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Subject: [PATCH 2/5] Add files via upload 22210009-avnish chokshi --- Assignment 4&5.ipynb | 655 +++++++++++++++++++++++++++++++++++++++++++ with_Controller1.slx | Bin 0 -> 27342 bytes with_Controller2.slx | Bin 0 -> 29667 bytes 3 files changed, 655 insertions(+) create mode 100644 Assignment 4&5.ipynb create mode 100644 with_Controller1.slx create mode 100644 with_Controller2.slx diff --git a/Assignment 4&5.ipynb b/Assignment 4&5.ipynb new file mode 100644 index 0000000..2e6ef73 --- /dev/null +++ b/Assignment 4&5.ipynb @@ -0,0 +1,655 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Inverse position Kinematics of stanford manipulator" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.5070054663916311, -0.43789010799563355, 0.6255361307144429, 1.2630475283927902], [1.2452165677665659, 0.8774422227801884, 0.1409177561264703, 2.2841814398178166], [-0.4885930992666423, 0.5187467888736881, 0.7673634961210261, 2.4994143036899032], [0, 0, 0, 1]]\n", + "Angle1=atan(0.283841586151369*(-0.283662795851432 - 1.57734377675279*I)*(1.86153709777502 + 0.240357146933759*I)) Angle2=-I*(1.27678049921774 - 1.5707963267949*I) Linear=0.877154490383536*I\n", + "Angle4=0 Angle5=pi/2 + 1.05910259453015*I Angle6=-0.233303922708297 - 1.45088683276874*I\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "s1,s2,s3,s4,s5,s6 = sym.symbols('s1,s2,s3,s4,s5,s6')\n", + "c1,c2,c3,c4,c5,c6 = sym.symbols('c1,c2,c3,c4,c5,c6')\n", + "d2,d3,d6 = 2,2,1\n", + "q1,q2,q3,q4,q5,q6 = pi/18,3*pi/18,pi/18,pi/18,pi/18,pi/18\n", + "r11,r21,r31,r41 = cos(q1)*(cos(q2)*(cos(q4)*cos(q5)*cos(q6)-sin(q4)*sin(q6))-sin(q2)*sin(q5)*cos(q6))-sin(q1)*(sin(q4)*cos(q5)*cos(q6)+cos(q4)*cos(q6)), sin(q1)*(cos(q2)*(cos(q4)*cos(q5)*cos(q6)-sin(q4)*sin(q6))-sin(q2)*sin(q5)*cos(q6))+cos(q1)*(sin(q4)*cos(q5)*cos(q6)+cos(q4)*cos(q6)), -sin(q2)*(cos(q4)*cos(q5)*cos(q6)-sin(q4)*sin(q6))-cos(q2)*sin(q5)*sin(q6), 0\n", + "r12,r22,r32,r42 = cos(q1)*(-cos(q2)*(cos(q4)*cos(q5)*sin(q6)+sin(q4)*cos(q6))+sin(q2)*sin(q5)*sin(q6))-sin(q1)*(-sin(q4)*cos(q5)*sin(q6)+cos(q4)*cos(q6)), sin(q1)*(-cos(q2)*(cos(q4)*cos(q5)*sin(q6)+sin(q4)*cos(q6))+sin(q2)*sin(q5)*sin(q6))+cos(q1)*(-sin(q4)*cos(q5)*sin(q6)+cos(q4)*cos(q6)), +sin(q2)*(cos(q4)*cos(q5)*cos(q6)+sin(q4)*sin(q6))+cos(q2)*sin(q5)*sin(q6), 0\n", + "r13,r23,r33,r43 = cos(q1)*(cos(q2)*cos(q4)*sin(q5)+sin(q2)*cos(q5))-sin(q1)*sin(q4)*sin(q5), sin(q1)*(cos(q2)*cos(q4)*sin(q5)+sin(q2)*cos(q5))+cos(q1)*sin(q4)*sin(q5), -sin(q2)*cos(q4)*sin(q5)+cos(q2)*cos(q5), 0\n", + "r14,r24,r34,r44 = cos(q1)*sin(q2)*d3-sin(q1)*d2+d6*(cos(q1)*cos(q2)*cos(q4)*sin(q5)+cos(q1)*cos(q5)*sin(q2)-sin(q1)*sin(q4)*sin(q5)), sin(q1)*sin(q2)*d3+cos(q1)*d2+d6*(cos(q1)*sin(q4)*sin(q5)+cos(q2)*cos(q4)*sin(q1)*sin(q5)+cos(q5)*sin(q1)*sin(q2)), cos(q2)*d3+d6*(cos(q2)*cos(q5)-cos(q4)*sin(q2)*sin(q5)),1\n", + "f_mat = [[r11,r12,r13,r14],[r21,r22,r23,r24],[r31,r32,r33,r34],[r41,r42,r43,r44]]\n", + "print(f_mat)\n", + "\n", + "EQn1 = sym.Eq(c1*s2*s3-s1*d2,0.16)\n", + "\n", + "\"\"\"sym.Eq(Function('cos')(s1)*Function('sin')(s2)*s3-Function('sin')(s1)*d2,0.16)#eq1 = sym.Eq((s1**2-1)**0.5*s2*s3-s1*d2,1)\"\"\"\n", + "EQn2 = sym.Eq(s1*s2*s3+d2*c1,1.05)\n", + "\n", + "\"\"\"sym.Eq(Function('sin')(s1)*Function('sin')(s2)*s3+Function('cos')(s1)*d2,1.05)\"\"\"\n", + "EQn3 = sym.Eq(c2*s3,1.45)\n", + "\n", + "\"\"\"sym.Eq(Function('cos')(s2)*s3,1.45)\"\"\"\n", + "EQn4 = sym.Eq(c1**2+s1**2,1)\n", + "EQn5 = sym.Eq(c2**2+s2**2,1)\n", + "result = sym.solve([EQn1,EQn2,EQn3,EQn4,EQn5],s1,s2,s3,c1,c2)\n", + "\n", + "#print(result[0])\n", + "(s1,s2,s3,c1,c2)=result[0]\n", + "print(\"Angle1=\"+str(atan(s1/c1))+\" Angle2=\"+str(atan(s2/c2))+\" Linear=\"+str(s3))\n", + "rotMat = [[c1*c2,-s1,c1*s2,0],[s1*c2,c1,s1*s2,0],[-s2,0,c2,0],[0,0,0,1]]\n", + "w = np.transpose(rotMat)*(f_mat)\n", + "#print(w)\n", + "EQn6 = sym.Eq(c5,w[2][2])\n", + "EQn7 = sym.Eq(s4,w[1][2]/w[0][2])\n", + "EQn8 = sym.Eq(s6,-w[2][1]/w[2][0])\n", + "result1 = sym.solve([EQn6,EQn7,EQn8],[s4,c5,s6])\n", + "#print(result1)\n", + "print(\"Angle4=\"+str(atan(result1.get(s4)))+\" Angle5=\"+str(acos(result1.get(c5))) +\" Angle6=\"+str(atan(result1.get(s6))))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Inverse postion Kinematics of SCARA manipulator" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Angle1=0.643501108793284 Angle2=0.927295218001612 Linear=0.200000000000000\n", + "Angle4=0.343023940420703\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "s1,s2,s3,s4,s5,s6 = sym.symbols('s1,s2,s3,s4,s5,s6')\n", + "c1,c2,c3,c4,c5,c6 = sym.symbols('c1,c2,c3,c4,c5,c6')\n", + "d2,d3,d6 = 1,1,0.5\n", + "EQn1 = sym.Eq(d2*c1+d3*c2,1.4)\n", + "\n", + "\"\"\"\"sym.Eq(Function('cos')(s1)*Function('sin')(s2)*s3-Function('sin')(s1)*d2,0.16)#eq1 = sym.Eq((s1**2-1)**0.5*s2*s3-s1*d2,1)\"\"\"\n", + "EQn2 = sym.Eq(d2*s1+d3*s2,1.4)\n", + "\n", + "\"\"\"sym.Eq(Function('sin')(s1)*Function('sin')(s2)*s3+Function('cos')(s1)*d2,1.05)\"\"\"\n", + "EQn3 = sym.Eq(s3,0.2)\n", + "\n", + "\"\"\"sym.Eq(Function('cos')(s2)*s3,1.45)\"\"\"\n", + "EQn4 = sym.Eq(c1**2+s1**2,1)\n", + "EQn5 = sym.Eq(c2**2+s2**2,1)\n", + "result = sym.solve([EQn1,EQn2,EQn3,EQn4,EQn5],s1,s2,s3,c1,c2)\n", + "\n", + "#print(result[0])\n", + "(s1,s2,s3,c1,c2)=result[0]\n", + "print(\"Angle1=\"+str(atan(s1/c1))+\" Angle2=\"+str(atan(s2/c2))+\" Linear=\"+str(s3))\n", + "\n", + "EQn6 = sym.Eq(s2*c4+c2*s4,0.9)\n", + "EQn7 = sym.Eq(c2*c4+s2*s4,0.8)\n", + "result1 = sym.solve([EQn6,EQn7],[s4,c4])\n", + "#print(result1)\n", + "print(\"Angle4=\"+str(atan(result1.get(s4))))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. Joint Velocities using end-effector velocities" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matrix([[0.0546875000000000], [0.205078125000000], [0]])\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "\n", + "jacob = Matrix([[-11.156448908138957, 9.335387362109374, 0.0], [-8.657598394923445, 5.004596890082059, 0.0], [4.328799197461723, 2.5022984450410295, 0.0]])#, [0, 0, 1], [0, 0, 1], [0, 0, 1]\n", + "#j_in = jacob.inv()\n", + "j_jtrans = jacob*jacob.transpose()\n", + "#assuming 0 acceleration b matrix will be 0\n", + "#print(j_jtrans)\n", + "joint_vel = jacob.transpose()*j_jtrans.inv()*Matrix([1,1,1]) \n", + "print(joint_vel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Q6 - Inverse Kinematics of Spherical wrist" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Angle1=-0.337889611165861 Angle2=0.785398163397448 Angle3=0.785398163397448\n" + ] + } + ], + "source": [ + "import sympy as sym\n", + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "\n", + "[[r11,r12,r13],[r21,r22,r23],[r31,r32,r33]] = [[0.9,0.9,0.9],[0.9,0.9,0.9],[0.9,0.9,0.9]]\n", + "s1,s2,s3 = sym.symbols('s1,s2,s3')\n", + "c1,c2,c3 = sym.symbols('c1,c2,c3')\n", + "eq1 = sym.Eq(c1,r33)\n", + "eq2 = sym.Eq(c2*s1,r13)\n", + "eq3 = sym.Eq(s2*s1,r23)\n", + "eq4 = sym.Eq(-s1*c3,r31)\n", + "eq5 = sym.Eq(-s1*s3,r32)\n", + "eq6 = sym.Eq(c1**1+s1**2,1)\n", + "result = sym.solve([eq1,eq2,eq3,eq4,eq5,eq6],s1,s2,s3,c1,c2,c3)\n", + "#print(result[0])\n", + "(s1,s2,s3,c1,c2,c3)=result[0]\n", + "print(\"Angle1=\"+str(atan(s1/c1))+\" Angle2=\"+str(atan(s2/c2))+\" Angle3=\"+str(atan(s3/c3)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Q9 - Dynamics and control of Stanford Manipulator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(-0.474963330849782, -0.211985631137779, 1.68837199692485, 0.880005587680033, 0.977272782896934)\n", + "(-0.932157359915714, -0.498837519664837, 1.67302121923184, 0.362053388818509, 0.866695522646006)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import control as ct\n", + "import sympy as sym\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "import matplotlib.animation as animation\n", + "import mpl_toolkits.mplot3d.axes3d as p3\n", + "\n", + "jeff,beff,ks = 5,3,1\n", + "kd,kp = 1,0.3\n", + "dyn = ct.tf([1],[jeff,beff])\n", + "stiff = ct.tf([ks],[1])\n", + "h1 = ct.series(stiff,dyn)\n", + "f1 = ct.tf([kd],[1])\n", + "h2 = ct.feedback(h1,f1,sign=-1)\n", + "feed_kp = ct.tf([kp],[1])\n", + "feed_s = ct.tf([1],[1,0])\n", + "h3 = ct.series(feed_kp,h2,feed_s)\n", + "\n", + "def inv_kin(ox,oy,oz):\n", + " s1,s2,s3,s4,s5,s6 = sym.symbols('s1,s2,s3,s4,s5,s6')\n", + " c1,c2,c3,c4,c5,c6 = sym.symbols('c1,c2,c3,c4,c5,c6')\n", + " d2,d3,d6 = 1,1,0.5\n", + " q1,q2,q3,q4,q5,q6 = pi/18,pi/18,pi/18,pi/18,pi/18,pi/18\n", + " r11,r21,r31,r41 = 0.16,0.16,0.16,ox\n", + " r12,r22,r32,r42 = 1.05,1.05,1.05,oy\n", + " r13,r23,r33,r43 = 1.45,1.45,1.45,oz\n", + " r14,r24,r34,r44 = 0,0,0,1\n", + " f_mat = [[r11,r12,r13,r14],[r21,r22,r23,r24],[r31,r32,r33,r34],[r41,r42,r43,r44]]\n", + " #print(f_mat)\n", + " #s3=0.5\n", + " eq1 = sym.Eq(c1*s2*s3-s1*d2,r41)#sym.Eq(Function('cos')(s1)*Function('sin')(s2)*s3-Function('sin')(s1)*d2,0.16)#eq1 = sym.Eq((s1**2-1)**0.5*s2*s3-s1*d2,1)\n", + " eq2 = sym.Eq(s1*s2*s3+d2*c1,r42)#sym.Eq(Function('sin')(s1)*Function('sin')(s2)*s3+Function('cos')(s1)*d2,1.05)\n", + " eq3 = sym.Eq(c2*s3,r43)#sym.Eq(Function('cos')(s2)*s3,1.45)\n", + " eq4 = sym.Eq(c1**2+s1**2,1)\n", + " eq5 = sym.Eq(c2**2+s2**2,1)\n", + " result = sym.solve([eq1,eq2,eq3,eq4,eq5],s1,s2,s3,c1,c2)#s3,\n", + " print(result[0])\n", + " (s1,s2,s3,c1,c2)=result[0] #s3,\n", + " return (s1,s2,s3,c1,c2)\n", + "\n", + "def get_angles(p1,p2):\n", + " (p1s1,p1s2,p1s3,p1c1,p1c2) = inv_kin(p1[0],p1[1],p1[2])\n", + " (p2s1,p2s2,p2s3,p2c1,p2c2) = inv_kin(p2[0],p2[1],p2[2])\n", + " p1q1, p1q2 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2))\n", + " p2q1, p2q2 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2))\n", + " u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + " return (p1q1,p1q2,p2q1,p2q2,float(p1s3),float(p2s3))\n", + "# %% Simulation :\n", + "\n", + "t0 = 1\n", + "t1 = 20\n", + "dt = 0.1\n", + "nt = int(t1 / dt ) + 1 # Number of points of sim time\n", + "t = np.linspace( t0 , t1 , nt )\n", + "# u = 3* np.ones( nt )\n", + "#end point 1\n", + "p1 = [0.16,1.05,1.65]\n", + "p2 = [0.63,1.14,1.45]\n", + "(p1q1,p1q2,p2q1,p2q2,p1s3,p2s3) = get_angles(p1,p2)\n", + "# (p1s1,p1s2,p1s3,p1c1,p1c2) = inv_kin(p1[0],p1[1],p1[2])\n", + "# (p2s1,p2s2,p2s3,p2c1,p2c2) = inv_kin(p2[0],p2[1],p2[2])\n", + "# p1q1, p1q2 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2))\n", + "# p2q1, p2q2 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2))\n", + "u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + "v = np.linspace(p1q2,p2q2,nt)\n", + "w = np.linspace(p1s3,p2s3,nt)\n", + "# %% Simulation :\n", + "(t,x)=ct.forced_response(h3,t,u,X0=p1q1)\n", + "(t,y)=ct.forced_response(h3,t,v,X0=p1q2)\n", + "(t,z)=ct.forced_response(h3,t,w,X0=0)#t, y, x = ct.forced_response(h3 , t , u ,0)\n", + "# %% Plotting :\n", + "plt.close( 'all ')\n", + "fig_width_cm = 24\n", + "fig_height_cm = 18\n", + "plt . figure (1 , figsize =( fig_width_cm /2.54 , fig_height_cm /2.54))\n", + "plt . subplot (3 , 1 , 1)\n", + "plt.plot(t , x , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q1' ,))\n", + "plt.subplot(3 , 1 , 2)\n", + "plt.plot(t , y , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q2' ,))\n", + "plt.subplot(3 , 1 , 3)\n", + "plt.plot(t , z , 'blue')\n", + "plt.xlabel( 't [ s ]')\n", + "plt.grid()\n", + "plt.legend( labels =( 'd' ,))\n", + "plt.show()\n", + "#plt . savefig ( ’ sim_tf . pdf ’)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Q10 - Dynamics and control of SCARA manipulator" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.397355871000212, 0.652644128999788, 1.65000000000000, 0.917664596561109, -0.757664596561109)\n", + "Angle4=atan(4.0/(25.0*c2 + 25.0*s2))\n", + "(0.202947885659393, 0.937052114340607, 1.45000000000000, 0.979189540235384, -0.349189540235384)\n", + "Angle4=atan(4.0/(25.0*c2 + 25.0*s2))\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import control as ct\n", + "import sympy as sym\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "import matplotlib.animation as animation\n", + "import mpl_toolkits.mplot3d.axes3d as p3\n", + "\n", + "jeff,beff,ks = 5,3,1\n", + "kd,kp = 1,0.3\n", + "dyn = ct.tf([1],[jeff,beff])\n", + "stiff = ct.tf([ks],[1])\n", + "h1 = ct.series(stiff,dyn)\n", + "f1 = ct.tf([kd],[1])\n", + "h2 = ct.feedback(h1,f1,sign=-1)\n", + "feed_kp = ct.tf([kp],[1])\n", + "feed_s = ct.tf([1],[1,0])\n", + "h3 = ct.series(feed_kp,h2,feed_s)\n", + "\n", + "def inv_kin(ox,oy,oz):\n", + " s1,s2,s3,s4,s5,s6 = sym.symbols('s1,s2,s3,s4,s5,s6')\n", + " c1,c2,c3,c4,c5,c6 = sym.symbols('c1,c2,c3,c4,c5,c6')\n", + " d2,d3,d6 = 1,1,0.5\n", + " q1,q2,q3,q4,q5,q6 = pi/18,pi/18,pi/18,pi/18,pi/18,pi/18\n", + " r11,r21,r31,r41 = 0.16,0.16,0.16,ox\n", + " r12,r22,r32,r42 = 1.05,1.05,1.05,oy\n", + " r13,r23,r33,r43 = 1.45,1.45,1.45,oz\n", + " r14,r24,r34,r44 = 0,0,0,1\n", + " f_mat = [[r11,r12,r13,r14],[r21,r22,r23,r24],[r31,r32,r33,r34],[r41,r42,r43,r44]]\n", + " #print(f_mat)\n", + " #s3=0.5\n", + " eq1 = sym.Eq(d2*c1+d3*c2,ox)#sym.Eq(Function('cos')(s1)*Function('sin')(s2)*s3-Function('sin')(s1)*d2,0.16)#eq1 = sym.Eq((s1**2-1)**0.5*s2*s3-s1*d2,1)\n", + " eq2 = sym.Eq(d2*s1+d3*s2,oy)#sym.Eq(Function('sin')(s1)*Function('sin')(s2)*s3+Function('cos')(s1)*d2,1.05)\n", + " eq3 = sym.Eq(s3,oz)#sym.Eq(Function('cos')(s2)*s3,1.45)\n", + " eq4 = sym.Eq(c1**2+s1**2,1)\n", + " eq5 = sym.Eq(c2**2+s2**2,1)\n", + " result = sym.solve([eq1,eq2,eq3,eq4,eq5],s1,s2,s3,c1,c2)\n", + " print(result[0])\n", + " iq1 = sym.Eq(s2*c4+c2*s4,r21)\n", + " iq2 = sym.Eq(c2*c4+s2*s4,r11)\n", + " result1 = sym.solve([iq1,iq2],[s4,c4])\n", + " #print(result1)\n", + " print(\"Angle4=\"+str(atan(result1.get(s4))))\n", + " (s1,s2,s3,c1,c2)=result[0] #s3,\n", + " return (s1,s2,s3,result1.get(s4),c1,c2,result1.get(c4))\n", + "\n", + "def get_angles(p1,p2):\n", + " (p1s1,p1s2,p1s3,p1s4,p1c1,p1c2,p1c4) = inv_kin(p1[0],p1[1],p1[2])\n", + " (p2s1,p2s2,p2s3,p2s4,p2c1,p2c2,p2c4) = inv_kin(p2[0],p2[1],p2[2])\n", + " p1q1, p1q2 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2))\n", + " p2q1, p2q2 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2))\n", + " u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + " return (p1q1,p1q2,p2q1,p2q2,float(p1s3),float(p2s3))\n", + "# %% Simulation :\n", + "\n", + "t0 = 1\n", + "t1 = 20\n", + "dt = 0.1\n", + "nt = int(t1 / dt ) + 1 # Number of points of sim time\n", + "t = np.linspace( t0 , t1 , nt )\n", + "# u = 3* np.ones( nt )\n", + "#end point 1\n", + "p1 = [0.16,1.05,1.65]\n", + "p2 = [0.63,1.14,1.45]\n", + "(p1q1,p1q2,p2q1,p2q2,p1s3,p2s3) = get_angles(p1,p2)\n", + "# (p1s1,p1s2,p1s3,p1c1,p1c2) = inv_kin(p1[0],p1[1],p1[2])\n", + "# (p2s1,p2s2,p2s3,p2c1,p2c2) = inv_kin(p2[0],p2[1],p2[2])\n", + "# p1q1, p1q2 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2))\n", + "# p2q1, p2q2 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2))\n", + "u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + "v = np.linspace(p1q2,p2q2,nt)\n", + "w = np.linspace(p1s3,p2s3,nt)\n", + "# %% Simulation :\n", + "(t,x)=ct.forced_response(h3,t,u,X0=p1q1)\n", + "(t,y)=ct.forced_response(h3,t,v,X0=p1q2)\n", + "(t,z)=ct.forced_response(h3,t,w,X0=0)#t, y, x = ct.forced_response(h3 , t , u ,0)\n", + "# %% Plotting :\n", + "plt.close( 'all ')\n", + "fig_width_cm = 24\n", + "fig_height_cm = 18\n", + "plt . figure (1 , figsize =( fig_width_cm /2.54 , fig_height_cm /2.54))\n", + "plt . subplot (3 , 1 , 1)\n", + "plt.plot(t , x , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q1' ,))\n", + "plt.subplot(3 , 1 , 2)\n", + "plt.plot(t , y , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q2' ,))\n", + "plt.subplot(3 , 1 , 3)\n", + "plt.plot(t , z , 'blue')\n", + "plt.xlabel( 't [ s ]')\n", + "plt.grid()\n", + "plt.legend( labels =( 'd' ,))\n", + "plt.show()\n", + "#plt . savefig ( ’ sim_tf . pdf ’)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "11. Dynamics and Control of PUMA Manipulator" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(-0.474963330849782, -0.887864517260367, -0.936914622305684, 0.880005587680033, 0.460104986921479, -0.349558279132103)\n", + "Angle4=atan(4.0/(25.0*c2 + 25.0*s2))\n", + "(-0.932157359915714, -0.983400457462024, -0.779685316451944, 0.362053388818509, 0.181448450705654, -0.626171547827935)\n", + "Angle4=atan(4.0/(25.0*c2 + 25.0*s2))\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import control as ct\n", + "import sympy as sym\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "import matplotlib.animation as animation\n", + "import mpl_toolkits.mplot3d.axes3d as p3\n", + "\n", + "jeff,beff,ks = 5,3,1\n", + "kd,kp = 1,0.3\n", + "dyn = ct.tf([1],[jeff,beff])\n", + "stiff = ct.tf([ks],[1])\n", + "h1 = ct.series(stiff,dyn)\n", + "f1 = ct.tf([kd],[1])\n", + "h2 = ct.feedback(h1,f1,sign=-1)\n", + "feed_kp = ct.tf([kp],[1])\n", + "feed_s = ct.tf([1],[1,0])\n", + "h3 = ct.series(feed_kp,h2,feed_s)\n", + "\n", + "def inv_kin(ox,oy,oz):\n", + " s1,s2,s3,s4,s5,s6 = sym.symbols('s1,s2,s3,s4,s5,s6')\n", + " c1,c2,c3,c4,c5,c6 = sym.symbols('c1,c2,c3,c4,c5,c6')\n", + "\n", + " d2,d3,d4 = 1,1,0.5\n", + " q1,q2,q3,q4,q5,q6 = pi/18,pi/18,pi/18,pi/18,pi/18,pi/18\n", + " r11,r21,r31,r41 = 0.16,0.16,0.16,ox\n", + " r12,r22,r32,r42 = 1.05,1.05,1.05,oy\n", + " r13,r23,r33,r43 = 1.45,1.45,1.45,oz\n", + " r14,r24,r34,r44 = 0,0,0,1\n", + " f_mat = [[r11,r12,r13,r14],[r21,r22,r23,r24],[r31,r32,r33,r34],[r41,r42,r43,r44]]\n", + " #print(f_mat)\n", + " #s3=0.5\n", + " eq1 = sym.Eq(c1*(d2*c2+d3*c3 + d4*s3)-d2*s1,ox)#sym.Eq(Function('cos')(s1)*Function('sin')(s2)*s3-Function('sin')(s1)*d2,0.16)#eq1 = sym.Eq((s1**2-1)**0.5*s2*s3-s1*d2,1)\n", + " eq2 = sym.Eq(s1*(d2*c2+d3*c3+d4*s3)+d2*c1,oy)#sym.Eq(Function('sin')(s1)*Function('sin')(s2)*s3+Function('cos')(s1)*d2,1.05)\n", + " eq3 = sym.Eq(d4*c3-d3*s3-d2*s2,oz)#sym.Eq(Function('cos')(s2)*s3,1.45)\n", + " eq4 = sym.Eq(c1**2+s1**2,1)\n", + " eq5 = sym.Eq(c2**2+s2**2,1)\n", + " eq6 = sym.Eq(c3**2+s3**2,1)\n", + " result = sym.solve([eq1,eq2,eq3,eq4,eq5,eq6],s1,s2,s3,c1,c2,c3)\n", + " print(result[0])\n", + " iq1 = sym.Eq(s2*c4+c2*s4,r21)\n", + " iq2 = sym.Eq(c2*c4+s2*s4,r11)\n", + " result1 = sym.solve([iq1,iq2],[s4,c4])\n", + " #print(result1)\n", + " print(\"Angle4=\"+str(atan(result1.get(s4))))\n", + " (s1,s2,s3,c1,c2,c3)=result[0] #s3,\n", + " return (s1,s2,s3,result1.get(s4),c1,c2,c3,result1.get(c4))\n", + "\n", + "def get_angles(p1,p2):\n", + " (p1s1,p1s2,p1s3,p1s4,p1c1,p1c2,p1c3,p1c4) = inv_kin(p1[0],p1[1],p1[2])\n", + " (p2s1,p2s2,p2s3,p2s4,p2c1,p2c2,p2c3,p2c4) = inv_kin(p2[0],p2[1],p2[2])\n", + " p1q1, p1q2,p1q3 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2)), float(atan(p1s3/p1c3))\n", + " p2q1, p2q2,p2q3 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2)), float(atan(p2s3/p2c3))\n", + " u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + " return (p1q1,p1q2,p2q1,p2q2,p1q3,p2q3)\n", + "# %% Simulation :\n", + "\n", + "t0 = 1\n", + "t1 = 20\n", + "dt = 0.1\n", + "nt = int(t1 / dt ) + 1 # Number of points of sim time\n", + "t = np.linspace( t0 , t1 , nt )\n", + "# u = 3* np.ones( nt )\n", + "#end point 1\n", + "p1 = [0.16,1.05,1.65]\n", + "p2 = [0.63,1.14,1.45]\n", + "(p1q1,p1q2,p2q1,p2q2,p1s3,p2s3) = get_angles(p1,p2)\n", + "# (p1s1,p1s2,p1s3,p1c1,p1c2) = inv_kin(p1[0],p1[1],p1[2])\n", + "# (p2s1,p2s2,p2s3,p2c1,p2c2) = inv_kin(p2[0],p2[1],p2[2])\n", + "# p1q1, p1q2 = float(atan(p1s1/p1c1)),float(atan(p1s2/p1c2))\n", + "# p2q1, p2q2 = float(atan(p2s1/p2c1)),float(atan(p2s2/p2c2))\n", + "u = np.linspace(p1q1,p2q1,nt)# u = np.linspace(0,np.pi/6,nt)\n", + "v = np.linspace(p1q2,p2q2,nt)\n", + "w = np.linspace(p1s3,p2s3,nt)\n", + "# %% Simulation :\n", + "(t,x)=ct.forced_response(h3,t,u,X0=p1q1)\n", + "(t,y)=ct.forced_response(h3,t,v,X0=p1q2)\n", + "(t,z)=ct.forced_response(h3,t,w,X0=0)#t, y, x = ct.forced_response(h3 , t , u ,0)\n", + "# %% Plotting :\n", + "plt.close( 'all ')\n", + "fig_width_cm = 24\n", + "fig_height_cm = 18\n", + "plt . figure (1 , figsize =( fig_width_cm /2.54 , fig_height_cm /2.54))\n", + "plt . subplot (3 , 1 , 1)\n", + "plt.plot(t , x , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q1' ,))\n", + "plt.subplot(3 , 1 , 2)\n", + "plt.plot(t , y , 'blue')\n", + "plt . xlabel ( 't [ s ] ')\n", + "plt.grid()\n", + "plt.legend( labels =( 'q2' ,))\n", + "plt.subplot(3 , 1 , 3)\n", + "plt.plot(t , z , 'blue')\n", + "plt.xlabel( 't [ s ]')\n", + "plt.grid()\n", + "plt.legend( labels =( 'd' ,))\n", + "plt.show()\n", + "#plt . savefig ( ’ sim_tf . pdf ’)\n", + "\n", + "x1_arr,y1_arr = cos(x),-sin(x)\n", + "x2_arr,y2_arr = (cos(x)+cos(y)),-(sin(x)+sin(y))\n", + "x3_arr,y3_arr = np.linspace(p1[0],p2[0],nt),np.linspace(p1[1],p2[1],nt)# cos(x)*sin(y)*z - sin(x),sin(x)*sin(y)*z + cos(x)#cos(z),sin(z)\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(\n", + " 111, aspect=\"equal\", autoscale_on=True, xlim=(-2, 2), ylim=(-2, 2)\n", + ")\n", + "# ax = p3.Axes3D(fig)\n", + "ax.grid(alpha=1)\n", + "ax.set_title(\"PUMA Manipulator\")\n", + "ax.set_xticklabels([])\n", + "ax.set_yticklabels([])\n", + "(line, ) = ax.plot(\n", + " [], [], \".-\", lw=1, color=\"#2b8cbe\"\n", + ") \n", + "(line2, ) = ax.plot(\n", + " [], [], \".-\", lw=1, color='green'\n", + ") \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.2 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "570feb405e2e27c949193ac68f46852414290d515b0ba6e5d90d076ed2284471" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/with_Controller1.slx b/with_Controller1.slx new file mode 100644 index 0000000000000000000000000000000000000000..c87e6b002581cb88d7baa15b65d92d64e8c3bbd9 GIT binary patch literal 27342 zcmaI7V{~R+vo;!ZY}>ZeF+1tlww*h+la6iMwr$(CZ6~Lnz0cWaKkqljw?@si##sNV 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z-^c&qLjRHY(P{k;5gPe_5dTL=_%CDokI0Yy<$sWn?}aJ;4>$9VppTy0e?aN)UHdoa zKRIxJM16Fv{(~w&`#(_s=3)Jj`OzHu4>RuFCHa57ybo5a7VRec5p$oV~D KRk!);?Ee91OGyU+ literal 0 HcmV?d00001 From 0d13b04ad29fc9af37889409b7776746c4a34dbd Mon Sep 17 00:00:00 2001 From: avnish31 <112109871+avnish31@users.noreply.github.com> Date: Mon, 21 Nov 2022 18:40:09 +0530 Subject: [PATCH 3/5] Add files via upload final submission --- Task 1 mini project.py | 131 +++++++++++++++++++++++++++++++++++++++++ Task_2 mini project.py | 124 ++++++++++++++++++++++++++++++++++++++ Task_3 mini project.py | 112 +++++++++++++++++++++++++++++++++++ 3 files changed, 367 insertions(+) create mode 100644 Task 1 mini project.py create mode 100644 Task_2 mini project.py create mode 100644 Task_3 mini project.py diff --git a/Task 1 mini project.py b/Task 1 mini project.py new file mode 100644 index 0000000..e5aaffb --- /dev/null +++ b/Task 1 mini project.py @@ -0,0 +1,131 @@ +from turtle import color +import numpy as np +from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign +import matplotlib.pyplot as plt +import matplotlib.animation as animation +l1 = 10 +l2 = 10 +# global path_x,path_y,x2,y2,x1,y1 +# increment = 0.1 # angle incremement +# rot_num = 3 +# angle_minus_last = np.arange(0, rot_num * 2 * pi, increment) +# R_Angles = np.append(angle_minus_last, rot_num * 2 * pi) + +x0 = 0 +y0 = 0 +num=200 +no_points =int(input("enter no. of points:")) +ax_points = np.zeros(no_points,dtype=float) +by_points = np.zeros(no_points,dtype=float) + +x2_arr = np.zeros(200*no_points,dtype=float) #Point 2 +y2_arr = np.zeros(200*no_points,dtype=float) +x2,y2 = 0,0 + +x1,y1 =0,0 +x1_arr = np.zeros(200*no_points,dtype=float) #Point 3 +y1_arr = np.zeros(200*no_points,dtype=float) +for n in range(0,no_points): + coord = input("Enter x,y coordinates of point "+str(n)+":") + ax_points[n]=float(coord.split(",")[0]) + by_points[n]=float(coord.split(",")[1]) + +#Linear interpolation +def lin_inter(ax_points,by_points): + each_point =0 + for i in range(0,num*(no_points-1)): + if i%200==0: + a1,b1 = ax_points[each_point],by_points[each_point] + a2,b2 = ax_points[each_point+1],by_points[each_point+1] + each_point+=1 + x2 = a1 + (a2-a1)*(i%200)/num + y2 = b1 + (b2-b1)*(i%200)/num + x2_arr[i] = x2 + y2_arr[i] = y2 + theta2 = -arccos((x2**2+y2**2-l1**2-l2**2)/(2*l1*l2)) + theta1 = arccos((x2*(l1+l2*cos(theta2))+y2*l2*sin(theta2))/(x2**2 +y2**2)) + #print(theta1*180/3.14) + x1 = l1*cos(theta1) + y1 = l1*sin(theta1) + x1_arr[i]= x1 + y1_arr[i] = y1 + return x1_arr,y1_arr,x2_arr,y2_arr + +#circular Interpolation +def circle_inter(ax_points,by_points,n0p): + count =0 + for n in range (0,n0p-2): + B = [[ax_points[n]**2 - ax_points[n+1]**2 + by_points[n]**2 - by_points[n+1]**2], + [ax_points[n+1]**2 - ax_points[n+2]**2 + by_points[n+1]**2 - by_points[n+2]**2]] + A = [[2*(ax_points[n]-ax_points[n+1]),2*(by_points[n]-by_points[n+1])], + [2*(ax_points[n+1]-ax_points[n+2]),2*(by_points[n+1]-by_points[n+2])]] + a_inv = np.linalg.inv(np.array(A)) + centr_mat = a_inv.dot(np.array(B)) + r_sq = (ax_points[n+1]-centr_mat[0])**2 + (by_points[n+1]-centr_mat[1])**2 + print(centr_mat) + # print((ax_points[2]-ax_points[0])//200) + for i in range(0,200): + xi = ax_points[n] + i*(ax_points[n+1]-ax_points[n])/200 + yi = centr_mat[1] + np.sqrt(r_sq-(xi-centr_mat[0])**2) + if i==0: + xi,yi = ax_points[count],by_points[count] + x2,y2=xi,yi + x2_arr[count*200+i] = x2 + y2_arr[count*200+i] = y2 + theta2 = -arccos((x2**2+y2**2-l1**2-l2**2)/(2*l1*l2)) + theta1 = arccos((x2*(l1+l2*cos(theta2))+y2*l2*sin(theta2))/(x2**2 +y2**2)) + #print(theta1*180/3.14) + x1 = l1*cos(theta1) + y1 = l1*sin(theta1) + x1_arr[count*200+i]= x1 + y1_arr[count*200+i] = y1 + count+=1 + return x1_arr,y1_arr,x2_arr,y2_arr +choice = int(input("Enter 1 for Linear Interpolation and 2 for circular Interpolation :")) +if choice == 1: + x1_arr,y1_arr,x2_arr,y2_arr = lin_inter(ax_points,by_points) +elif choice == 2: + x1_arr,y1_arr,x2_arr,y2_arr = circle_inter(ax_points,by_points,no_points) +else: + print("Valid Choice") +fig = plt.figure() +ax = fig.add_subplot( + 111, aspect="equal", autoscale_on=False, xlim=(-10, 25), ylim=(-10, 25) +) + +# add grid lines, title and take out the axis tick labels +ax.grid(alpha=1) +ax.set_title("Elbow Manipulator") +ax.set_xticklabels([]) +ax.set_yticklabels([]) +(line, ) = ax.plot( + [], [], "o-", lw=7, color="#2b8cbe" +) +(line2, ) = ax.plot( + [], [], ".", lw=2, color='green' +) +# initialization function +def init(): + line.set_data([], []) + return (line,) + +path_x,path_y = [x2_arr[1]],[y2_arr[1]] + +# animation function +def animate(i): + x_points = [x0, x1_arr[i], x2_arr[i]] + y_points = [y0, y1_arr[i], y2_arr[i]] + path_x.append(x2_arr[i]) + path_y.append(y2_arr[i]) + line.set_data(x_points, y_points) + line2.set_data(path_x,path_y) + + return (line,line2,)#line2 +ani = animation.FuncAnimation( + fig, animate, init_func=init, frames=len(x1_arr)-1, interval=40, blit=True, repeat=False +) +## to save animation, uncomment the line below. Ensure ffmpeg is installed: +ani.save('Trajectory_2R.mp4', fps=30, extra_args=['-vcodec', 'libx264']) + +# show the animation +plt.show() diff --git a/Task_2 mini project.py b/Task_2 mini project.py new file mode 100644 index 0000000..335bb46 --- /dev/null +++ b/Task_2 mini project.py @@ -0,0 +1,124 @@ +from turtle import color +import numpy as np +from numpy import sin, cos, sqrt, absolute, arccos, arctan, sign +import matplotlib.pyplot as plt +import matplotlib.animation as animation +l1 = 20 +l2 = 20 +m1,m2 = 0.5,0.5 +a1,a2 = 1,1 + +half_wall = 3 +cent = input("Enter wall position as x,y :") +wx,wy = float(cent.split(",")[0]),float(cent.split(",")[1]) +deg = float(input("Enter orientation in degrees :")) +deg = deg%360 +scale_fact = 0.1 +fn = float(input("Enter normal force :")) +f = fn*scale_fact +wx1,wy1 = wx + half_wall*cos(deg*3.14/180),wy - half_wall*sin(deg*3.14/180) +wx2,wy2 = wx - half_wall*cos(deg*3.14/180),wy + half_wall*sin(deg*3.14/180) +nrx,nry = wx,wy +if np.absolute(wx1)np.absolute(wx2): + nrx,nry = wx2,wy2 +x2,y2 = wx,wy +x2_arr = np.zeros(200) #Point 2 +y2_arr = np.zeros(200) +x1_arr = np.zeros(200) #Point 2 +y1_arr = np.zeros(200) +i0,j0 = 2,2 + +fx0,fy0 = wx,wy +if deg <= 180: + degf = deg+ wx/np.absolute(wx) * 90 +else: + degf = deg- wx/np.absolute(wx) * 90 +#For Torque analysis +# fx,fy = fn*cos(degf*3.14/180),fn*sin(degf*3.14/180) +# tau1,tau2 = -l1*sin(teta1)*fx+l1*cos(teta1)*fy,-l2*sin(teta2)*fx+l2*cos(teta1)*fy + +fx1,fy1 = fx0 + f*cos(degf*3.14/180),fy0 - f*sin(degf*3.14/180) +fx_arr = np.linspace(fx0,fx1, 200) +fy_arr = np.linspace(fy0,fy1, 200) +# teta2 = -arccos((x2**2+y2**2-l1**2-l2**2)/(2*l1*l2)) +# teta1 = arccos((x2*(l1+l2*cos(theta2))+y2*l2*sin(theta2))/(x2**2 +y2**2)) +for i in range(0,200): + if(nrx == wx): + x2 = i0 + (wx-i0)*(i/200) + y2 = j0 + (wy-j0)*(i/200) + else: + if i<100: + x2 = i0 + (nrx-i0)*(i/100) + y2 = j0 + (nry-j0)*(i/100) + else: + x2 = nrx + (wx-nrx)*(i%100/100) + y2 = nry + (wy-nry)*(i%100/100) + x2_arr[i] = x2 + y2_arr[i] = y2 + theta2 = -wx/np.absolute(wx) * arccos((x2**2+y2**2-l1**2-l2**2)/(2*l1*l2)) + theta1 = arccos((x2*(l1+l2*cos(theta2))+y2*l2*sin(theta2))/(x2**2 +y2**2)) + #print(theta1*180/3.14) + x1 = l1*cos(theta1) + y1 = l1*sin(theta1) + x1_arr[i]= x1 + y1_arr[i] = y1 + +fig = plt.figure() +ax = fig.add_subplot( + 111, aspect="equal", autoscale_on=False, xlim=(-20, 20), ylim=(-20, 20) +) + +# add grid lines, title and take out the axis tick labels +ax.grid(alpha=1) +ax.set_title("Elbow Manipulator") +ax.set_xticklabels([]) +ax.set_yticklabels([]) +(line, ) = ax.plot( + [], [], "o-", lw=7, color="#2b8cbe" +) +(line2, ) = ax.plot( + np.linspace(wx1, wx2, 100), np.linspace(wy1,wy2,100), ".", lw=2, color='black' +) +(line3, ) = ax.plot( + [], [], ".-", lw=2, color='red' +) +# initialization function +def init(): + line.set_data([], []) + return (line,) + +path_x,path_y = [],[] + +# animation function +def animate(i): + if i Date: Mon, 21 Nov 2022 18:41:05 +0530 Subject: [PATCH 4/5] Add files via upload final --- Assign_2.ipynb | 191 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 191 insertions(+) create mode 100644 Assign_2.ipynb diff --git a/Assign_2.ipynb b/Assign_2.ipynb new file mode 100644 index 0000000..fef5526 --- /dev/null +++ b/Assign_2.ipynb @@ -0,0 +1,191 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. Postion vector for end effector SCARA." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Position :[10. 0. -3. 1.]\n", + "Jacobian :([[0.0, 10.0, 0.0], [0.0, 5.0, 0.0], [0, 0, 1]], [[0, 0, 1], [0, 0, 1], [0, 0, 1]])\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "import matplotlib.pyplot as plt\n", + "a1,a2 = 5,5\n", + "q = input(\"Enter the joint angles in degrees q1,q2 :\")\n", + "d = float(input(\"Enter extension of end-effector :\"))\n", + "ang1,ang2 = float(q.split(\",\")[0]) , float(q.split(\",\")[1])\n", + "q1,q2 = ang1*3.14/180, ang2*3.14/180\n", + "end_pos = [0,0,0,1]\n", + "theta,alpha,dis,a = 0,0,0,0\n", + "dh = [[cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), cos(theta)*a],\n", + "[sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), sin(theta)*a],\n", + "[0, sin(alpha), cos(alpha),d],\n", + "[0,0,0,1]]\n", + "t = [[cos(q1+q2),sin(q1+q2),0,a1*cos(q1)+a2*cos(q1+q2)],\n", + "[sin(q1+q2),-cos(q1+q2),0,a1*sin(q1)+a2*sin(q1+q2)],\n", + "[0,0,-1,-d],\n", + "[0,0,0,1]]\n", + "res = np.dot(t,end_pos)\n", + "print(\"Position :\" +str(res) )\n", + "z0,z1,z2 =np.array([0,0,1]),np.array([0,0,1]),np.array([0,0,1])\n", + "o,o1,o2,o3 = np.array([0,0,0]),np.array([a1*cos(q1),a1*sin(q1),0]),np.array([a1*cos(q1)+a2*cos(q1+q2),a1*sin(q1)+ a2*sin(q1+q2),0]),np.array([a1*cos(q1)+a2*cos(q1+q2),a1*sin(q1)+ a2*sin(q1+q2),d])\n", + "jacob = [np.transpose(np.cross(z0,o3-o)).tolist(),np.transpose(np.cross(z1,o3-o1)).tolist(),np.transpose(z2).tolist()],[np.transpose(z0).tolist(),np.transpose(z1).tolist(),np.transpose(z2).tolist()]\n", + "print(\"Jacobian :\"+ str(jacob))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. Postion vector for end effector Standford." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0. 0.]\n", + "[0. 0. 0.]\n", + "[0.00000000e+00 2.82887083e-20 3.00000000e+00]\n", + "[0.00000000e+00 2.82887083e-20 3.00000000e+00 1.00000000e+00]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "import matplotlib.pyplot as plt\n", + "a1,a2 = 5,5\n", + "q = input(\"Enter the joint angles in degrees q1,q2 :\")\n", + "d = float(input(\"Enter extension of end-effector :\"))\n", + "ang1,ang2 = float(q.split(\",\")[0]) , float(q.split(\",\")[1])\n", + "q1,q2 = ang1*3.14/180, ang2*3.14/180\n", + "end_pos = [0,0,0,1]\n", + "#theta,alpha,dis,a = 0,0,0,0\n", + "def get_dh(theta,alpha,d,a):\n", + " dh = [[cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), cos(theta)*a],\n", + " [sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), sin(theta)*a],\n", + " [0, sin(alpha), cos(alpha),d],\n", + " [0,0,0,1]]\n", + " return dh\n", + "qs = [q1,q2,0]\n", + "ds = [0,0,d]\n", + "aas = [0,0,0]\n", + "alphas = [-3.14/2,3.14/2,0]\n", + "t = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n", + "z0,z1,z2 =np.array([0,0,1]),np.array([0,0,1]),np.array([0,0,1])\n", + "o = [[],[],[]]\n", + "#t = get_dh(qs[0],alphas[0],ds[0],aas[0])\n", + "#print(t)\n", + "for i in range(0,3):\n", + " #t2 = get_dh(qs[i],alphas[i],ds[i],aas[i])\n", + " t = np.dot(t,get_dh(qs[i],alphas[i],ds[i],aas[i]))\n", + " o[i] = np.dot(t,[0,0,0,1])[0:3]\n", + " #print(o[i])\n", + " #print(t)\n", + "res = np.dot(t,end_pos)\n", + "print(res)\n", + "# print([-cos(q1)*sin(q2)*d, sin(q1)*sin(q2)*d, -cos(q2)*d,1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "8,10. Jacobian Matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jacob :([[-11.156448908138957, 9.335387362109374, 0.0], [-8.657598394923445, 5.004596890082059, 0.0], [-4.328799197461723, 2.5022984450410295, 0.0]], [[0, 0, 1], [0, 0, 1], [0, 0, 1]])\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "\n", + "a1,a2,a3 = 5,5,5\n", + "q = input(\"Enter the joint angles in degrees q1,q2,q3 :\")\n", + "\n", + "ang1,ang2,ang3 = float(q.split(\",\")[0]) , float(q.split(\",\")[1]),float(q.split(\",\")[2])\n", + "q1,q2,q3 = ang1*3.14/180, ang2*3.14/180,ang3*3.14/180\n", + "end_pos = [0,0,0,1]\n", + "#theta,alpha,dis,a = 0,0,0,0\n", + "def get_dh(theta,alpha,d,a):\n", + " dh = [[cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), cos(theta)*a],\n", + " [sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), sin(theta)*a],\n", + " [0, sin(alpha), cos(alpha),d],\n", + " [0,0,0,1]]\n", + " return dh\n", + "qs = [q1,q2,q3]\n", + "ds = [0,0,0]\n", + "aas = [a1,a2,a3]\n", + "alphas = [0,0,0]\n", + "t = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n", + "z0,z1,z2 =np.array([0,0,1]),np.array([0,0,1]),np.array([0,0,1])\n", + "o = [[],[],[]]\n", + "o0 = [0,0,0]\n", + "for i in range(0,3):\n", + " t = np.dot(t,get_dh(qs[i],alphas[i],ds[i],aas[i]))\n", + " o[i] = np.dot(t,[0,0,0,1])[0:3]\n", + "jacob = [np.transpose(np.cross(z0,o[2]-o0)).tolist(),np.transpose(np.cross(z1,o[2]-o[0])).tolist(),np.transpose(np.cross(z1,o[2]-o[1])).tolist()],[np.transpose(z0).tolist(),np.transpose(z1).tolist(),np.transpose(z2).tolist()]\n", + "print(\"Jacob :\" + str(jacob))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.2 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "570feb405e2e27c949193ac68f46852414290d515b0ba6e5d90d076ed2284471" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 88b2dc0b2490cec1f521ed5b02840a5aadb34148 Mon Sep 17 00:00:00 2001 From: avnish31 <112109871+avnish31@users.noreply.github.com> Date: Mon, 21 Nov 2022 18:41:22 +0530 Subject: [PATCH 5/5] Add files via upload final --- Assign_3.ipynb | 228 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 228 insertions(+) create mode 100644 Assign_3.ipynb diff --git a/Assign_3.ipynb b/Assign_3.ipynb new file mode 100644 index 0000000..8ca7073 --- /dev/null +++ b/Assign_3.ipynb @@ -0,0 +1,228 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. DH parameter" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matrix([[sin(01), -sin(01)*cos(a1), sin(01)*sin(a1), a*sin(01)], [sin(01), sin(01)*sin(a1), -sin(01)*sin(a1), a*sin(01)], [0, sin(a1), sin(a1), 0], [0, 0, 0, 1]])\n", + "Matrix([[-sin(01)*sin(02)*cos(a1) + sin(01)*sin(02), -sin(01)*sin(02)*sin(a2)*cos(a1) - sin(01)*sin(02)*cos(a2) + sin(01)*sin(a1)*sin(a2), sin(01)*sin(02)*sin(a2)*cos(a1) + sin(01)*sin(02)*sin(a2) + sin(01)*sin(a1)*sin(a2), -a*sin(01)*sin(02)*cos(a1) + a*sin(01)*sin(02) + a*sin(01)], [sin(01)*sin(02)*sin(a1) + sin(01)*sin(02), sin(01)*sin(02)*sin(a1)*sin(a2) - sin(01)*sin(02)*cos(a2) - sin(01)*sin(a1)*sin(a2), -sin(01)*sin(02)*sin(a1)*sin(a2) + sin(01)*sin(02)*sin(a2) - sin(01)*sin(a1)*sin(a2), a*sin(01)*sin(02)*sin(a1) + a*sin(01)*sin(02) + a*sin(01)], [sin(02)*sin(a1), sin(02)*sin(a1)*sin(a2) + sin(a1)*sin(a2), -sin(02)*sin(a1)*sin(a2) + sin(a1)*sin(a2), a*sin(02)*sin(a1)], [0, 0, 0, 1]])\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "n = int(input(\"Enter the no. of links: \"))\n", + "matr = input(\"Enter the DH Parameters in matrix form eg:-[[alpha1,theta1,d1,a1],[alpha2,theta2,d2,a2]..] :\")\n", + "links = matr.removeprefix(\"[[\").removesuffix(\"]]\").split(\"],[\")\n", + "alphas,thetas,dis,ais = [],[],[],[]\n", + "if len(links) == n:\n", + " for link in links:\n", + " params = link.split(\",\")\n", + " alphas.append(float(params[0]))\n", + " thetas.append(float(params[1]))\n", + " dis.append(float(params[2]))\n", + " ais.append(float(params[3]))\n", + "else:\n", + " print(\"Please mention parameters for all links.\")\n", + "c, s, d, a = symbols('c s d a')\n", + "ident = Matrix([[1, 0, 0, 0],\n", + " [0,1, 0, 0],\n", + " [0, 0, 1,0],\n", + " [0,0,0,1]])\n", + "for i in range(0,n):\n", + " theta = symbols('0'+str(i+1))\n", + " alpha = symbols('a'+str(i+1))\n", + " exp = Matrix([[Function('sin')(theta), -Function('sin')(theta)*Function('cos')(alpha), Function('sin')(theta)*Function('sin')(alpha), Function('sin')(theta)*a],\n", + " [Function('sin')(theta), Function('sin')(theta)*Function('sin')(alpha), -Function('sin')(theta)*Function('sin')(alpha), Function('sin')(theta)*a],\n", + " [0, Function('sin')(alpha), Function('sin')(alpha),dis[i]],\n", + " [0,0,0,1]])\n", + " # exp = Matrix([[Function('sin')(theta), -s*(thetas[i])*c*alphas[i], s*thetas[i]*s*alphas[i], c*thetas[i]*a],\n", + " # [s*thetas[i], c*(thetas[i])*c*alphas[i], -c*thetas[i]*s*alphas[i], s*thetas[i]*a],\n", + " # [0, s*alphas[i], c*alphas[i],dis[i]],\n", + " # [0,0,0,1]])\n", + " ident*= exp\n", + " print(ident)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Jacobian matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.00637061166594731 -3.99999492691016 0]\n", + "[-0.00318530583297366 -1.99999746345508 0 0 0 1]\n", + "End Effector Position = [-3.99999492691016 0.00637061166594731 0]\n", + "Matrix([[-0.00637061166594731, -0.00318530583297366], [-3.99999492691016, -1.99999746345508], [0, 0], [0, 0], [0, 0], [1, 1]])\n", + "Matrix([[-0.0191118349978419], [-11.9999847807305], [0], [0], [0], [4.00000000000000]])\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "\n", + "def get_dh(theta,alpha,d,a):\n", + " dh = Matrix([[cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), cos(theta)*a],\n", + " [sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), sin(theta)*a],\n", + " [0, sin(alpha), cos(alpha),d],\n", + " [0,0,0,1]])\n", + " return dh\n", + "\n", + "n = int(input(\"Enter the no. of links: \"))\n", + "qis = input(\"Enter the joint velocities eg: q1,q2,q3..:\")\n", + "qis_array = []\n", + "for q in qis.split(','):\n", + " qis_array.append(float(q))\n", + "qis_array = Matrix(qis_array)\n", + "matr = input(\"Enter the DH Parameters in matrix form eg:-[[alpha1,theta1,d1,a1],[alpha2,theta2,d2,a2]..] :\")\n", + "links = matr.removeprefix(\"[[\").removesuffix(\"]]\").split(\"],[\")\n", + "alphas,thetas,dis,ais = [],[],[],[]\n", + "ois,z0,o0 = [],np.array([0,0,1]),np.array([0,0,0])\n", + "jacob = []\n", + "if len(links) == n:\n", + " for link in links:\n", + " params = link.split(\",\")\n", + " alphas.append(float(params[0]))\n", + " thetas.append(float(params[1]))\n", + " dis.append(float(params[2]))\n", + " ais.append(float(params[3]))\n", + " t = Matrix([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]])\n", + " for i in range(0,n):\n", + " # t = np.dot(t,get_dh(thetas[i],alphas[i],dis[i],ais[i]))\n", + " t = t*get_dh(thetas[i],alphas[i],dis[i],ais[i])\n", + " ois.append(np.array(t.col(3)[0:3]))\n", + " print(np.cross(z0,ois[n-1]-o0))\n", + " c=0\n", + " jacob.append(np.append(np.cross(z0,ois[n-1]-o0),[0,0,1]))\n", + " for o in ois[0:n-1]:\n", + " c+=1\n", + " jacob.append(np.append(np.cross(z0,ois[n-1]-o),[0,0,1]))\n", + " print(np.append(np.cross(z0,ois[n-1]-o),[0,0,1]))\n", + " print(\"End Effector Position = \"+ str(np.dot(t,[0,0,0,1])[0:3]))\n", + " #print(jacob)\n", + " jacob = Matrix(np.transpose(jacob))\n", + " print(jacob)\n", + " print(jacob*qis_array)\n", + "else:\n", + " print(\"Please mention parameters for all links.\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "11. Derive equations of motion fron D(q) and V(q)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sympy import *\n", + "from numpy import pi, sin, cos, sqrt, absolute, arccos, arctan, sign\n", + "n = int(input(\"Enetr no. of links or D.O.F :\"))\n", + "d = input(\"Enter the D matrix (Use q1,q2... for joint variables and l1,l2... ) eq-[[d11,d12,d13..],[d21,d22,d23..]...]\")\n", + "v = input(\"Enter the values of V (Use q1,q2... for joint variables and l1,l2... ) eg-v0:\")\n", + "q,l,m,mi = [],[],[],[]\n", + "\n", + "for i in range(0,n):\n", + " q[i] = symbols('q'+str(i+1))\n", + " l[i] = symbols('l'+str(i+1))\n", + " m[i] = symbols('m'+str(i+1))\n", + " mi[i] = symbols('mi'+str(i+1))\n", + "rows = d.removeprefix(\"[[\").removesuffix(\"]]\").split(\"],[\")\n", + "arr = []\n", + "#converting str to exp\n", + "for row in rows:\n", + " ele = row.split(\",\")\n", + " r_arr =[]\n", + " for e in ele:\n", + " if e.__contains__('m'):\n", + " e.replace()\n", + " r_arr.append(e)\n", + " arr.append(r_arr)\n", + "\n", + "#hard-coded example \n", + "mat = [[m[0]*l[0]**2/4 + m[1]*l[0]**2+mi[0], m[1]*l[0]*l[1]*Function('cos')(q[0]+q[1])],[m[1]*l[0]*l[1]*Function('cos')(q[0]+q[1]),m[1]*l[1]**2/4+mi[1]]]\n", + "d_mat = Matrix(arr)\n", + "n=2\n", + "ck=[]\n", + "for k in range(0,n):\n", + " c =[]\n", + " for i in range(0,n):\n", + " c_row =[]\n", + " for j in range(0,n):\n", + " exp = mat[k][j]\n", + " c1 = (diff(exp,q[i]))\n", + " exp = mat[k][i]\n", + " c2 = (diff(exp,q[j]))\n", + " exp = mat[i][j]\n", + " c3 = (diff(exp,q[k]))\n", + " c_row.append((c1+c2-c3)/2)\n", + " c.append(c_row)\n", + " ck.append(c)#array of matrices\n", + "\n", + "exp = m[0]*9.81*l[0]*Function('sin')(q[0])\n", + "phi_q =[]\n", + "for i in range(0,n):\n", + " phi_q[i] = diff(exp,q[i])\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3.8.2 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.2" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "570feb405e2e27c949193ac68f46852414290d515b0ba6e5d90d076ed2284471" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}

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