MidsemBookVignesh.ipynb

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  "metadata": {
    "colab": {
      "name": "MidsemBookVignesh.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "mount_file_id": "1kSTCh34Q3XluhfkVTFm0_XKe6-LU_hhw",
      "authorship_tag": "ABX9TyOm32HQKewzIufjeGAkhLg/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/IntrovertInDisguise/iitgn-robotics/blob/main/MidsemBookVignesh.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3nKJ0oek-MtY"
      },
      "source": [
        "#Vignesh Ramakrishnan\n",
        "#21310037\n",
        "#Importing libraries\n",
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy.integrate as integrate \n",
        "import matplotlib.animation as animation\n",
        "from matplotlib.animation import FuncAnimation\n",
        "from matplotlib import rc\n",
        "from IPython.display import HTML\n",
        "from numpy import sin, cos,arctan,arccos\n",
        "from collections import deque"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2s--HESbLLt0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4b0b65be-754e-4bdf-c794-1ebae6a38970"
      },
      "source": [
        "\n",
        "#Rotational matrix along x\n",
        "def RotX(theta):\n",
        "  theta=np.radians(theta)\n",
        "  return np.array([[1,0,0,0],[0,np.cos(theta),-np.sin(theta),0],[0,np.sin(theta),np.cos(theta),0],[0,0,0,1]])\n",
        "\n",
        "\n",
        "#Rotational matrix along y\n",
        "def RotY(theta):\n",
        "  theta=np.radians(theta)\n",
        "  return np.array([[np.cos(theta),0,-np.sin(theta),0],[0,1,0,0],[np.sin(theta),0,np.cos(theta),0],[0,0,0,1]])\n",
        "\n",
        "\n",
        "#Rotational matrix along z\n",
        "def RotZ(theta):\n",
        "  theta=np.radians(theta)\n",
        "  return np.array([[np.cos(theta),-np.sin(theta),0,0],[np.sin(theta),np.cos(theta),0,0],[0,0,1,0],[0,0,0,1]])\n",
        "\n",
        "\n",
        "#Translational matrix along x\n",
        "def TransX(dist):\n",
        "  return np.array([[1,0,0,dist],[0,1,0,0],[0,0,1,0],[0,0,0,1]])\n",
        "\n",
        "#Translational matrix along y\n",
        "def TransY(dist):\n",
        "  return np.array([[1,0,0,0],[0,1,0,dist],[0,0,1,0],[0,0,0,1]])\n",
        "\n",
        "#Translational matrix along z\n",
        "def TransZ(dist):\n",
        "  return np.array([[1,0,0,0],[0,1,0,0],[0,0,1,dist],[0,0,0,1]])\n",
        " \n",
        "#[d,theta,a,alpha]\n",
        "def AFromDHVals(DH):\n",
        "  n=np.shape(DH)[0] #From repo, only this index\n",
        "  A=np.identity(4)\n",
        "  for i in range(n):\n",
        "    Anext=TransZ(DH[i][0]) @ RotZ(DH [i][1]) @ RotX(DH [i][3]) @ TransX(DH[i][2]) \n",
        "    A=np.matmul(A,Anext)\n",
        "  return A\n",
        "#DH=[[0,90,1,0],[0,45,1,0]]\n",
        "#print(AFromDHVals(DH))\n",
        "\n"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.70710678 -0.70710678  0.         -0.70710678]\n",
            " [ 0.70710678 -0.70710678  0.          1.70710678]\n",
            " [ 0.          0.          1.          0.        ]\n",
            " [ 0.          0.          0.          1.        ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YU-H7OLfpw-s",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3a440923-7459-4e46-8a41-e6e3cd580fbd"
      },
      "source": [
        "#Repository Jacobian1\n",
        "\n",
        "import numpy as np\n",
        "import sys\n",
        "import sympy as sym\n",
        "\n",
        "class manipulator():\n",
        "\n",
        "  def __init__(self, no_of_links, type_of_joints, dh_params):\n",
        "    super().__init__()\n",
        "    self.no_of_links = no_of_links\n",
        "    self.type_of_joints = list(type_of_joints)\n",
        "    self.dh_params = dh_params\n",
        "    if len(self.dh_params) != self.no_of_links:\n",
        "      print(\"ERROR: Please make sure the number of rows in the DH parameters provided is equal to the number of links.\")\n",
        "      sys.exit()\n",
        "    self.dh_matrices = []\n",
        "    for i in range(0, self.no_of_links):    \n",
        "      temp = self.dh_params[i]\n",
        "      theta = temp[0]\n",
        "      d = temp[1]\n",
        "      a = temp[2]\n",
        "      alpha = temp[3]\n",
        "      A1 = np.array([[np.cos(theta), -np.sin(theta), 0, 0],[np.sin(theta), np.cos(theta), 0, 0],[0, 0, 1, 0],[0, 0, 0, 1]])\n",
        "      A2 = np.array([[1, 0, 0, 0],[0, 1, 0, 0],[0, 0, 1, d],[0, 0, 0, 1]])\n",
        "      A3 = np.array([[1, 0, 0, a],[0, 1, 0, 0],[0, 0, 1, 0],[0, 0, 0, 1]])\n",
        "      A4 = np.array([[1, 0, 0, 0],[0, np.cos(alpha), -np.sin(alpha), 0],[0, np.sin(alpha), np.cos(alpha), 0],[0, 0, 0, 1]])\n",
        "      A_final = A1@A2@A3@A4\n",
        "      self.dh_matrices.append(A_final)\n",
        "    self.dh_matrices = np.array(self.dh_matrices)\n",
        "\n",
        "    self.transform_matrices = []\n",
        "    self.rotation_matrices = []\n",
        "\n",
        "    for i in range(1, self.no_of_links+1):\n",
        "      temp = self.dh_matrices[0]\n",
        "      for j in range(1, i):\n",
        "        temp = temp@self.dh_matrices[j]\n",
        "      rot_temp = temp\n",
        "      rot_temp = np.delete(rot_temp, (3), axis = 0)\n",
        "      rot_temp = np.delete(rot_temp, (3), axis = 1)\n",
        "      self.transform_matrices.append(temp)\n",
        "      self.rotation_matrices.append(rot_temp)\n",
        "\n",
        "    self.transform_matrices = np.array(self.transform_matrices)\n",
        "    self.rotation_matrices = np.array(self.rotation_matrices)\n",
        "\n",
        "    self.end_effector_posn = np.delete(self.transform_matrices[len(self.transform_matrices)-1]@np.array([[0],[0],[0],[1]]), (3), axis = 0)\n",
        "\n",
        "    self.z = []\n",
        "    self.origins = []\n",
        "    self.z.append(np.array([[0],[0],[1]]))\n",
        "    self.origins.append(np.array([[0],[0],[0]]))\n",
        "\n",
        "    for i in range(0, self.no_of_links):\n",
        "      temp_z = self.rotation_matrices[i]@np.array([[0],[0],[1]])\n",
        "      self.z.append(temp_z)\n",
        "      temp_origin = self.transform_matrices[i]@np.array([[0],[0],[0],[1]])\n",
        "      temp_origin = np.delete(temp_origin, (3), axis = 0)\n",
        "      self.origins.append(temp_origin)\n",
        "    \n",
        "    self.z = np.array(self.z)\n",
        "    self.origins = np.array(self.origins)  \n",
        "    self.jacobian = []\n",
        "    for i in range(0,self.no_of_links):\n",
        "      if self.type_of_joints[i] == \"R\":\n",
        "        temp_1 = np.cross(self.z[i], self.end_effector_posn-self.origins[i], axis = 0)\n",
        "        temp_2 = self.z[i]\n",
        "      if self.type_of_joints[i] == \"P\":\n",
        "        temp_1 = self.z[i]\n",
        "        temp_2 = np.array([[0],[0],[0]])\n",
        "      temp_jacobian = np.vstack((temp_1, temp_2))\n",
        "      self.jacobian.append(temp_jacobian)\n",
        "    self.jacobian = np.array(self.jacobian)\n",
        "    self.jacobian = self.jacobian.reshape((self.no_of_links,6))\n",
        "    self.jacobian = np.transpose(self.jacobian)\n",
        "    self.Jv = np.delete(self.jacobian,(3,4,5), axis = 0)\n",
        "\n",
        "    print(\"End Effector Position:\")\n",
        "    print(self.end_effector_posn)\n",
        "    print(\"Manipulator Jacobian:\")\n",
        "    print(self.jacobian)\n",
        "    print(\"Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\")\n",
        "    print(self.Jv)\n",
        "\n",
        "my_robot = manipulator(3, \"RRR\", [[np.pi/3,0,1,0],[0,0,0,np.pi/2],[0,0,0,np.pi/2]])\n",
        "print(\"STANFORD MANIPULATOR:\")\n",
        "stanford_manipulator = manipulator(3, \"RRP\", [[0,0,0,-np.pi/2],[0,2,0,np.pi/2],[0,2,0,0]])\n",
        "print(\"SCARA MANIPULATOR:\")\n",
        "SCARA = manipulator(3, \"RRP\", [[0,0,2,0],[0,0,2,np.pi],[0,2,0,0]])\n",
        "print(\"PPP MANIPULATOR:\")\n",
        "PPP = manipulator(3, \"PPP\", [[0,1,0,-np.pi/2],[-np.pi/2,2,0,-np.pi/2],[0,3,0,0]])\n",
        "print(\"6R MANIPULATOR:\")\n",
        "R6 = manipulator(6, \"RRRRRR\", [[np.pi/2,1,0,-np.pi/2],[0,0,1,0],[0,0,1,np.pi/2],[0,0,0,np.pi/2],[0,0,0,-np.pi/2],[0,1,0,0]])"
      ],
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "End Effector Position:\n",
            "[[0.5      ]\n",
            " [0.8660254]\n",
            " [0.       ]]\n",
            "Manipulator Jacobian:\n",
            "[[-8.66025404e-01  0.00000000e+00 -0.00000000e+00]\n",
            " [ 5.00000000e-01  0.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00  0.00000000e+00  8.66025404e-01]\n",
            " [ 0.00000000e+00  0.00000000e+00 -5.00000000e-01]\n",
            " [ 1.00000000e+00  1.00000000e+00  6.12323400e-17]]\n",
            "Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\n",
            "[[-0.8660254  0.        -0.       ]\n",
            " [ 0.5        0.         0.       ]\n",
            " [ 0.         0.         0.       ]]\n",
            "STANFORD MANIPULATOR:\n",
            "End Effector Position:\n",
            "[[0.]\n",
            " [2.]\n",
            " [2.]]\n",
            "Manipulator Jacobian:\n",
            "[[-2.000000e+00  2.000000e+00  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  1.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  0.000000e+00]\n",
            " [ 0.000000e+00  1.000000e+00  0.000000e+00]\n",
            " [ 1.000000e+00  6.123234e-17  0.000000e+00]]\n",
            "Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\n",
            "[[-2.  2.  0.]\n",
            " [ 0.  0.  0.]\n",
            " [ 0.  0.  1.]]\n",
            "SCARA MANIPULATOR:\n",
            "End Effector Position:\n",
            "[[ 4.0000000e+00]\n",
            " [-2.4492936e-16]\n",
            " [-2.0000000e+00]]\n",
            "Manipulator Jacobian:\n",
            "[[ 2.4492936e-16  2.4492936e-16  0.0000000e+00]\n",
            " [ 4.0000000e+00  2.0000000e+00 -1.2246468e-16]\n",
            " [-0.0000000e+00 -0.0000000e+00 -1.0000000e+00]\n",
            " [ 0.0000000e+00  0.0000000e+00  0.0000000e+00]\n",
            " [ 0.0000000e+00  0.0000000e+00  0.0000000e+00]\n",
            " [ 1.0000000e+00  1.0000000e+00  0.0000000e+00]]\n",
            "Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\n",
            "[[ 2.4492936e-16  2.4492936e-16  0.0000000e+00]\n",
            " [ 4.0000000e+00  2.0000000e+00 -1.2246468e-16]\n",
            " [-0.0000000e+00 -0.0000000e+00 -1.0000000e+00]]\n",
            "PPP MANIPULATOR:\n",
            "End Effector Position:\n",
            "[[3.]\n",
            " [2.]\n",
            " [1.]]\n",
            "Manipulator Jacobian:\n",
            "[[ 0.000000e+00  0.000000e+00  1.000000e+00]\n",
            " [ 0.000000e+00  1.000000e+00  6.123234e-17]\n",
            " [ 1.000000e+00  6.123234e-17 -6.123234e-17]\n",
            " [ 0.000000e+00  0.000000e+00  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  0.000000e+00]\n",
            " [ 0.000000e+00  0.000000e+00  0.000000e+00]]\n",
            "Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\n",
            "[[ 0.000000e+00  0.000000e+00  1.000000e+00]\n",
            " [ 0.000000e+00  1.000000e+00  6.123234e-17]\n",
            " [ 1.000000e+00  6.123234e-17 -6.123234e-17]]\n",
            "6R MANIPULATOR:\n",
            "End Effector Position:\n",
            "[[1.2246468e-16]\n",
            " [2.0000000e+00]\n",
            " [2.0000000e+00]]\n",
            "Manipulator Jacobian:\n",
            "[[-2.00000000e+00 -6.12323400e-17  0.00000000e+00  1.50403894e-49\n",
            "  -6.12323400e-17 -1.50403894e-49]\n",
            " [ 1.22464680e-16  1.00000000e+00  1.00000000e+00  0.00000000e+00\n",
            "  -1.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00 -2.00000000e+00 -1.00000000e+00  0.00000000e+00\n",
            "   0.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00 -1.00000000e+00 -1.00000000e+00  0.00000000e+00\n",
            "   1.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00  6.12323400e-17  6.12323400e-17  1.50403894e-49\n",
            "  -6.12323400e-17 -1.50403894e-49]\n",
            " [ 1.00000000e+00  6.12323400e-17  6.12323400e-17  1.00000000e+00\n",
            "   6.12323400e-17  1.00000000e+00]]\n",
            "Velocity Jacobian (can be multiplied with qdot to obtain end-effector velocity):\n",
            "[[-2.00000000e+00 -6.12323400e-17  0.00000000e+00  1.50403894e-49\n",
            "  -6.12323400e-17 -1.50403894e-49]\n",
            " [ 1.22464680e-16  1.00000000e+00  1.00000000e+00  0.00000000e+00\n",
            "  -1.00000000e+00  0.00000000e+00]\n",
            " [ 0.00000000e+00 -2.00000000e+00 -1.00000000e+00  0.00000000e+00\n",
            "   0.00000000e+00  0.00000000e+00]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qd2V7wFWyR6D"
      },
      "source": [
        "# Task 1: Milacron manifold block inspection"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3AQsiCLR26Il"
      },
      "source": [
        "Linklengths=[0.25,0.25,0.25]\n",
        "Linkmasses=[0.8,0.8,0.8]\n",
        "Amax=[0.45,0.075,0.1]\n",
        "Bmax=[0.45,-0.075,0.1]\n",
        "Cmax=[0.25,0.075,0.1]\n",
        "Dmax=[0.25,-0.075,0.1]"
      ],
      "execution_count": 87,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-UTsCzloyjOL"
      },
      "source": [
        "#### Robot 1: Stanford type(RRP)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Of_R3LwFtOfP"
      },
      "source": [
        "#Forward Kinematics i.e. end effector positions from joint positions\n",
        "def For_Pos_Kin_Stanford(jointloc,lengthsoflinks):\n",
        "  theta1,theta2,dz3=jointloc[0],jointloc[1],jointloc[2]\n",
        "  d1,d2,d3=lengthsoflinks[0],lengthsoflinks[1],lengthsoflinks[2]\n",
        "  DH=[[d1,theta1,0,-90],[d2,theta2,0,90],[-dz3,0,0,0]]  \n",
        "  P0=np.array([0,0,dz3-d1,1])\n",
        "  A=AFromDHVals(DH)\n",
        "  return A @ P0\n"
      ],
      "execution_count": 142,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cG-ZvOWQYLOl"
      },
      "source": [
        "def For_Pos_Kin_Stanford_NoDH(jointloc,lengthsoflinks):\n",
        "  theta1,theta2,dy2=jointloc[0],jointloc[1],jointloc[2]\n",
        "  l1,l2,l3=lengthsoflinks[0],lengthsoflinks[1],lengthsoflinks[2]\n",
        "  P2mat = np.transpose(np.array([0,dy2,0,1]))\n",
        "  P1mat=((RotX(theta2) @ TransX(-l2)) @ P2mat)\n",
        "  P0mat=((RotZ(theta1) @ TransZ(l1)) @ P1mat)\n",
        "  return P0mat"
      ],
      "execution_count": 148,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A_lI0Xw6Kq5r",
        "outputId": "5f2308a9-1bf7-4399-a7c8-be188b58e14a"
      },
      "source": [
        "\n",
        "#inverse kinematics i.e. joint positions from endeffector positions: My Code\n",
        "def Inv_Pos_Kin_Stanford(P0,lengthsoflinks):\n",
        "  P_x=P0[0]\n",
        "  P_y=P0[1]\n",
        "  P_z=P0[2]\n",
        "  l_1,l_2=lengthsoflinks[0],lengthsoflinks[1]\n",
        "  r= ((P_x**2) + (P_y**2))**0.5 #revolute link radius\n",
        "  phi= np.arctan2(P_y,P_x) # revolute link angle\n",
        " \n",
        "  theta_1=np.arctan2(P_x,P_y)- np.arctan2(l_2,((r**2)-(l_2**2))**0.5 ) # theta_1=np.arctan2(P_x,P_y)- np.arctan2(l_2,-((r**2)-(l_2**2))**0.5 ) # also valid\n",
        "\n",
        "  \n",
        "  theta_1_v2=np.arctan2(P_x,P_y)- np.arctan2(l_2,-((r**2)-(l_2**2))**0.5 )\n",
        "    \n",
        "\n",
        "  l_hor=((P_x*np.cos(theta_1))+(P_y*np.sin(theta_1))) #Horizontal position of joint 2\n",
        "  l_vert=l_1-P_z #Vertical position of joint 2\n",
        "\n",
        "\n",
        "\n",
        "  theta_2=np.arctan2(l_hor,l_vert) #  theta_2=np.arctan2(-l_hor,-l_vert) #also valid\n",
        "\n",
        "  #if theta_2 < 0 :\n",
        "  theta_2_v2=np.arctan2(-l_hor,-l_vert)\n",
        "  \n",
        "  d_3= (l_hor* np.sin(theta_2))+(l_vert* np.cos(theta_2))\n",
        "  return [[np.degrees(theta_1),np.degrees(theta_2),d_3],[np.degrees(theta_1_v2),np.degrees(theta_2_v2),d_3]]\n",
        "\n",
        "\n",
        "\n",
        "jointloc=Inv_Pos_Kin_Stanford(Amax,Linklengths)\n",
        "print(jointloc)\n",
        "print(For_Pos_Kin_Stanford(jointloc[1],Linklengths))\n"
      ],
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[47.30799649413152, 67.3943310604584, 0.3902320599631367], [-66.23264091018274, -112.6056689395416, 0.3902320599631367]]\n",
            "[ 0.32181249 -0.11046336  0.34609667  1.        ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NyuZEnmOHrB5",
        "outputId": "3dbd6f70-f5f7-4ebb-d75a-0a6e37a16d74"
      },
      "source": [
        " #From Repository\n",
        "def invKinStanford_RepoCode(endeffector_position,lengthsoflinks):\n",
        "    theta1 = np.arctan(endeffector_position[1]/endeffector_position[0])\n",
        "    r = np.sqrt(endeffector_position[0]**2 + endeffector_position[1]**2)\n",
        "    s = endeffector_position[2] - lengthsoflinks[0]\n",
        "    theta2 = np.arctan(s/r)\n",
        "    d3 = np.sqrt(r**2 + s**2) - lengthsoflinks[1]\n",
        "    #print(\"First Solution: \\n\", \"Theta1 = \", theta1, \"\\n Theta2 =\", theta2,\"\\n Extension: \", d3, \"\\n\")\n",
        "    #print(\"Second Solution: \\n\", \"Theta1 = \", np.pi + theta1, \"\\n Theta2 =\", np.pi - theta2,\"\\n Extension:\", d3)\n",
        "    return [[theta1,theta2,d3],[np.pi + theta1,np.pi - theta2,d3]]\n",
        "          \n",
        "\n",
        "inverse_kinematics([30,30,30],[10,10])"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 45.        ,  25.23940182,  36.9041576 ],\n",
              "       [225.        , 154.76059818,  36.9041576 ]])"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WlDjFV180ZZC"
      },
      "source": [
        "#### Robot 2: PUMA type(RRR)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gu3GGXSCnejW"
      },
      "source": [
        "#Forward Kinematics i.e. end effector positions from joint positions\n",
        "def For_Pos_Kin_PUMA(jointloc,lengthsoflinks):\n",
        "  theta1,theta2,theta3=jointloc[0],jointloc[1],jointloc[2]\n",
        "  d1,d2,d3=lengthsoflinks[0],lengthsoflinks[1],lengthsoflinks[2]\n",
        "  DH=[[d1,theta1,d2,0],[,theta2,0,90],[-dz3,0,0,0]]\n",
        "  P0=np.array([0,0,d1-dz3,1])\n",
        "  A=AFromDHVals(DH)\n",
        "  return A @ P0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OxvduHxznewZ",
        "outputId": "5f8e7917-7310-457f-e6cd-24b30783e034"
      },
      "source": [
        " def Inv_Pos_Kin_PUMA(P0,lengthsoflinks):\n",
        "   xc,yc,zc=P0[0],P0[1],P0[2]\n",
        "   l1,l2,l3=lengthsoflinks[0],lengthsoflinks[1],lengthsoflinks[2]\n",
        "   theta1 = np.rad2deg(np.arctan2(yc,xc))\n",
        "   D = (xc*xc+yc*yc+(l1-zc)*(l1-zc)-l2*l2-l3*l3)/(2*l2*l3)\n",
        "   if D>=1 or D<=-1:\n",
        "     print(\"singular configuration\")\n",
        "   if D>1 or D<-1:\n",
        "     print(\"outside workspace\")\n",
        "   theta3 = (np.arctan2((-np.sqrt(1-D*D)),D))\n",
        "   theta2 = np.rad2deg(np.arctan2(zc-l1,(np.sqrt(xc*xc+yc*yc)))-np.arctan2((l3*np.sin(theta3)),(l2+l3*np.cos(theta3))))\n",
        "   theta3 = np.rad2deg(theta3)\n",
        "   return [[theta1,theta2,theta3]]\n",
        "\n",
        "print(Inv_Pos_Kin_PUMA([0.05,0.3,0],Linklengths))\n",
        "jointloc=Inv_Pos_Kin_PUMA([0.5,0,0],Linklengths)\n",
        "print(For_Pos_Kin_SCARA(jointloc[0],Linklengths))"
      ],
      "execution_count": 140,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[80.53767779197439, -1.3633017452217766, -76.11345963737101]]\n",
            "singular configuration\n",
            "outside workspace\n",
            "[nan nan nan nan]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in sqrt\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kuEiTmoSIdu4"
      },
      "source": [
        "def inverse_kinematics_PUMARepo(l1,l2,l3,xc,yc,zc):\n",
        "    theta1 = np.rad2deg(math.atan2(yc,xc))\n",
        "    D = (xc*xc+yc*yc+(l1-zc)*(l1-zc)-l2*l2-l3*l3)/(2*l2*l3)\n",
        "    if D>=1 or D<=-1:\n",
        "        print(\"singular configuration\")\n",
        "    if D>1 or D<-1:\n",
        "        print(\"outside workspace\")\n",
        "    theta3 = (math.atan2((-math.sqrt(1-D*D)),D))\n",
        "    theta2 = np.rad2deg(math.atan2(zc-l1,(math.sqrt(xc*xc+yc*yc)))-math.atan2((l3*math.sin(theta3)),(l2+l3*math.cos(theta3))))\n",
        "    theta3 = np.rad2deg(theta3)\n",
        "    return theta1,theta2,theta3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5k711nc40Z91"
      },
      "source": [
        "#### Robot 3: SCARA type(RRP)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jy55qr8oZ4CO"
      },
      "source": [
        "def For_Pos_Kin_SCARA(jointloc,lengthsoflinks):\n",
        "  theta1,theta2,dz3=jointloc[0],jointloc[1],jointloc[2]\n",
        "  d1,d2,d3=lengthsoflinks[0],lengthsoflinks[1],lengthsoflinks[2]\n",
        "  DH=[[d1,theta1,d2,0],[0,theta2,d3,0],[-dz3,0,0,0]]\n",
        "  P0=np.array([0,0,d1-dz3,1])\n",
        "  A=AFromDHVals(DH)\n",
        "  return A @ P0\n",
        "\n"
      ],
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8TrPrnoALyzZ",
        "outputId": "ca69868e-ae1e-4702-dbe6-eec8895ff1b8"
      },
      "source": [
        " #Inverse Kinematics of SCARA from my old code\n",
        " def Inv_Pos_Kin_SCARA(P0,lengthsoflinks):\n",
        "   l_1=lengthsoflinks[0]\n",
        "   l_2=lengthsoflinks[1]\n",
        "   h=lengthsoflinks[2]\n",
        "   P_x=P0[0]\n",
        "   P_y=P0[1]\n",
        "   P_z=P0[2]\n",
        "   theta_2=np.arccos(((P_x**2+P_y**2)-(l_1**2+l_2**2))/(2*l_1*l_2)) # + or -\n",
        "   theta_1=np.arctan2(((l_2*P_x*np.sin(theta_2))+P_y*(l_1+l_2*np.cos(theta_2))),(-(l_2*P_y*np.sin(theta_2))+P_x*(l_1+l_2*np.cos(theta_2))))\n",
        "   d_3=h-P_z\n",
        "   print()\n",
        "   return np.array([[np.degrees(theta_1),np.degrees(theta_2),d_3],[np.degrees(theta_1),np.degrees(-theta_2),d_3]])\n",
        "\n",
        "print(Inv_Pos_Kin_SCARA([0.5,0,0],Linklengths))\n",
        "jointloc=Inv_Pos_Kin_SCARA([0.5,0,0],Linklengths)\n",
        "print(For_Pos_Kin_SCARA(jointloc[0],Linklengths))"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "[[ 0.    0.    0.25]\n",
            " [ 0.   -0.    0.25]]\n",
            "\n",
            "[0.5 0.  0.  1. ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pIMOyZlnbDwn"
      },
      "source": [
        "## Task 1a"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-Sqo6wnVbnMD",
        "outputId": "feebe5f2-2827-4e61-9e0f-6d3407f57cf2"
      },
      "source": [
        "Linklengths=[0.25,0.25,0.25]\n",
        "Linkmasses=[0.8,0.8,0.8]\n",
        "Amax=[0.45,0.075,0.1]\n",
        "Bmax=[0.45,-0.075,0.1]\n",
        "Cmax=[0.25,0.075,0.1]\n",
        "Dmax=[0.25,-0.075,0.1]\n",
        "\n",
        "#Calculating required link lengths\n",
        "def StanfordLinkLengthReqd(Amax,Bmax,Cmax,Dmax):\n",
        "  l1new=max(0.25,abs(Amax[2]),abs(Bmax[2]),abs(Cmax[2]),abs(Dmax[2]))\n",
        "  l2new=max(0.25,abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1]))\n",
        "  l3new=( ((l1new-max(abs(Amax[2]),abs(Bmax[2]),abs(Cmax[2]),abs(Dmax[2])))**2+ (max(abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1]))))**2 + max(0.25,abs(Amax[0]),abs(Bmax[0]),abs(Cmax[0]),abs(Dmax[0]))**2)**0.5\n",
        "  return [l1new,l2new,l3new]\n",
        "print('Stanford Link lengths required:',StanfordLinkLengthReqd(Amax,Bmax,Cmax,Dmax))\n",
        "lstan=StanfordLinkLengthReqd(Amax,Bmax,Cmax,Dmax)\n",
        "\n",
        "\n",
        "\n",
        "def SCARALinkLengthReqd(Amax,Bmax,Cmax,Dmax):\n",
        "  l1new=max(0.25,abs(Amax[2]),abs(Bmax[2]),abs(Cmax[2]),abs(Dmax[2]))\n",
        "  l2new=(max(0.25,abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1])))\n",
        "  l3new=((max(abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1])))**2 + max(abs(Amax[0]),abs(Bmax[0]),abs(Cmax[0]),abs(Dmax[0]))**2-l2new**2)**0.5\n",
        "  return [l1new,l2new,l3new]\n",
        "print('SCARA Link lengths required:',SCARALinkLengthReqd(Amax,Bmax,Cmax,Dmax))\n",
        "lScara=SCARALinkLengthReqd(Amax,Bmax,Cmax,Dmax)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "def PUMALinkLengthReqd(Amax,Bmax,Cmax,Dmax):\n",
        "  l1new=max(0.25,abs(Amax[2]),abs(Bmax[2]),abs(Cmax[2]),abs(Dmax[2]))\n",
        "  l2new=(max(0.25,abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1])))\n",
        "  l3new=((max(abs(Amax[1]-Bmax[1]),abs(Cmax[1]-Dmax[1])))**2 + max(abs(Amax[0]),abs(Bmax[0]),abs(Cmax[0]),abs(Dmax[0]))**2+(l1new-max(abs(Amax[2]),abs(Bmax[2]),abs(Cmax[2]),abs(Dmax[2])))**2-l2new**2)**0.5\n",
        "  return [l1new,l2new,l3new]\n",
        "print('PUMA Link lengths required:',PUMALinkLengthReqd(Amax,Bmax,Cmax,Dmax))\n",
        "lPUMA=PUMALinkLengthReqd(Amax,Bmax,Cmax,Dmax)\n",
        "\n",
        "#Verification\n",
        "jointloc=invKinStanford_RepoCode(Amax,lstan)\n",
        "#print(jointloc)\n",
        "print(For_Pos_Kin_Stanford_NoDH(jointloc[0],lstan))\n",
        "\n"
      ],
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Stanford Link lengths required: [0.25, 0.25, 0.48192971479252034]\n",
            "SCARA Link lengths required: [0.25, 0.25, 0.4031128874149275]\n",
            "PUMA Link lengths required: [0.25, 0.25, 0.4301162633521313]\n",
            "[-0.25066258  0.22950923  0.24872353  1.        ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "egsyOFJGbHvK"
      },
      "source": [
        "## Task 1b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iCNQBMdjbL2G"
      },
      "source": [
        "## Task 1c\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IPc-AjOhbT8b"
      },
      "source": [
        "## Task 1d"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TNlvZDDrbW7b"
      },
      "source": [
        "## Task 1e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s2ZeG36-OBtC"
      },
      "source": [
        "##Task 3b"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "9D9AIW_oOEIN",
        "outputId": "ad29b309-f1db-4fa1-abd3-f1440ffab05e"
      },
      "source": [
        "import xlrd\n",
        "loc = (\"/content/drive/MyDrive/Colab Notebooks/Gait_DATA.xlsx\")\n",
        " \n",
        "wb = xlrd.open_workbook(loc)\n",
        "sheet = wb.sheet_by_index(0)\n",
        "for i in range(sheet.nrows):\n",
        "  p=sheet.row_values(i)\n",
        "  plt.scatter(p[0],p[1])\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.title('Ankle trajectory')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}