Bipod_Run_v4_thbodlocked_nograv.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "a76235ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset\n",
    "from pyomo.environ import*\n",
    "from pyomo.opt import SolverFactory\n",
    "from pyomo.opt import SolverStatus, TerminationCondition\n",
    "import sympy as sym\n",
    "import numpy as np\n",
    "from IPython.display import display\n",
    "from sympy import pprint\n",
    "\n",
    "import dill\n",
    "dill.load_session('simplified_bipod_thbodlocked_no_xy_final_mark.db')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "6744cb0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "func_map = {'sin':sin, 'cos':cos} \n",
    "\n",
    "sym_list = [g] + [BLD] + [foot_angle] + [foot_length] +\\\n",
    "           [cg] + [lx_boom] + [ly_boom] +\\\n",
    "           [y_boomOffset] + [y_bodyOffset] + [x_footOffset] +\\\n",
    "           [COMR[link,leg] for leg in legs for link in links]+\\\n",
    "           [masses[base] for base in bases] +\\\n",
    "           [masses[link,leg] for leg in legs for link in links] +\\\n",
    "           [lengths[base] for base in bases] +\\\n",
    "           [lengths[link,leg] for leg in legs for link in links] +\\\n",
    "           [inertias['body']] + [inertias['boom','X']] + [inertias['boom','Y']] +\\\n",
    "           [inertias[link,leg] for leg in legs for link in links] +\\\n",
    "           [th[link,leg] for leg in legs for link in links] +\\\n",
    "           [dth[link,leg] for leg in legs for link in links] +\\\n",
    "           [ddth[link,leg] for leg in legs for link in links] +\\\n",
    "           [tau['left',leg] for leg in legs] + [tau['right',leg] for leg in legs] +\\\n",
    "           [lamda['x',leg] for leg in legs] + [lamda['y',leg] for leg in legs] +\\\n",
    "           [GRF['x',leg] for leg in legs] + [GRF['y',leg] for leg in legs]\n",
    "\n",
    "lamb_EOMs = {}\n",
    "\n",
    "DOFs = []\n",
    "\n",
    "for leg in legs:\n",
    "    for link in links:\n",
    "        DOFs = DOFs + ['theta_{0}'.format(link+leg)]\n",
    "\n",
    "# for dof_i,dof in enumerate(DOFs):\n",
    "#     print(dof_i)\n",
    "#    1\n",
    "\n",
    "\n",
    "        \n",
    "# print(len(DOFs))\n",
    "# print(len(EOMs))     \n",
    "for dof_i,dof in enumerate(DOFs):\n",
    "    lamb_EOMs.update({dof: sym.lambdify(sym_list,EOMs[dof_i],modules = [func_map])})\n",
    "# print(EOMs[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "88822ead",
   "metadata": {},
   "outputs": [],
   "source": [
    "# PARAMETERS:\n",
    "\n",
    "COMR_ = {'ULA': 41.14/174.5,\n",
    "         'LLA': 132.2/300,\n",
    "         'URA': 41.14/174.5,\n",
    "         'LRA': 190.4/295.5,\n",
    "         'ULB': 41.14/174.5,\n",
    "         'LLB': 132.2/300,\n",
    "         'URB': 41.14/174.5,         \n",
    "         'LRB': 190.4/295.5}\n",
    "\n",
    "masses_ = {'body': 5756.78/1000,\n",
    "           'boom': 2470.66/1000,\n",
    "           'ULA': 153.81/1000,\n",
    "           'LLA': 346.45/1000,\n",
    "           'URA': 153.81/1000,\n",
    "           'LRA': 499.95/1000,\n",
    "           'ULB': 153.81/1000,\n",
    "           'LLB': 346.45/1000,\n",
    "           'URB': 153.81/1000,\n",
    "           'LRB': 499.95/1000}\n",
    "\n",
    "lengths_ = {'body': 253/1000,\n",
    "            'boom': None,\n",
    "            'ULA': 174.5/1000,\n",
    "            'LLA': 300.0/1000,\n",
    "            'URA': 174.5/1000,\n",
    "            'LRA': 295.5/1000,\n",
    "            'ULB': 174.5/1000,\n",
    "            'LLB': 300.0/1000,\n",
    "            'URB': 174.5/1000,\n",
    "            'LRB': 295.5/1000}\n",
    "\n",
    "''' ****** '''\n",
    "inertias_ = {'body': 32124078.52*1e-9, # body rotate about its center \n",
    "             'boom_X': 1947254622.19*1e-9,\n",
    "             'boom_Y': 1947254622.19*1e-9,\n",
    "             'ULA': 600933.68*1e-9, # rotates as pendulumn\n",
    "             'LLA': 4659658.63*1e-9,\n",
    "             'URA': 600933.68*1e-9,\n",
    "             'LRA': 7369968.50*1e-9,\n",
    "             'ULB': 600933.68*1e-9, # rotates as pendulumn \n",
    "             'LLB': 4659658.63*1e-9,\n",
    "             'URB': 600933.68*1e-9,\n",
    "             'LRB': 7369968.50*1e-9}\n",
    "\n",
    "all_links = []\n",
    "all_links_inertia = []\n",
    "leg_links = []\n",
    "[leg_links.append(link+leg) for leg in legs for link in links]\n",
    "[all_links.append(base) for base in bases]\n",
    "[all_links.append(link+leg) for leg in legs for link in links]\n",
    "all_links_inertia.append('body')\n",
    "all_links_inertia.append('boom_X')\n",
    "all_links_inertia.append('boom_Y')\n",
    "[all_links_inertia.append(link+leg) for leg in legs for link in links]\n",
    "\n",
    "\n",
    "total_mass = 0.0\n",
    "for mass in masses_:\n",
    "    total_mass += masses_[mass]\n",
    "total_mass\n",
    "\n",
    "WDOFs = ['X','Y'] \n",
    "signs = ['-ve','+ve'] \n",
    "ground_constraints = ['contact','friction','slip_+ve','slip_-ve'] # Group all constraints occuring at the ground\n",
    "sides = ['left','right']\n",
    "coordinates = {'X':0 , 'Y':1}\n",
    "motor_w_angle = {'left': 'UL' ,'right': 'UR'}\n",
    "\n",
    "def get_var_list_zeros(m,n):\n",
    "    var_list = [m.g] + [m.BLD] + [m.foot_angle] + [m.foot_length] +\\\n",
    "               [m.cg] + [m.lx_boom] + [m.ly_boom] +\\\n",
    "               [m.y_boomOffset] + [m.y_bodyOffset] + [m.x_footOffset] +\\\n",
    "               [m.COMR[link+leg] for leg in legs for link in links]+\\\n",
    "               [m.masses[base] for base in bases] +\\\n",
    "               [m.masses[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.lengths[base] for base in bases] +\\\n",
    "               [m.lengths[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.inertias['body']] + [m.inertias['boom_X']] + [m.inertias['boom_Y']] +\\\n",
    "               [m.inertias[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.q[n,dof] for dof in DOFs] +\\\n",
    "               [m.dq[n,dof] for dof in DOFs] +\\\n",
    "               [m.ddq[n,dof] for dof in DOFs] +\\\n",
    "               [0 for leg in legs] + [0 for leg in legs] +\\\n",
    "               [0 for leg in legs] + [0 for leg in legs] +\\\n",
    "               [0 for leg in legs] + [0 for leg in legs]\n",
    "    return var_list\n",
    "\n",
    "def get_var_list_values(m,n):\n",
    "    \n",
    "    BW = 1\n",
    "    tau_value = {}\n",
    "    connection_force_value = {}\n",
    "    GRF_X_value = {}\n",
    "    GRF_Y_value = {}\n",
    "    \n",
    "    for leg in legs:\n",
    "        \n",
    "        [tau_value.update({(side,leg): BW*(m.tau_torque[n,side,leg])}) for side in sides]\n",
    "        #[connection_force_value.update({(wdof,leg):BW*(m.connect_force[n,'+ve',wdof,leg]-m.connect_force[n,'-ve',wdof,leg])}) for wdof in WDOFs]\n",
    "        #[connection_force_value.update({(wdof,leg):0.0})for wdof in WDOFs]\n",
    "        [connection_force_value.update({(wdof,leg):BW*(m.connect_force[n,wdof,leg])}) for wdof in WDOFs]\n",
    "        GRF_X_value.update({(leg):0})\n",
    "        GRF_Y_value.update({(leg):0})\n",
    "\n",
    "    var_list = [m.g] + [m.BLD] + [m.foot_angle] + [m.foot_length] +\\\n",
    "               [m.cg] + [m.lx_boom] + [m.ly_boom] +\\\n",
    "               [m.y_boomOffset] + [m.y_bodyOffset] + [m.x_footOffset] +\\\n",
    "               [m.COMR[link+leg] for leg in legs for link in links]+\\\n",
    "               [m.masses[base] for base in bases] +\\\n",
    "               [m.masses[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.lengths[base] for base in bases] +\\\n",
    "               [m.lengths[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.inertias['body']] + [m.inertias['boom_X']] + [m.inertias['boom_Y']] +\\\n",
    "               [m.inertias[link+leg] for leg in legs for link in links] +\\\n",
    "               [m.q[n,dof] for dof in DOFs] +\\\n",
    "               [m.dq[n,dof] for dof in DOFs] +\\\n",
    "               [m.ddq[n,dof] for dof in DOFs] +\\\n",
    "               [tau_value['left',leg] for leg in legs] + [tau_value['right',leg] for leg in legs] +\\\n",
    "               [connection_force_value['X',leg] for leg in legs] + [connection_force_value['Y',leg] for leg in legs] +\\\n",
    "               [GRF_X_value[leg] for leg in legs] + [GRF_Y_value[leg] for leg in legs]\n",
    "    return var_list\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7648c860",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------\n",
      "Stall torque =  140.4238410596027\n",
      "Max speed =  55.8\n",
      "--------------\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Plot Torque Speed Curve'''\n",
    "import matplotlib.pyplot as plt\n",
    "x_p = np.linspace(0, 54, num=54)\n",
    "x_n = np.linspace(-54, 0, num=54)\n",
    "no_load_speed = 55.8\n",
    "# from graph\n",
    "max_torque = 38.0\n",
    "speed_max_torque = 40.7\n",
    "\n",
    "m_grad = (max_torque-0.0)/(speed_max_torque-no_load_speed)\n",
    "\n",
    "stall_torque = 0.0 - m_grad*no_load_speed\n",
    "\n",
    "y_p = m_grad*x_p+stall_torque\n",
    "y_n = m_grad*x_n-stall_torque\n",
    "\n",
    "stall_torque_p = []\n",
    "stall_torque_n = []\n",
    "rated_torque_p = []\n",
    "rated_torque_n = []\n",
    "\n",
    "for ii in range(len(x_p)):\n",
    "    stall_torque_p.append(stall_torque)\n",
    "    stall_torque_n.append(-stall_torque)\n",
    "    rated_torque_p.append(max_torque)\n",
    "    rated_torque_n.append(-max_torque)\n",
    "\n",
    "plt.grid()\n",
    "plt.plot(x_p, y_p,'b')\n",
    "plt.plot(x_n, stall_torque_p,'b')\n",
    "\n",
    "plt.fill_between(x_p, y_p, alpha=0.4, color = 'cyan')\n",
    "plt.fill_between(x_n, stall_torque_p, alpha=0.4,color = 'cyan')\n",
    "\n",
    "plt.plot(x_n, y_n,'r')\n",
    "plt.plot(x_p, stall_torque_n,'r')\n",
    "\n",
    "plt.fill_between(x_n, y_n, alpha=0.4,color = 'pink')\n",
    "plt.fill_between(x_p, stall_torque_n, alpha=0.4,color = 'pink')\n",
    "\n",
    "plt.axis((-60,60,-160,160))\n",
    "plt.title('New Torque Speed Curve')\n",
    "plt.xlabel('Speed (rad/s)')\n",
    "plt.ylabel('Torque (Nm)')\n",
    "print('--------------')\n",
    "\n",
    "print('Stall torque = ',stall_torque)\n",
    "print('Max speed = ',no_load_speed)\n",
    "\n",
    "print('--------------')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "1a4acc84",
   "metadata": {},
   "outputs": [],
   "source": [
    "test = 'Torque_Test'\n",
    "N = 60\n",
    "TT = 0.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "e032aa7a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: DEPRECATED: The default domain for Param objects is 'Any'.  However,\n",
      "    we will be changing that default to 'Reals' in the future.  If you really\n",
      "    intend the domain of this Param (lengths) to be 'Any', you can suppress\n",
      "    this warning by explicitly specifying 'within=Any' to the Param\n",
      "    constructor.  (deprecated in 5.6.9, will be removed in 6.0) (called from\n",
      "    /home/mark/miniconda3/lib/python3.9/site-\n",
      "    packages/pyomo/core/base/param.py:77)\n"
     ]
    }
   ],
   "source": [
    "m = ConcreteModel('Biped')\n",
    "\n",
    "#SETS-------------------------\n",
    "m.N = RangeSet(N)\n",
    "m.ground_constraints = Set(initialize = ground_constraints)\n",
    "m.legs = Set(initialize = legs)\n",
    "m.links = Set(initialize = links)\n",
    "m.bases = Set(initialize = bases)\n",
    "m.all_links = Set(initialize = all_links)\n",
    "m.leg_links = Set(initialize = leg_links)\n",
    "m.all_links_inertia = Set(initialize = all_links_inertia)\n",
    "m.DOFs = Set(initialize = DOFs)\n",
    "m.WDOFs = Set(initialize = WDOFs)\n",
    "m.signs = Set(initialize = signs)\n",
    "m.sides = Set(initialize = sides)\n",
    "\n",
    "#Params--------------------------\n",
    "m.g = Param(initialize = 0.0)\n",
    "m.BLD = Param(initialize = 60/1000)\n",
    "m.foot_angle = Param(initialize = 135*(np.pi/180))\n",
    "m.foot_length = Param(initialize = 42.5/1000)\n",
    "m.cg = Param(initialize = 1.149)\n",
    "m.lx_boom = Param(initialize = 2.575)\n",
    "m.ly_boom = Param(initialize = 2.493)\n",
    "m.y_boomOffset = Param(initialize = 0.101)\n",
    "m.y_bodyOffset = Param(initialize = 8.36/1000)\n",
    "m.x_footOffset = Param(initialize = 1.63/1000)\n",
    "\n",
    "m.COMR = Param(m.leg_links, initialize = COMR_)\n",
    "m.masses = Param(m.all_links, initialize = masses_)\n",
    "m.lengths = Param(m.all_links, initialize = lengths_)\n",
    "m.inertias = Param(m.all_links_inertia, initialize = inertias_)\n",
    "\n",
    "\n",
    "#VARIABLES----------------------\n",
    "#gen coordinates\n",
    "m.q = Var(m.N,m.DOFs)\n",
    "m.dq = Var(m.N,m.DOFs)\n",
    "m.ddq = Var(m.N,m.DOFs)\n",
    "\n",
    "''' CONSTRAINTS  - Integration'''\n",
    "# variable timestep\n",
    "hm = TT/N # master timestep\n",
    "m.h = Var(m.N, bounds = (0.8,1.2)) #m.h = Var(m.N, bounds = (0.5,1.5))\n",
    "\n",
    "def BwEuler_p(m,n,dof):\n",
    "    if n > 1:\n",
    "        return m.q[n,dof] == m.q[n-1,dof] + hm*m.h[n]*m.dq[n,dof]\n",
    "    else:\n",
    "        return Constraint.Skip\n",
    "m.integrate_p = Constraint(m.N, m.DOFs, rule = BwEuler_p)\n",
    "\n",
    "def BwEuler_v(m,n,dof):\n",
    "    if n > 1:\n",
    "        return m.dq[n,dof] == m.dq[n-1,dof] + hm*m.h[n]*m.ddq[n,dof]\n",
    "    else:\n",
    "        return Constraint.Skip \n",
    "m.integrate_v = Constraint(m.N, m.DOFs, rule = BwEuler_v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "a4845a5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "''' CONSTRAINTS  - CONNECTION POINT'''\n",
    "m.connect_position = Var(m.N, m.WDOFs, m.sides, m.legs) # connection point\n",
    "m.connect_force = Var(m.N, m.WDOFs, m.legs,bounds = (-10*total_mass*9.81,10*total_mass*9.81)) # connection force\n",
    "\n",
    "# Lamdify\n",
    "lamb_connect_position = {} # (WDOFs,sides,leg)\n",
    "[lamb_connect_position.update({(wdof,side,leg): sym.lambdify(sym_list,connect_position[side,leg][coordinates[wdof]],modules = [func_map])}) for leg in legs for side in sides for wdof in WDOFs]\n",
    "\n",
    "# Equate the connection equations from the previous script to the model m\n",
    "def def_connect_position_equation(m,n,wdof,side,leg):\n",
    "    var_list = get_var_list_zeros(m,n)    \n",
    "    return m.connect_position[n,wdof,side,leg] == lamb_connect_position[wdof,side,leg](*var_list)\n",
    "m.connect_position_equation = Constraint(m.N, m.WDOFs, m.sides, m.legs, rule = def_connect_position_equation)\n",
    "\n",
    "# Ensure that there is no distance between the X (and Y) of link connection points\n",
    "def def_connect_position(m,n,wdof,leg):\n",
    "    return  m.connect_position[n,wdof,'right',leg] - m.connect_position[n,wdof,'left',leg] == 0.0\n",
    "m.connect_position_constraint = Constraint(m.N, m.WDOFs, m.legs, rule= def_connect_position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "d2ac6d0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Variable of foot position\n",
    "m.foot_position = Var(m.N, m.WDOFs, m.legs)\n",
    "for n in range(1,N+1):\n",
    "    for leg in legs:\n",
    "        m.foot_position[n,'Y',leg].setlb(0.0)\n",
    "\n",
    "#Get the foot position in WDOF\n",
    "lamb_foot_position = {}\n",
    "[lamb_foot_position.update({(wdof,leg): sym.lambdify(sym_list,foot_position['right',leg][coordinates[wdof]],modules = [func_map])}) for leg in legs for wdof in WDOFs]\n",
    "\n",
    "def def_foot_position(m,n,wdof,leg):\n",
    "    var_list = get_var_list_zeros(m,n)\n",
    "    return m.foot_position[n,wdof,leg] == lamb_foot_position[wdof,leg](*var_list)\n",
    "m.def_foot_position = Constraint(m.N, m.WDOFs, m.legs, rule = def_foot_position)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "912e52e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''Torque Speed - Speed Torque Curve'''\n",
    "\n",
    "m.tau_torque = Var(m.N, m.sides, m.legs, bounds = (-max_torque,max_torque))\n",
    "m.tau_velocity = Var(m.N, m.sides, m.legs, bounds = (-no_load_speed,no_load_speed))\n",
    "\n",
    "lamb_tau_velocity = {}\n",
    "[lamb_tau_velocity.update({(side,leg): sym.lambdify(sym_list,w_links[motor_w_angle[side],leg],modules = [func_map])}) for leg in legs for side in sides]\n",
    "\n",
    "def def_angular_velocity(m,n,side,leg):\n",
    "    var_list = get_var_list_zeros(m,n)\n",
    "    return m.tau_velocity[n,side,leg] == lamb_tau_velocity[side,leg](*var_list)\n",
    "m.left_angular_velocity_constraint = Constraint(m.N, m.sides, m.legs, rule = def_angular_velocity)\n",
    "\n",
    "# assume straight line\n",
    "def def_TW_right(m,n,side,leg):\n",
    "    return m.tau_torque[n,side,leg] <= m.tau_velocity[n,side,leg]*m_grad + stall_torque\n",
    "m.TW_right_constraint = Constraint(m.N, m.sides, m.legs, rule = def_TW_right)\n",
    "\n",
    "def def_TW_left(m,n,side,leg):\n",
    "    return m.tau_torque[n,side,leg] >= m.tau_velocity[n,side,leg]*m_grad - stall_torque\n",
    "m.TW_left_constraint = Constraint(m.N, m.sides, m.legs, rule = def_TW_left)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "f3893956",
   "metadata": {},
   "outputs": [],
   "source": [
    "def def_max_change_torque(m,n,side,leg):\n",
    "    if n<(N-1):\n",
    "        return abs(m.tau_torque[n+1,side,leg] - m.tau_torque[n,side,leg]) <= 5 \n",
    "    else:\n",
    "        return abs(m.tau_torque[n,side,leg] - m.tau_torque[n-1,side,leg]) <= 5\n",
    "m.max_change_torque = Constraint(m.N, m.sides, m.legs, rule = def_max_change_torque)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "d7a938a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the angles for the knees - only use this when actuated \n",
    "# This ensures links does not cross\n",
    "m.knee_angle = Var(m.N, m.sides, m.legs, bounds = (0.0,140*(np.pi)/180))\n",
    "\n",
    "def def_knee_angle(m,n,side,leg):\n",
    "    if side == 'left':\n",
    "        return m.knee_angle[n,side,leg] == 2*np.pi - m.q[n,'theta_LL'+leg]\n",
    "    else:\n",
    "        return m.knee_angle[n,side,leg] == m.q[n,'theta_LR'+leg]   \n",
    "m.knee_angle_constraint = Constraint(m.N, m.sides, m.legs, rule = def_knee_angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "58a09f72",
   "metadata": {},
   "outputs": [],
   "source": [
    "#test code\n",
    "\n",
    "sign_symbols = ['+','-']\n",
    "boundaries = ['setub','setlb']\n",
    "\n",
    "# for n in range(1,N+1):\n",
    "#     for leg in legs:\n",
    "#         for index in range(len(boundaries)):\n",
    "#             eval('m.q[n,\\'theta_UL\\'+leg].{0}(np.pi*(0.5{1}1/1.5))'.format(boundaries[index],sign_symbols[index]))\n",
    "#             eval('m.q[n,\\'theta_LL\\'+leg].{0}(np.pi*(1{1}1/2))'.format(boundaries[index],sign_symbols[index]))  \n",
    "#             eval('m.q[n,\\'theta_UR\\'+leg].{0}(np.pi*(0.5{1}1/1.5))'.format(boundaries[index],sign_symbols[index]))    \n",
    "#             eval('m.q[n,\\'theta_LR\\'+leg].{0}(np.pi*(1{1}1/2))'.format(boundaries[index],sign_symbols[index]))\n",
    "\n",
    "\n",
    "for n in range(1,N+1):\n",
    "    if test == 'High_Drop' or test == 'Low_Drop' or test == 'Drop_Hop' or test == 'Hop':\n",
    "        x_low_lim = -1.0\n",
    "        x_high_lim = 1.0\n",
    "        y_low_lim = -0.5\n",
    "        y_high_lim = 2.0\n",
    "        \n",
    "        if test == 'Drop_Hop' or test == 'Hop':\n",
    "            [m.tau_torque[1,side,leg].fix(0.0) for side in sides for leg in legs]\n",
    "        else:\n",
    "            [m.tau_torque[n,side,leg].fix(0.0) for side in sides for leg in legs]\n",
    "            \n",
    "    else:\n",
    "        x_low_lim = -1.0\n",
    "        x_high_lim = 2.0\n",
    "        y_low_lim = -0.5\n",
    "        y_high_lim = 1.5\n",
    "        \n",
    "        if test == 'Sprint' or test == 'Periodic_Walk' or test == 'Periodic_Walk_Stop' or test == 'Start_Periodic_Walk':\n",
    "            pass\n",
    "        else:\n",
    "            [m.tau_torque[1,side,leg].fix(0.0) for side in sides for leg in legs]\n",
    "            \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "372f7e5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# m.foot_position[1, 'X', 'A'].fix(0.0)\n",
    "# m.foot_position[1, 'X', 'B'].fix(0.0)\n",
    "\n",
    "# for n in range(1,N+1):\n",
    "#     m.foot_position[n, 'Y', 'A'].fix(0.6)\n",
    "#     m.foot_position[n, 'Y', 'B'].fix(0.7)\n",
    "\n",
    "m.foot_position[1,'X','A'].fix(0)\n",
    "m.foot_position[1,'Y','A'].fix(0.7)\n",
    "    \n",
    "m.foot_position[1,'X','B'].fix(0)\n",
    "m.foot_position[1,'Y','B'].fix(0.7)\n",
    "\n",
    "m.foot_position[15,'X','A'].fix(0.1)\n",
    "m.foot_position[15,'X','B'].fix(-0.1)\n",
    "\n",
    "\n",
    "m.foot_position[30,'X','A'].fix(0)\n",
    "m.foot_position[30,'Y','A'].setub(0.6)\n",
    "    \n",
    "m.foot_position[30,'X','B'].fix(0)\n",
    "m.foot_position[30,'Y','B'].setub(0.6)\n",
    "    \n",
    "m.foot_position[45,'X','A'].fix(-0.1)\n",
    "m.foot_position[45,'X','B'].fix(0.1)\n",
    "    \n",
    "m.foot_position[N,'X','A'].fix(0)\n",
    "m.foot_position[N,'Y','A'].fix(0.7)\n",
    "    \n",
    "m.foot_position[N,'X','B'].fix(0)\n",
    "m.foot_position[N,'Y','B'].fix(0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "0b53951b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# COST FUNCTION -------------------------------------------------------------------------------------------------------------\n",
    "def CostFun(m):\n",
    "    row = 1e4 # scale the penalty\n",
    "    tau_sum = 0.0\n",
    "    pen_sum = 0.0\n",
    "    transport_sum = 0.0\n",
    "    tau_diff = 0.0\n",
    "   \n",
    "    \n",
    "    T = sum(m.h[n] for n in range(1,N+1))\n",
    "    \n",
    "    for n in range(1,N+1):\n",
    "        for leg in legs:\n",
    "            for side in sides:\n",
    "                tau_sum += (m.tau_torque[n,side,leg])**2\n",
    "#                 tau_diff = sum(diff(m.tau_torque[n,side,leg]))\n",
    "#                 if n<N:\n",
    "#                     tau_diff += (m.tau_torque[n+1,side,leg] - m.tau_torque[n,side,leg])**2\n",
    "                \n",
    "\n",
    "    return tau_sum #+ tau_diff\n",
    "m.Cost = Objective(rule = CostFun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "18ba8f8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "''' Turning EOM back to pyomo (from sympy) '''\n",
    "#create the constraints\n",
    "\n",
    "\n",
    "def EOM_th_ULA(m,n):\n",
    "    var_list = get_var_list_values(m,n)\n",
    "    return lamb_EOMs['theta_ULA'](*var_list) == 0\n",
    "m.EOM_th_ULA_constraint = Constraint(m.N, rule = EOM_th_ULA)\n",
    "\n",
    "def EOM_th_LLA(m,n):\n",
    "    var_list = get_var_list_values(m,n)\n",
    "    return lamb_EOMs['theta_LLA'](*var_list) == 0\n",
    "m.EOM_th_LLA_constraint = Constraint(m.N, rule = EOM_th_LLA)\n",
    "\n",
    "def EOM_th_URA(m,n):\n",
    "    var_list = get_var_list_values(m,n)   \n",
    "    return lamb_EOMs['theta_URA'](*var_list) == 0\n",
    "m.EOM_th_URA_constraint = Constraint(m.N, rule = EOM_th_URA)\n",
    "\n",
    "def EOM_th_LRA(m,n):\n",
    "    var_list = get_var_list_values(m,n)    \n",
    "    return lamb_EOMs['theta_LRA'](*var_list) == 0\n",
    "m.EOM_th_LRA_constraint = Constraint(m.N, rule = EOM_th_LRA)\n",
    "\n",
    "def EOM_th_ULB(m,n):\n",
    "    var_list = get_var_list_values(m,n)\n",
    "    return lamb_EOMs['theta_ULB'](*var_list) == 0\n",
    "m.EOM_th_ULB_constraint = Constraint(m.N, rule = EOM_th_ULB)\n",
    "\n",
    "def EOM_th_LLB(m,n):\n",
    "    var_list = get_var_list_values(m,n)\n",
    "    return lamb_EOMs['theta_LLB'](*var_list) == 0\n",
    "m.EOM_th_LLB_constraint = Constraint(m.N, rule = EOM_th_LLB)\n",
    "\n",
    "def EOM_th_URB(m,n):\n",
    "    var_list = get_var_list_values(m,n)   \n",
    "    return lamb_EOMs['theta_URB'](*var_list) == 0\n",
    "m.EOM_th_URB_constraint = Constraint(m.N, rule = EOM_th_URB)\n",
    "\n",
    "def EOM_th_LRB(m,n):\n",
    "    var_list = get_var_list_values(m,n)    \n",
    "    return lamb_EOMs['theta_LRB'](*var_list) == 0\n",
    "m.EOM_th_LRB_constraint = Constraint(m.N, rule = EOM_th_LRB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "212b52d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ipopt 3.14.10: linear_solver=ma86\n",
      "expect_infeasible_problem=yes\n",
      "print_level=5\n",
      "max_iter=600000\n",
      "max_cpu_time=12000\n",
      "Tol=1e-06\n",
      "\n",
      "\n",
      "******************************************************************************\n",
      "This program contains Ipopt, a library for large-scale nonlinear optimization.\n",
      " Ipopt is released as open source code under the Eclipse Public License (EPL).\n",
      "         For more information visit https://github.com/coin-or/Ipopt\n",
      "******************************************************************************\n",
      "\n",
      "This is Ipopt version 3.14.10, running with linear solver ma86.\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:    11198\n",
      "Number of nonzeros in inequality constraint Jacobian.:     1428\n",
      "Number of nonzeros in Lagrangian Hessian.............:     4772\n",
      "\n",
      "Total number of variables............................:     3161\n",
      "                     variables with only lower bounds:      114\n",
      "                variables with lower and upper bounds:     1017\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:     2864\n",
      "Total number of inequality constraints...............:      720\n",
      "        inequality constraints with only lower bounds:        0\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:      720\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  0.0000000e+00 6.27e+00 1.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  1.3708271e-01 1.27e+00 1.42e+07  -1.0 5.85e+01    -  9.96e-03 8.52e-01f  1\n",
      "   2  6.6311208e-01 1.19e+00 6.95e+07  -1.0 1.19e+02   4.0 1.40e-02 4.59e-02h  1\n",
      "   3r 6.6311208e-01 1.19e+00 9.99e+02   0.1 0.00e+00   4.4 0.00e+00 0.00e+00R  1\n",
      "   4r 5.3520885e-01 6.32e-01 9.95e+02   0.1 1.03e+04    -  8.14e-03 1.08e-03f  1\n",
      "   5r 5.1592959e-01 3.16e-01 9.89e+02   0.1 2.84e+03    -  9.01e-03 5.79e-03f  1\n",
      "   6r 4.3558920e-01 3.14e-01 9.86e+02   0.1 2.75e+02    -  4.46e-02 4.63e-03f  1\n",
      "   7r 3.6718048e-01 3.10e-01 9.78e+02   0.1 2.35e+02    -  4.45e-02 8.05e-03f  1\n",
      "   8r 3.1350868e-01 3.93e-01 9.70e+02   0.1 1.56e+02   0.0 7.22e-03 8.03e-03f  1\n",
      "   9r 3.4564978e-01 3.96e-01 9.40e+02   0.1 8.15e+01  -0.5 6.14e-02 3.06e-02f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10r 4.5885828e-01 4.08e+00 9.29e+02   0.1 2.78e+03    -  3.48e-04 5.86e-02f  1\n",
      "  11r 7.4429667e-01 4.12e+00 9.27e+02   0.1 5.89e+02  -1.0 7.74e-03 5.06e-03f  1\n",
      "  12r 1.1596060e+00 4.14e+00 9.14e+02   0.1 8.75e+02  -1.4 1.09e-02 2.61e-03f  1\n",
      "  13r 7.9256394e-01 3.77e+00 8.01e+02   0.1 4.33e+02    -  1.26e-01 9.31e-02f  1\n",
      "  14r 9.5392926e-01 3.62e+00 1.58e+03   0.1 8.96e+02    -  2.30e-01 6.55e-02f  1\n",
      "  15r 9.0805310e-01 3.32e+00 1.21e+03   0.1 3.35e+02    -  6.96e-03 1.04e-01f  1\n",
      "  16r 5.5776669e-01 2.44e+00 8.94e+02   0.1 1.13e+02    -  2.49e-01 2.60e-01f  1\n",
      "  17r 4.6185243e-01 2.02e+00 7.33e+02   0.1 1.17e+02    -  3.06e-01 1.69e-01f  1\n",
      "  18r 1.0074791e+00 1.64e+00 5.73e+02   0.1 1.46e+01  -0.1 1.06e-01 2.15e-01f  1\n",
      "  19r 1.0421116e+00 1.55e+00 7.54e+02   0.1 1.08e+02    -  2.05e-01 5.46e-02f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20r 1.0579253e+00 1.34e+00 6.76e+02   0.1 8.54e+01    -  6.23e-01 1.40e-01f  1\n",
      "  21r 7.5694139e-01 7.90e-01 6.85e+02   0.1 6.36e+01    -  1.00e+00 4.27e-01f  1\n",
      "  22r 7.2153448e-01 2.07e-01 5.36e+00   0.1 3.80e+01    -  1.00e+00 1.00e+00f  1\n",
      "  23r 8.3078385e-01 1.12e-01 2.20e+00  -1.3 7.59e+00    -  8.70e-01 8.82e-01f  1\n",
      "  24r 4.7075689e-01 9.68e-02 1.29e+02  -2.0 2.40e+01    -  3.42e-01 5.49e-01f  1\n",
      "  25r 4.7549410e-01 9.63e-02 3.80e+01  -2.0 6.09e-01  -0.6 4.32e-01 2.26e-01f  1\n",
      "  26r 4.8424191e-01 9.69e-02 9.34e+01  -2.0 1.55e+00  -1.1 3.14e-01 1.39e-01f  1\n",
      "  27r 4.9276799e-01 9.68e-02 8.85e+01  -2.0 6.13e-01  -0.6 3.44e-01 2.71e-01f  1\n",
      "  28r 5.0023986e-01 9.66e-02 8.33e+01  -2.0 2.58e+00  -1.1 1.35e-01 8.98e-02f  1\n",
      "  29r 5.0197753e-01 9.64e-02 8.17e+01  -2.0 1.28e+02  -1.6 3.67e-03 2.64e-03f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30r 5.1306685e-01 9.62e-02 7.46e+01  -2.0 1.93e+00  -1.2 1.84e-01 1.24e-01f  1\n",
      "  31r 5.1667980e-01 9.61e-02 6.98e+01  -2.0 3.09e+01  -1.6 1.75e-02 1.02e-02f  1\n",
      "  32r 5.3170876e-01 9.58e-02 6.93e+01  -2.0 2.24e+00  -1.2 1.69e-01 1.24e-01f  1\n",
      "  33r 5.5537311e-01 9.56e-02 7.52e+01  -2.0 7.15e-01  -0.8 5.15e-01 3.95e-01f  1\n",
      "  34r 5.6681060e-01 9.56e-02 1.14e+02  -2.0 2.64e+00  -1.3 1.45e-01 7.01e-02f  1\n",
      "  35r 5.9161039e-01 9.56e-02 2.09e+02  -2.0 1.36e+02    -  2.53e-01 1.55e-02f  1\n",
      "  36r 7.3889275e-01 9.46e-02 8.89e+02  -2.0 5.49e+01    -  1.00e+00 8.02e-02f  1\n",
      "  37r 5.6931495e+00 8.59e-02 2.25e+01  -2.0 3.53e+01    -  1.00e+00 1.00e+00f  1\n",
      "  38r 5.7722792e+00 8.60e-02 2.33e+02  -2.0 1.02e+01    -  1.00e+00 1.96e-01f  1\n",
      "  39r 6.1098827e+00 8.62e-02 1.05e-01  -2.0 7.78e+00    -  1.00e+00 1.00e+00f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  40r 6.1470170e+00 8.62e-02 1.60e+01  -3.0 6.41e-01    -  1.00e+00 9.31e-01f  1\n",
      "  41r 2.2713363e+01 8.18e-02 1.79e+02  -3.0 2.65e+02    -  1.57e-01 2.37e-01f  1\n",
      "  42r 4.8527149e+01 1.15e-01 1.22e+02  -3.0 1.73e+02    -  3.54e-01 3.44e-01f  1\n",
      "  43r 5.3227262e+01 1.06e-01 4.95e+02  -3.0 9.64e+01    -  5.17e-01 9.17e-02f  1\n",
      "  44r 5.3305850e+01 1.06e-01 2.72e+02  -3.0 8.56e+01    -  3.45e-01 2.62e-03h  1\n",
      "  45r 5.5984721e+01 9.62e-02 4.07e+02  -3.0 8.51e+01    -  3.82e-01 9.00e-02f  1\n",
      "  46r 5.8891044e+01 8.57e-02 2.48e+02  -3.0 7.47e+01    -  8.43e-01 1.09e-01f  1\n",
      "  47r 5.8931524e+01 8.55e-02 4.24e+02  -3.0 3.54e+01    -  8.26e-01 2.67e-03h  1\n",
      "  48r 6.0072132e+01 7.70e-02 2.93e+02  -3.0 2.56e+01    -  1.00e+00 9.87e-02f  1\n",
      "  49r 6.0948638e+01 5.86e-02 1.76e+02  -3.0 6.29e+00    -  1.00e+00 3.68e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  50r 6.0859927e+01 5.54e-02 2.57e-01  -3.0 4.25e+00    -  1.00e+00 1.00e+00f  1\n",
      "  51r 6.0873307e+01 5.54e-02 3.73e-04  -3.0 1.66e-01    -  1.00e+00 1.00e+00h  1\n",
      "  52r 6.0874356e+01 5.54e-02 5.46e+00  -4.5 3.88e-01    -  9.82e-01 9.40e-01f  1\n",
      "  53r 6.2179623e+01 4.24e-02 8.20e+01  -4.5 2.03e+02    -  1.85e-01 1.18e-01f  1\n",
      "  54r 6.3009738e+01 3.88e-02 7.65e+02  -4.5 1.76e+02    -  5.88e-01 3.79e-02f  1\n",
      "  55r 6.3164820e+01 3.82e-02 7.91e+02  -4.5 1.68e+02    -  7.87e-02 6.55e-03f  1\n",
      "  56r 6.3330665e+01 3.76e-02 9.37e+02  -4.5 1.67e+02    -  4.63e-01 6.90e-03f  1\n",
      "  57r 6.8839862e+01 2.39e-02 8.00e+02  -4.5 1.65e+02    -  4.64e-05 1.53e-01f  1\n",
      "  58r 7.2321894e+01 2.19e-02 7.11e+02  -4.5 1.36e+02    -  3.70e-01 7.49e-02f  1\n",
      "  59r 7.2326689e+01 2.19e-02 6.20e+02  -4.5 1.36e+02    -  1.00e+00 2.18e-04h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  60r 7.8014546e+01 1.86e-02 4.70e+02  -4.5 1.25e+02    -  1.51e-01 2.44e-01f  1\n",
      "  61r 7.8871160e+01 1.81e-02 4.46e+02  -4.5 1.02e+02    -  1.00e+00 3.49e-02f  1\n",
      "  62r 7.8851594e+01 1.75e-02 4.17e+02  -4.5 1.66e+01    -  1.00e+00 2.85e-02h  1\n",
      "  63r 7.9137742e+01 1.05e-02 2.39e+02  -4.5 1.49e+01    -  1.00e+00 4.04e-01h  1\n",
      "  64r 7.9391039e+01 5.40e-03 1.21e+02  -4.5 8.27e+00    -  1.00e+00 4.83e-01h  1\n",
      "  65r 7.9692397e+01 9.21e-06 3.03e-02  -4.5 4.10e+00    -  1.00e+00 1.00e+00h  1\n",
      "  66  8.6386097e+01 3.25e-01 3.25e+02  -1.0 2.04e+02    -  4.93e-01 1.00e+00f  1\n",
      "  67  6.0366759e+01 4.28e-02 2.54e+01  -1.0 7.89e+01    -  8.96e-01 1.00e+00f  1\n",
      "  68  5.9932400e+01 6.67e-02 2.56e+01  -1.0 8.02e+01    -  5.23e-01 1.00e+00f  1\n",
      "  69  5.6873996e+01 3.64e-02 4.05e+00  -1.0 6.01e+01    -  8.30e-01 8.40e-01f  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  70  5.6103791e+01 1.14e-02 7.94e-02  -1.0 1.48e+02    -  1.00e+00 1.00e+00h  1\n",
      "  71  5.1743477e+01 9.35e-03 2.60e+00  -2.5 3.57e+01    -  9.40e-01 1.00e+00f  1\n",
      "  72  5.0995125e+01 1.13e-01 6.21e-03  -2.5 3.70e+02    -  1.00e+00 1.00e+00h  1\n",
      "  73  5.0979601e+01 2.90e-06 6.65e-06  -2.5 7.60e+02    -  1.00e+00 1.00e+00H  1\n",
      "  74  5.0818079e+01 1.44e-05 1.76e-04  -3.8 1.38e+00    -  1.00e+00 1.00e+00f  1\n",
      "  75  5.0808007e+01 5.90e-08 6.74e-07  -5.7 9.09e-02    -  1.00e+00 1.00e+00h  1\n",
      "  76  5.0807896e+01 6.72e-10 8.14e-11  -7.0 2.54e-02    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 76\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   5.0807896171734178e+01    5.0807896171734178e+01\n",
      "Dual infeasibility......:   8.1446072108803946e-11    8.1446072108803946e-11\n",
      "Constraint violation....:   6.7197714059830105e-10    6.7197714059830105e-10\n",
      "Variable bound violation:   8.0511627364998617e-09    8.0511627364998617e-09\n",
      "Complementarity.........:   9.0959223393250639e-08    9.0959223393250639e-08\n",
      "Overall NLP error.......:   9.0959223393250639e-08    9.0959223393250639e-08\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 78\n",
      "Number of objective gradient evaluations             = 15\n",
      "Number of equality constraint evaluations            = 78\n",
      "Number of inequality constraint evaluations          = 78\n",
      "Number of equality constraint Jacobian evaluations   = 77\n",
      "Number of inequality constraint Jacobian evaluations = 77\n",
      "Number of Lagrangian Hessian evaluations             = 76\n",
      "Total seconds in IPOPT                               = 21.524\n",
      "\n",
      "EXIT: Optimal Solution Found.\n"
     ]
    }
   ],
   "source": [
    "# solving\n",
    "#opt = SolverFactory('ipopt',executable = '/home/uct/Trajectory_Optimization/IPOPT/build/bin/ipopt')\n",
    "opt = SolverFactory('ipopt')\n",
    "opt.options[\"linear_solver\"] = 'ma86'\n",
    "\n",
    "# solver options\n",
    "opt.options[\"expect_infeasible_problem\"] = 'yes'\n",
    "#pt.options[\"linear_system_scaling\"] = 'none'\n",
    "#opt.options[\"mu_strategy\"] = \"adaptive\"\n",
    "opt.options[\"print_level\"] = 5     # prints a log with each iteration (you want to this - it's the only way to see progress.)\n",
    "opt.options[\"max_iter\"] = 30000*20   # maximum number of iterations\n",
    "opt.options[\"max_cpu_time\"] = 600*20 # maximum cpu time in seconds\n",
    "opt.options[\"Tol\"] = 1e-6          # the tolerance for feasibility. Considers constraints satisfied when they're within this margin.\n",
    "\n",
    "results = opt.solve(m, tee = True)\n",
    "\n",
    "# model.piston_complementarity.deactivate()\n",
    "# result = default_solver('/usr/local/bin/ipopt', approximate_hessian=False).solve(model, tee=True)\n",
    "# if result.solver.termination_condition != TerminationCondition.optimal: quit()\n",
    "# # solve for discrete piston control3\n",
    "# model.piston_complementarity.activate()\n",
    "# result = default_solver('/usr/local/bin/ipopt', approximate_hessian=False, warm_start=True).solve(model, tee=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "a2dbf94e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal\n"
     ]
    }
   ],
   "source": [
    "print(results.solver.termination_condition) # check if optimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "800c8acf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "15693749",
   "metadata": {},
   "outputs": [],
   "source": [
    "# tau_sum = 0.0\n",
    "# for n in range(1,N+1):\n",
    "#     for leg in legs:\n",
    "#         for side in sides:\n",
    "#             tau_sum += (m.tau_torque[n,side,leg])**2\n",
    "# print(tau_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "82ced369",
   "metadata": {},
   "outputs": [
    {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#animate it\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as ani\n",
    "from IPython.display import HTML\n",
    "%matplotlib inline\n",
    "\n",
    "fig1, ax1 = plt.subplots(1,1) #create axes\n",
    "ax1.set_aspect('equal')\n",
    "\n",
    "# arrays to store values\n",
    "N_time = []\n",
    "\n",
    "def plot_robot(i,m,ax): #update function for animation\n",
    "    ax.clear()\n",
    "    ax.set_xlim([x_low_lim,x_high_lim])\n",
    "    ax.set_ylim([y_low_lim,y_high_lim])\n",
    "    N_time.append(i)\n",
    "     \n",
    "    plot_body = {}\n",
    "    plot_boom = {}\n",
    "    plot_boom_COM = {}\n",
    "    plot_UR = {}\n",
    "    plot_LR = {}\n",
    "    plot_UL = {}\n",
    "    plot_LL = {}\n",
    "    plot_foot = {}\n",
    "    abs_angles = {}\n",
    "    bod_angle = 0\n",
    "    \n",
    "    # plot body\n",
    "    plot_body.update({('x_back'):0 - 0.5*m.lengths['body']*cos(bod_angle)})\n",
    "    plot_body.update({('y_back'):1 - m.y_bodyOffset.value - 0.5*m.lengths['body']*sin(bod_angle)})\n",
    "    plot_body.update({('x_front'):0 + 0.5*m.lengths['body']*cos(bod_angle)})\n",
    "    plot_body.update({('y_front'):1 - m.y_bodyOffset.value + 0.5*m.lengths['body']*sin(bod_angle)})  \n",
    "    ax.plot([plot_body['x_back'],plot_body['x_front']],[plot_body['y_back'],plot_body['y_front']],color='xkcd:green')\n",
    "    \n",
    "    # plot boom\n",
    "    plot_boom.update({('x_back'): 0.0})\n",
    "    plot_boom.update({('y_back'): m.y_bodyOffset.value})\n",
    "    plot_boom.update({('x_front'):0 })\n",
    "    plot_boom.update({('y_front'):1 })  \n",
    "    ax.plot([plot_boom['x_back'],plot_boom['x_front']],[plot_boom['y_back'],plot_boom['y_front']],color='xkcd:black')\n",
    "\n",
    "    # plot boom COM\n",
    "    plot_boom_COM.update({('x'): (m.cg.value/m.lx_boom.value)*0})\n",
    "    plot_boom_COM.update({('y'): (m.cg.value/m.ly_boom.value)*1})\n",
    "    ax.plot([plot_boom_COM['x']],[plot_boom_COM['y']],color='xkcd:purple',marker=\"o\")\n",
    "\n",
    "    for leg in legs:\n",
    "        if leg == 'A':\n",
    "            link_colour = ['blue','red']\n",
    "        else:\n",
    "            link_colour = ['green','purple']\n",
    "        \n",
    "        \n",
    "        #plot upper right\n",
    "        abs_angles.update({('RU',leg): bod_angle + m.q[i,'theta_UR'+leg].value})\n",
    "        plot_UR.update({('top','X',leg): 0 + m.BLD.value*cos(bod_angle)})\n",
    "        plot_UR.update({('top','Y',leg): 1 - m.y_bodyOffset.value + m.BLD.value*sin(bod_angle)})\n",
    "        plot_UR.update({('bot','X',leg): plot_UR['top','X',leg] - m.lengths['UR'+leg]*cos(abs_angles['RU',leg])})\n",
    "        plot_UR.update({('bot','Y',leg): plot_UR['top','Y',leg] - m.lengths['UR'+leg]*sin(abs_angles['RU',leg])})\n",
    "        ax.plot([plot_UR['top','X',leg],plot_UR['bot','X',leg]],[plot_UR['top','Y',leg],plot_UR['bot','Y',leg]],color='xkcd:{0}'.format(link_colour[0]))\n",
    "        \n",
    "        #plot lower right\n",
    "        abs_angles.update({('RL',leg): m.q[i,'theta_LR'+leg].value - (np.pi-abs_angles['RU',leg])})\n",
    "        plot_LR.update({('top','X',leg): plot_UR['bot','X',leg]})\n",
    "        plot_LR.update({('top','Y',leg): plot_UR['bot','Y',leg]})\n",
    "        plot_LR.update({('bot','X',leg): plot_UR['bot','X',leg] - m.lengths['LR'+leg]*cos(abs_angles['RL',leg])})\n",
    "        plot_LR.update({('bot','Y',leg): plot_UR['bot','Y',leg] - m.lengths['LR'+leg]*sin(abs_angles['RL',leg])})\n",
    "        ax.plot([plot_LR['top','X',leg],plot_LR['bot','X',leg]],[plot_LR['top','Y',leg],plot_LR['bot','Y',leg]],color='xkcd:{0}'.format(link_colour[0]))\n",
    "        \n",
    "        #plot foot\n",
    "        plot_foot.update({('top','X',leg): plot_LR['bot','X',leg]})\n",
    "        plot_foot.update({('top','Y',leg): plot_LR['bot','Y',leg]})\n",
    "        plot_foot.update({('bot','X',leg): plot_LR['bot','X',leg] + m.foot_length.value*cos(m.foot_angle.value - (np.pi)/2)})\n",
    "        plot_foot.update({('bot','Y',leg): plot_LR['bot','Y',leg] - m.foot_length.value*sin(m.foot_angle.value - (np.pi)/2)})\n",
    "        ax.plot([plot_foot['top','X',leg],plot_foot['bot','X',leg]],[plot_foot['top','Y',leg],plot_foot['bot','Y',leg]],color='xkcd:{0}'.format(link_colour[0]))\n",
    "\n",
    "        #plot upper left\n",
    "        abs_angles.update({('LU',leg): bod_angle + m.q[i,'theta_UL'+leg].value})\n",
    "        plot_UL.update({('top','X',leg): 0 - m.BLD.value*cos(bod_angle)})\n",
    "        plot_UL.update({('top','Y',leg): 1 - m.y_bodyOffset.value - m.BLD.value*sin(bod_angle)})\n",
    "        plot_UL.update({('bot','X',leg): plot_UL['top','X',leg] - m.lengths['UL'+leg]*cos(abs_angles['LU',leg])})\n",
    "        plot_UL.update({('bot','Y',leg): plot_UL['top','Y',leg]- m.lengths['UL'+leg]*sin(abs_angles['LU',leg])})\n",
    "        ax.plot([plot_UL['top','X',leg],plot_UL['bot','X',leg]],[plot_UL['top','Y',leg],plot_UL['bot','Y',leg]],color='xkcd:{0}'.format(link_colour[0]))\n",
    "\n",
    "        #plot lower left\n",
    "        abs_angles.update({('LL',leg):m.q[i,'theta_LL'+leg].value - (np.pi-abs_angles['LU',leg])})\n",
    "        plot_LL.update({('top','X',leg): plot_UL['bot','X',leg]})\n",
    "        plot_LL.update({('top','Y',leg): plot_UL['bot','Y',leg]})\n",
    "        plot_LL.update({('bot','X',leg): plot_UL['bot','X',leg] - m.lengths['LL'+leg]*cos(abs_angles['LL',leg])})\n",
    "        plot_LL.update({('bot','Y',leg): plot_UL['bot','Y',leg] - m.lengths['LL'+leg]*sin(abs_angles['LL',leg])})\n",
    "        ax.plot([plot_LL['top','X',leg],plot_LL['bot','X',leg]],[plot_LL['top','Y',leg],plot_LL['bot','Y',leg]],color='xkcd:{0}'.format(link_colour[0]))     \n",
    "    \n",
    " \n",
    "\n",
    "    \n",
    "    ax.legend([\"Body\",\"GRF*0.01\"], frameon=True)\n",
    "    \n",
    "    ax.plot([-10,10],[0,0]) # plot the ground\n",
    "    \n",
    "    \n",
    "update = lambda i: plot_robot(i,m,ax1) # lambdify update function\n",
    "\n",
    "animate = ani.FuncAnimation(fig1,update,range(1,N+1),interval = 50,repeat=True)\n",
    "\n",
    "HTML(animate.to_html5_video()) #you need to convert the animation to HTML5 to embed it in the notebook\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "986d9a54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8d32847340>"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,61,1)\n",
    "LeftA = []\n",
    "RightA = []\n",
    "LeftB = []\n",
    "RightB = []\n",
    "\n",
    "for n in range(1,N+1):\n",
    "    LeftA.append(m.tau_torque[n,'left','A'].value)\n",
    "    RightA.append(m.tau_torque[n,'right','A'].value)\n",
    "    LeftB.append(m.tau_torque[n,'left','B'].value)\n",
    "    RightB.append(m.tau_torque[n,'right','B'].value)\n",
    "    \n",
    "line1 = plt.plot(x,LeftA,label = 'A Left')\n",
    "line2 = plt.plot(x,LeftB,label = 'A Right')\n",
    "line3 = plt.plot(x,RightA,label = 'B Left')\n",
    "line4 = plt.plot(x,RightB,label = 'B Right')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "a0b8026e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.18723857983241957"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.tau_torque[5,'left','A'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "130388ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-12.345799144241422"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.q[1,'theta_ULA'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "6493c22f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # abs(m.tau_torque[25,'right','B'].value-m.tau_torque[24,'right','B'].value)#<=10\n",
    "# for n in range(1,N+1):\n",
    "#     if n<N:\n",
    "#         print(abs(m.tau_torque[n+1,'right','B'].value-m.tau_torque[n,'right','B'].value))\n",
    "    \n",
    "# # np.diff(m.tau_torque[n,'left','A'] for n in range(1,N+1)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "6d370031",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['leftA', 'rightA', 'leftB', 'rightB']\n",
      "0.0 0.0 0.0 0.0\n",
      "-1.5372283633353351e-10 -1.5507669140968098e-10 1.0236941230284517e-10 1.92508255379613e-10\n",
      "-0.06088453370839028 -0.0728875780745018 0.054932097870932825 0.0787191280550894\n",
      "-0.12342582470560425 -0.1422501860895296 0.10390863116143448 0.1565653815523342\n",
      "-0.18723857983241957 -0.20784660683640313 0.14717498180042082 0.23376990141104356\n",
      "-0.2520036764470313 -0.2695181517573444 0.18507746803802 0.3106405179461697\n",
      "-0.3174761225597158 -0.3272066301865624 0.21805172104138135 0.3875392107602565\n",
      "-0.3834848305466469 -0.3809638971503406 0.24661123449324335 0.46485500764806886\n",
      "-0.4499258176025719 -0.43095329291489026 0.27133868160683217 0.5429715495264261\n",
      "-0.5167505205458818 -0.47744427001460127 0.2928813844210778 0.6222281376795421\n",
      "-0.5839507924190755 -0.5208020579785092 0.3119510426134382 0.7028733852804873\n",
      "-0.6515419461321359 -0.5614743126825843 0.32932662047642314 0.7850120718442989\n",
      "-0.7195450004947699 -0.5999764182288859 0.3458583158323794 0.8685488929751075\n",
      "-0.7879690984062686 -0.6368765928458857 0.36247002367697906 0.9531375699711311\n",
      "-0.8567948999343957 -0.6727813400187517 0.3801578872549537 1.0381492728563957\n",
      "-0.9259595505000168 -0.7083211810580318 0.39998337537874484 1.1226779170683083\n",
      "-0.8574047579475782 -0.6516565430157739 0.3592562303915143 1.0571782373817444\n",
      "-0.7914931005636995 -0.5955018159921215 0.3208014414984388 0.990292476448197\n",
      "-0.7281656531134089 -0.539411226401091 0.283913855434902 0.9220784690610978\n",
      "-0.6674234557931668 -0.48301508952279937 0.2479295912250446 0.8527911479591426\n",
      "-0.6093140498157203 -0.4260120948444757 0.21222751215004823 0.7828170178708643\n",
      "-0.5539185903166697 -0.3681602853311672 0.17623294470317796 0.7126095390392793\n",
      "-0.5013395513369079 -0.3092672390082206 0.13942282815740992 0.6426337932854135\n",
      "-0.4516889545145312 -0.24918003079007686 0.1013312678647031 0.5733253075212851\n",
      "-0.4050770429858756 -0.18777566385913042 0.061554412137541474 0.5050641057527246\n",
      "-0.36160134469921795 -0.12495276566186655 0.019753735396187237 0.43816211434154756\n",
      "-0.32133611038041177 -0.060625422193352825 -0.02434286050776621 0.3728604387840678\n",
      "-0.2843221635860981 0.0052799434107458736 -0.07094233417433772 0.30933265742616456\n",
      "-0.25055726342093587 0.07282378140590742 -0.12019006270607217 0.2476907354316303\n",
      "-0.21998715844500236 0.14204800296322823 -0.17217533704001217 0.18799101235754917\n",
      "-0.19249760315184267 0.21296557050980408 -0.22693837021184426 0.13023862644281248\n",
      "-0.150840178878557 0.2572656438022656 -0.25072176912418254 0.07711320804668823\n",
      "-0.11097617476495562 0.30325955327643195 -0.27686645814901073 0.024994829603944137\n",
      "-0.07280043092966512 0.3508921707651362 -0.3053730014795008 -0.02615822787392438\n",
      "-0.03616983687935053 0.40007175055620564 -0.33621545437439826 -0.07640852353553573\n",
      "-0.0009006859446773211 0.4506654040584104 -0.36934653344195856 -0.125838506978262\n",
      "0.03323326778748455 0.5024962893311913 -0.4047027661432732 -0.17455138932264863\n",
      "0.06650218554529427 0.5553443080197131 -0.4422094930713277 -0.22267345374223732\n",
      "0.09922114924407054 0.6089521412665617 -0.48178563118437884 -0.2703573883439076\n",
      "0.1317510221707315 0.66303802848995 -0.5233481240516508 -0.3177862049594841\n",
      "0.1644993695207077 0.7173157099160119 -0.5668160002016303 -0.36517728535021626\n",
      "0.19792157930021492 0.7715205132733185 -0.6121139240535758 -0.41278605232067395\n",
      "0.23252226115113803 0.8254389948530247 -0.6591750440663778 -0.46090867556849924\n",
      "0.26885699253603157 0.8789383294660296 -0.7079428051673176 -0.5098830652602232\n",
      "0.30753453730034763 0.9319912283441104 -0.7583711792492744 -0.5600871518859716\n",
      "0.34921967191548664 0.984692707047624 -0.8104224382251813 -0.611933054933688\n",
      "0.3363633619752936 0.9176097308577993 -0.753220225476311 -0.5855680985450212\n",
      "0.3244308359447319 0.8502764224677306 -0.6964149092619969 -0.5585351201676048\n",
      "0.31276005208343266 0.7831406127336961 -0.6399950064638755 -0.5303546900802967\n",
      "0.30071825054701934 0.716492183526516 -0.5839366138324158 -0.5005783369696378\n",
      "0.2877048360012725 0.6504753968967314 -0.5282130658446701 -0.4687990491224469\n",
      "0.27315237375771434 0.5851106889719445 -0.4728052422768139 -0.43466280767489507\n",
      "0.25652731935076667 0.5203204552151867 -0.41771197194906035 -0.39788030249094436\n",
      "0.23733204181986275 0.4559552782666057 -0.36295986810766484 -0.35823756875592844\n",
      "0.21510931973192596 0.39181867653456753 -0.30861184800277996 -0.31560402343113003\n",
      "0.18944986124702604 0.32768956131347066 -0.2547735208692496 -0.26993636252399195\n",
      "0.16000261106880784 0.26334219957935495 -0.2015965938070685 -0.2212770725870471\n",
      "0.1264867433059782 0.19856368938516689 -0.14927846712920387 -0.16974690238617415\n",
      "0.08870352963929151 0.13316899368649737 -0.09805741107129998 -0.11553154243092738\n",
      "0.046545392141445395 0.0670130604637219 -0.048202673736101355 -0.058863304519514055\n"
     ]
    }
   ],
   "source": [
    "print(['leftA','rightA','leftB','rightB'])\n",
    "for n in range(1,N+1):\n",
    "    print(m.tau_torque[n,'left','A'].value,m.tau_torque[n,'right','A'].value,m.tau_torque[n,'left','B'].value,m.tau_torque[n,'right','B'].value)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "56f3f7e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8d2067ba00>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,N+1,1)\n",
    "LeftA = []\n",
    "RightA = []\n",
    "LeftB = []\n",
    "RightB = []\n",
    "\n",
    "for n in range(1,N+1):\n",
    "    LeftA.append(m.knee_angle[n,'left','A'].value*180/np.pi)\n",
    "    RightA.append(m.knee_angle[n,'right','A'].value*180/np.pi)\n",
    "    LeftB.append(m.knee_angle[n,'left','B'].value*180/np.pi)\n",
    "    RightB.append(m.knee_angle[n,'right','B'].value*180/np.pi)\n",
    "    \n",
    "line1 = plt.plot(x,LeftA,label = 'A Left')\n",
    "line2 = plt.plot(x,LeftB,label = 'A Right')\n",
    "line3 = plt.plot(x,RightA,label = 'B Left')\n",
    "line4 = plt.plot(x,RightB,label = 'B Right')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "5d2ba65f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8d20a24220>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(1,N+1,1)\n",
    "\n",
    "bGRFy = []\n",
    "bFootPos = []\n",
    "aGRFy = []\n",
    "aFootPos = []\n",
    "footScale = 1\n",
    "\n",
    "for n in range(1,N+1):\n",
    "#     bGRFy.append(m.GRF_y[n,'B'].value)\n",
    "    bFootPos.append(m.foot_position[n,'Y','B'].value*footScale)\n",
    "#     aGRFy.append(m.GRF_y[n,'A'].value)\n",
    "    aFootPos.append(m.foot_position[n,'Y','A'].value*footScale)\n",
    "\n",
    "# bGRFyline = plt.plot(x,bGRFy,label = 'B GRFy')\n",
    "bFootline = plt.plot(x,bFootPos,label = 'B Foot Pos (y)')\n",
    "# aGRFyline = plt.plot(x,aGRFy,label = 'A GRFy')\n",
    "aFootline = plt.plot(x,aFootPos,label = 'A Foot Pos (y)')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "20ac3be3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for n in range(1,N+1):\n",
    "#     print(m.GRF_y[n,'B'].value,m.foot_position[n,'X','B'].value,m.q[n,'y_body'].value)\n",
    "# # m.dq[N,'x_body'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "c8740966",
   "metadata": {},
   "outputs": [],
   "source": [
    "# guide"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "463c8ec3",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "e626f53b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6049134072246334\n",
      "2.6444153124757315\n",
      "2.681574153826649\n",
      "2.7157801403199575\n",
      "2.7465103890972173\n",
      "2.773333311841733\n",
      "2.795908401928379\n",
      "2.81398148936631\n",
      "2.827375955109195\n",
      "2.83598068237066\n",
      "2.8397356494802577\n",
      "2.8386160545677313\n",
      "2.832615750811533\n",
      "2.821730615575856\n",
      "2.8059423267301957\n",
      "2.785202911206804\n",
      "2.760049820830303\n",
      "2.7309576872828583\n",
      "2.6983547673563915\n",
      "2.6626367525426904\n",
      "2.624178125279472\n",
      "2.5833413528136044\n",
      "2.54048427921077\n",
      "2.4959661132324533\n",
      "2.450152415604755\n",
      "2.403419461631599\n",
      "2.356158290846502\n",
      "2.3087786508189123\n",
      "2.2617128943825895\n",
      "2.215419698137465\n",
      "2.170387241817047\n",
      "2.1269000700911667\n",
      "2.0852701322075644\n",
      "2.045836759550962\n",
      "2.0089654063892013\n",
      "1.9750448347149243\n",
      "1.944482499355578\n",
      "1.9176980762460483\n",
      "1.8951153839303725\n",
      "1.8771533487863294\n",
      "1.864217085010492\n",
      "1.856690489613353\n",
      "1.8549318722724628\n",
      "1.8592739726893495\n",
      "1.8700292695798293\n",
      "1.887500851606167\n",
      "1.9111661284497803\n",
      "1.9405311963442236\n",
      "1.9751421181219788\n",
      "2.0145894492153094\n",
      "2.058507117665661\n",
      "2.106566935634925\n",
      "2.1584699247049652\n",
      "2.21393543364334\n",
      "2.2726888184864675\n",
      "2.3344482921380485\n",
      "2.3989114473879423\n",
      "2.4657419028797367\n",
      "2.534556494580372\n",
      "2.604913407224634\n"
     ]
    }
   ],
   "source": [
    "for n in range(1,N+1):\n",
    "    print(m.q[n,'theta_URA'].value+2*np.pi)\n",
    "#m.foot_position[2,'X','B'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "58e08b3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "thULA = []\n",
    "thURA = []\n",
    "thULB = []\n",
    "thURB = []\n",
    "dthULA = []\n",
    "dthURA = []\n",
    "dthULB = []\n",
    "dthURB = []\n",
    "LeftA = []\n",
    "RightA = []\n",
    "LeftB = []\n",
    "RightB = []\n",
    "\n",
    "for n in range(1,N+1):\n",
    "    thULA.append(m.q[n,'theta_ULA'].value)\n",
    "    thURA.append(m.q[n,'theta_URA'].value)\n",
    "    thULB.append(m.q[n,'theta_ULB'].value)\n",
    "    thURB.append(m.q[n,'theta_URB'].value)\n",
    "    dthULA.append(m.dq[n,'theta_ULA'].value)\n",
    "    dthURA.append(m.dq[n,'theta_URA'].value)\n",
    "    dthULB.append(m.dq[n,'theta_ULB'].value)\n",
    "    dthURB.append(m.dq[n,'theta_URB'].value)\n",
    "    LeftA.append(m.tau_torque[n,'left','A'].value)\n",
    "    RightA.append(m.tau_torque[n,'right','A'].value)\n",
    "    LeftB.append(m.tau_torque[n,'left','B'].value)\n",
    "    RightB.append(m.tau_torque[n,'right','B'].value)\n",
    "    \n",
    "#     print(m.q[n,'theta_ULA'].value)\n",
    "# position_data = {'thULA':thULA,'thURA':thURA,'thULB':thULB,'thURB':thURB}\n",
    "# with open('position_data_test1.pkl','wb') as f:\n",
    "#     pickle.dump(position_data, f)\n",
    "# print(position_data['thULA'])\n",
    "heading0 = ['node']\n",
    "heading1 = ['thULA','thURA','thULB','thURB','dthULA','dthURA','dthULB','dthURB','tLeftA','tRightA','tLeftB','tRightB']\n",
    "heading = heading0+heading1\n",
    "import csv\n",
    "with open('torque_test4.csv','w') as f:\n",
    "    writer = csv.writer(f)\n",
    "    writer.writerow(heading)\n",
    "    for n in range(N):\n",
    "        node = [n]\n",
    "        data1 = [thULA[n],thURA[n],thULB[n],thURB[n],dthULA[n],dthURA[n],dthULB[n],dthURB[n],LeftA[n],RightA[n],LeftB[n],RightB[n]]\n",
    "        data = node+data1\n",
    "        writer.writerow(data)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92174121",
   "metadata": {},
   "outputs": [],
   "source": [
    "TT\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80da3a71",
   "metadata": {},
   "outputs": [],
   "source": [
    "# m.dq[1,'theta_URA'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf755fe9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for n in range(1,N+1):\n",
    "#     print(m.q[n,'y_body'].value)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7e8eb9c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#m.dq[N,'y_body'].value\n",
    "V_avg"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7336db3f",
   "metadata": {},
   "source": [
    "<!-- 1.4=72cm\n",
    "x=45cm -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6ac0cbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# m.foot_position[N,'Y','B'].value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b02b07c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# save1 = False\n",
    "# if save1 == True:\n",
    "#     data =  {'ybod' : m.q[N,'y_body'].value,\n",
    "#         'dxbod' : m.dq[N,'x_body'].value,\n",
    "#         'dthULA' : m.dq[N,'theta_ULA'].value,\n",
    "#         'dthLLA' : m.dq[N,'theta_LLA'].value,\n",
    "#         'dthURA' : m.dq[N,'theta_URA'].value,\n",
    "#         'dthLRA' : m.dq[N,'theta_LRA'].value,\n",
    "\n",
    "#         'dthULB' : m.dq[N,'theta_ULB'].value,\n",
    "#         'dthLLB' : m.dq[N,'theta_LLB'].value,\n",
    "#         'dthURB' : m.dq[N,'theta_URB'].value,\n",
    "#         'dthLRB' : m.dq[N,'theta_LRB'].value}\n",
    "#     with open('periodic_walk_start_v7.pkl', 'wb') as f: \n",
    "#         pickle.dump(data, f)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "314da3ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "save2 = False\n",
    "if save2 == True:\n",
    "    data =  {'ybod' : m.q[1,'y_body'].value,\n",
    "             'dybod' : m.dq[1,'y_body'].value,\n",
    "        'dxbod' : m.dq[1,'x_body'].value,\n",
    "             \n",
    "        'thULA' : m.q[1,'theta_ULA'].value,\n",
    "        'thLLA' : m.q[1,'theta_LLA'].value,\n",
    "        'thURA' : m.q[1,'theta_URA'].value,\n",
    "        'thLRA' : m.q[1,'theta_LRA'].value,\n",
    "\n",
    "        'thULB' : m.q[1,'theta_ULB'].value,\n",
    "        'thLLB' : m.q[1,'theta_LLB'].value,\n",
    "        'thURB' : m.q[1,'theta_URB'].value,\n",
    "        'thLRB' : m.q[1,'theta_LRB'].value,\n",
    "             \n",
    "             \n",
    "        'dthULA' : m.dq[1,'theta_ULA'].value,\n",
    "        'dthLLA' : m.dq[1,'theta_LLA'].value,\n",
    "        'dthURA' : m.dq[1,'theta_URA'].value,\n",
    "        'dthLRA' : m.dq[1,'theta_LRA'].value,\n",
    "\n",
    "        'dthULB' : m.dq[1,'theta_ULB'].value,\n",
    "        'dthLLB' : m.dq[1,'theta_LLB'].value,\n",
    "        'dthURB' : m.dq[1,'theta_URB'].value,\n",
    "        'dthLRB' : m.dq[1,'theta_LRB'].value}\n",
    "    with open('periodic_walk_N1_data_v10.pkl', 'wb') as f: \n",
    "        pickle.dump(data, f)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "64021090",
   "metadata": {},
   "outputs": [],
   "source": [
    "save2 = False\n",
    "if save2 == True:\n",
    "    data =  {'ybod' : m.q[N,'y_body'].value,\n",
    "             'dybod' : m.dq[N,'y_body'].value,\n",
    "        'dxbod' : m.dq[N,'x_body'].value,\n",
    "             \n",
    "        'thULA' : m.q[N,'theta_ULA'].value,\n",
    "        'thLLA' : m.q[N,'theta_LLA'].value,\n",
    "        'thURA' : m.q[N,'theta_URA'].value,\n",
    "        'thLRA' : m.q[N,'theta_LRA'].value,\n",
    "\n",
    "        'thULB' : m.q[N,'theta_ULB'].value,\n",
    "        'thLLB' : m.q[N,'theta_LLB'].value,\n",
    "        'thURB' : m.q[N,'theta_URB'].value,\n",
    "        'thLRB' : m.q[N,'theta_LRB'].value,\n",
    "             \n",
    "             \n",
    "        'dthULA' : m.dq[N,'theta_ULA'].value,\n",
    "        'dthLLA' : m.dq[N,'theta_LLA'].value,\n",
    "        'dthURA' : m.dq[N,'theta_URA'].value,\n",
    "        'dthLRA' : m.dq[N,'theta_LRA'].value,\n",
    "\n",
    "        'dthULB' : m.dq[N,'theta_ULB'].value,\n",
    "        'dthLLB' : m.dq[N,'theta_LLB'].value,\n",
    "        'dthURB' : m.dq[N,'theta_URB'].value,\n",
    "        'dthLRB' : m.dq[N,'theta_LRB'].value}\n",
    "    with open('periodic_walk_finalN_data_v10.pkl', 'wb') as f: \n",
    "        pickle.dump(data, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c4a79ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for n in range(1,N+1):\n",
    "#     print(m.knee_angle[n,'left','B'].value*180/np.pi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee0e8c3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# with open('periodic_walk_start_v.pkl','rb') as f:\n",
    "#     start = pickle.load(f)\n",
    "# start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "582834a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# start[0]['xbod']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d1cc54b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "34295717",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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