """
+
+    start = np.array(start)
+    end = np.array(end)
+    center = start
+
+    def posToInd(x, y):
+        x_ind = round((x-center[0])/reso)
+        y_ind = round((y-center[1])/reso)
+        return x_ind, y_ind
+
+    def indToPos(x_ind, y_ind):
+        x = center[0]+x_ind*reso
+        y = center[1]+y_ind*reso
+        return x, y
+    node_map = {}
+    open_set = PriorityQueue()
+    start_node = AstarNode()
+    start_node.x = start[0]
+    start_node.y = start[1]
+    start_node.x_ind, start_node.y_ind = posToInd(start[0], start[1])
+    start_node.parent = None
+    start_node.cost = 0.0
+
+    def addNodeToOpen(node):
+        g = node.cost
+        h = np.hypot(end[0]-node.x, end[1]-node.y)
+        open_set.put((g+h, g, node.x_ind, node.y_ind, node))
+    addNodeToOpen(start_node)
+    node_map[(start_node.x_ind, start_node.y_ind)] = start_node
+    cnt = 400
+    while not open_set.empty() and cnt > 0:
+        cur_node = open_set.get()[-1]
+
+        if np.hypot(cur_node.x-end[0], cur_node.y-end[1]) < reso:
+            break
+        for dx in [-1, 0, 1]:
+            for dy in [-1, 0, 1]:
+                if dx == 0 and dy == 0:
+                    continue
+                pro_x = cur_node.x + dx*reso
+                pro_y = cur_node.y + dy*reso
+                if not env.isValid((pro_x, pro_y)):
+                    continue
+                pro_x_ind, pro_y_ind = posToInd(pro_x, pro_y)
+                assert not (
+                    pro_x_ind == cur_node.x_ind and pro_y_ind == cur_node.y_ind)
+                if (pro_x_ind, pro_y_ind) not in node_map.keys():
+                    pro_node = AstarNode()
+                    pro_node.x = pro_x
+                    pro_node.y = pro_y
+                    pro_node.x_ind = pro_x_ind
+                    pro_node.y_ind = pro_y_ind
+                    pro_node.parent = None
+                    pro_node.cost = np.inf
+                    node_map[(pro_x_ind, pro_y_ind)] = pro_node
+                pro_node = node_map[(pro_x_ind, pro_y_ind)]
+                if cur_node.cost + np.hypot(dx, dy)*reso < pro_node.cost:
+                    pro_node.parent = cur_node
+                    pro_node.cost = cur_node.cost + np.hypot(dx, dy)*reso
+                    addNodeToOpen(pro_node)
+
+    # extract course
+    cur_node = cur_node
+    path = []
+    while cur_node != None:
+        path.append([cur_node.x, cur_node.y])
+        cur_node = cur_node.parent
+    path.reverse()
+    return path
+
+
+def calcVel(x, t):
+    assert len(x) == len(t)
+    x = np.array(x)
+    dx = np.diff(x, axis=0)
+    dt = np.diff(t)
+    v = np.array([_dx/_dt for _dx, _dt in zip(dx, dt)])
+    return v
+
+
+def calcAcc(x, t):
+    assert len(x) == len(t)
+    v = calcVel(x, t)
+    a = calcVel(v, t[:-1])
+    return a
+
+start = (-2.5, 0.0)
+end = (3.0, 0.0)
+start_v = (0.0,0.0)
+start_a = (0.0,0.0)
+end_v = (0.0,0.0)
+end_a = (0.0,0.0)
+reso = 0.2
+ts = 0.1
+
+figwidth = 6
+# A star search initial path
+complex_env = ComplexEnv()
+path = AstarSearch(reso, start, end, complex_env)
+path = np.array(path)
+
+origin, length = complex_env.getBbox()
+fig = plt.figure(figsize=(figwidth, figwidth/length[0]*length[1]))
+plt.axis([origin[0], origin[0]+length[0], origin[1], origin[1]+length[1]])
+plotEnv(complex_env)
+plt.plot(path[:,0],path[:,1])
+plt.title("Initial path")
+
+# convert path to B-spline trajectory
+ctrl_pts = NonUniformBspline.parameterizeToBspline(ts, path, np.zeros([4,2]))
+bs_raw = NonUniformBspline(ctrl_pts, 3, ts)
+t_min, t_max = bs_raw.getTimeSpan()
+traj_t = np.linspace(t_min,t_max,num=100)
+traj_raw = np.array([bs_raw.evaluateDeBoor(t) for t in traj_t])
+
+origin, length = complex_env.getBbox()
+fig = plt.figure(figsize=(figwidth, figwidth/length[0]*length[1]))
+plt.axis(np.array([origin[0], origin[0]+length[0], origin[1], origin[1]+length[1]]))
+plotEnv(complex_env)
+plt.plot(ctrl_pts[:,0],ctrl_pts[:,1],"--ok",linewidth=2)
+plt.plot(traj_raw[:,0],traj_raw[:,1],linewidth=2)
+plt.title("Initial Control Points")
+
+# B-spline control points optimization
+opt = BsplineOptimizer(complex_env)
+ctrl_pts_opt = opt.BsplineOptimizeTraj(ctrl_pts, ts, opt.SMOOTHNESS|opt.DISTANCE|opt.FEASIBILITY, 500, 500)
+bspline_opt = NonUniformBspline(ctrl_pts_opt, 3, ts)
+t_min, t_max = bspline_opt.getTimeSpan()
+traj_t = np.linspace(t_min, t_max, num=100)
+traj_opt = np.array([bspline_opt.evaluateDeBoor(t) for t in traj_t])
+
+origin, length = complex_env.getBbox()
+fig = plt.figure(figsize=(figwidth, figwidth/length[0]*length[1]))
+plt.axis(np.array([origin[0], origin[0]+length[0], origin[1], origin[1]+length[1]]))
+plotEnv(complex_env)
+plt.plot(ctrl_pts_opt[:,0],ctrl_pts_opt[:,1], '--ok')
+plt.plot(traj_opt[:,0],traj_opt[:,1], c='purple')
+plt.title("Optimized Bspline")
+
+plt.figure(figsize=(figwidth, figwidth/length[0]*length[1]))
+traj_opt_vel = calcVel(traj_opt, traj_t)
+traj_opt_acc = calcAcc(traj_opt, traj_t)
+plt.plot(traj_t[:-1], traj_opt_vel[:,0], "-", linewidth=2, label="vel_x")
+plt.plot(traj_t[:-1], traj_opt_vel[:,1], "-", linewidth=2, label="vel_y")
+plt.plot(traj_t[:-2], traj_opt_acc[:,0], "-", linewidth=2, label="acc_x")
+plt.plot(traj_t[:-2], traj_opt_acc[:,1], "-", linewidth=2, label="acc_y")
+plt.legend()
+plt.title("Optimized Bspline Vel/Acc")
+plt.show()
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