Local_FiveBar_Collocation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import casadi\n",
    "import numpy as np\n",
    "from utils.Lagrange import *\n",
    "from utils.LGL_collocation import LGL_collocation\n",
    "from utils.LocalChart import *\n",
    "import pinocchio as pin\n",
    "from pinocchio import casadi as cpin\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation, PillowWriter\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ntp = 50   # Number of collocation points / basis each phase (degree: Ntp-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ngc = 5\n",
    "nhc = 3\n",
    "ndof = ngc-nhc\n",
    "\n",
    "Lbase = 0.12\n",
    "Ldistal = 0.15\n",
    "Lproximal = 0.2\n",
    "mdistal = 0.8925\n",
    "mproximal = 1.2093\n",
    "\n",
    "Loffset = np.array([0, Lproximal, Ldistal, Ldistal, Lproximal])\n",
    "\n",
    "mass = np.array([mproximal, mdistal, mdistal, mproximal])\n",
    "Lcm = np.array([0.11, 0.0746, Ldistal-0.0746, Lproximal-0.11])\n",
    "Iz = np.array([7, 2.3, 2.3, 7])*1e-3\n",
    "\n",
    "inertia = [None]*ngc\n",
    "for i in range(ngc-1):\n",
    "    inertia[i] = pin.Inertia(mass[i], np.array([Lcm[i], 0.0, 0.0]), np.diag([0, Iz[i], Iz[i]])) # mass, com, inertia\n",
    "\n",
    "\n",
    "FiveBar = pin.Model()\n",
    "joint_id = 0  # Root\n",
    "\n",
    "for i in range(ngc):\n",
    "    joint_type = pin.JointModelRY()    # Define joint type (Revolute joint around Y-axis)\n",
    "    '''Add joint to the model'''\n",
    "    # joint_index = model.addJoint(parent_frame, joint_type, child_frame, joint name)\n",
    "    joint_id = FiveBar.addJoint(joint_id, joint_type, pin.SE3(np.eye(3), np.array([Loffset[i],0,0])), f'joint {i+1}')\n",
    "    '''Append body to the joint'''\n",
    "    # body_id = model.appendBodyToJoint(joint_id, inertia, joint_placement)\n",
    "    if i < ngc-1:\n",
    "        body_id = FiveBar.appendBodyToJoint(joint_id, inertia[i], pin.SE3.Identity())\n",
    "\n",
    "data = FiveBar.createData()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J_holonomic:(i0[5])->(o0[3x5,13nz]) SXFunction\n"
     ]
    }
   ],
   "source": [
    "q = casadi.SX.sym(\"q\", ngc, 1)\n",
    "dq = casadi.SX.sym(\"dq\", ngc, 1)\n",
    "\n",
    "# kinematic loop\n",
    "q1_ = q[0]\n",
    "q2_ = q1_+q[1]\n",
    "q3_ = q2_+q[2]\n",
    "q4_ = q3_+q[3]\n",
    "q5_ = q4_+q[4]\n",
    "\n",
    "F_q = [ Lproximal*np.cos(q1_) + Ldistal*np.cos(q2_) + Ldistal*np.cos(q3_) + Lproximal*np.cos(q4_) + Lbase,\n",
    "        Lproximal*np.sin(q1_) + Ldistal*np.sin(q2_) + Ldistal*np.sin(q3_) + Lproximal*np.sin(q4_),\n",
    "        np.sin(q5_) ]\n",
    "Fq = casadi.vertcat(*F_q)\n",
    "Jq = casadi.jacobian(Fq, q)\n",
    "# J(q) @ ddq = x(q,dq) = -dJ(q)/dt @ dq\n",
    "dJq_dt = casadi.jtimes(Jq, q, dq)   # shape = (nhc, ngc)\n",
    "F_holonomic = casadi.Function(\"F_holonomic\", [q], [Fq])\n",
    "J_holonomic = casadi.Function(\"J_holonomic\", [q], [Jq])\n",
    "\n",
    "print(J_holonomic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ConstrAcc:(i0[5],i1[5],i2[2])->(o0[10]) SXFunction\n"
     ]
    }
   ],
   "source": [
    "# open-chain dynamics\n",
    "cmodel = cpin.Model(FiveBar)\n",
    "cdata = cmodel.createData()\n",
    "\n",
    "# Mass matrix\n",
    "M = cpin.crba(cmodel, cdata, q)\n",
    "# Coriolis\n",
    "C = cpin.computeCoriolisMatrix(cmodel, cdata, q, dq)\n",
    "# Gravity\n",
    "G = cpin.computeGeneralizedGravity(cmodel, cdata, q)\n",
    "\n",
    "ConstrDyn = casadi.vertcat(casadi.horzcat(M, Jq.T), casadi.horzcat(Jq, casadi.DM.zeros(nhc, nhc)))\n",
    "\n",
    "u = casadi.SX.sym(\"u\", ndof, 1)             # control input\n",
    "uc = casadi.vertcat(*[u[0],0,0,0,u[-1]])    # number of active joints = ndof\n",
    "Tau = uc - C @ dq - G  \n",
    "\n",
    "'''\n",
    "un = casadi.SX.sym(\"un\", ngc, 1)\n",
    "F_Acc = casadi.Function(\n",
    "    \"F_Acc\",\n",
    "    [q, dq, un],\n",
    "    [casadi.vertcat(dq,\n",
    "                    cpin.aba(cmodel, cdata, q, dq, un))]\n",
    ")\n",
    "'''\n",
    "\n",
    "F_ConstrAcc = casadi.Function(\n",
    "    \"ConstrAcc\", \n",
    "    [q, dq, u], \n",
    "    [\n",
    "        casadi.vertcat(dq, \n",
    "                       casadi.horzcat(np.eye(ngc), np.zeros((ngc, nhc))) @ casadi.inv(ConstrDyn) @ casadi.vertcat(Tau, -dJq_dt@dq))\n",
    "    ]\n",
    ")\n",
    "\n",
    "print(F_ConstrAcc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Parameterization (Tangent Chart)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "LOCALCHART = LocalChart(ngc, nhc, ndof, J_holonomic)\n",
    "q_manifold_to_local, dq_manifold_to_local, dq_local_to_manifold, ddq_local_to_manifold = LOCALCHART.getFuncs()\n",
    "F_LocalAcc = LOCALCHART.F_LocalAcc(F_ConstrAcc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gauss–Legendre Collocation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "LGL_Pts, LGL_Wts = Normalize_LGL_Pts_Wts(Ntp)\n",
    "DL,_ = differentiation_matrix(Ntp, LGL_Pts)\n",
    "\n",
    "LGL = LGL_collocation(Ntp, ngc, ndof)\n",
    "StatesDiff, StateDiff, LocalsDiff, LocalDiff= LGL.getDiffFuncs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "lowerPositionLimit = -2*np.pi * np.ones((ngc))  # rad\n",
    "upperPositionLimit = 2*np.pi * np.ones((ngc))   # rad\n",
    "lowerVelocityLimit = -np.pi/2 * np.ones((ngc))  # rad/s\n",
    "upperVelocityLimit = np.pi/2 * np.ones((ngc))\n",
    "lowerTorqueLimit  = -5 * np.ones((ndof))\n",
    "upperTorqueLimit  = 5 * np.ones((ndof))\n",
    "\n",
    "q_waypoints = np.array([[1.3919,0.7860,1.9008,0.7278,1.4766], \n",
    "                        [2.0851,-0.6221,3.5712,-0.7617,2.0107],\n",
    "                        [2.6021,-0.5985,4.0018,-1.4423,1.7201]])\n",
    "\n",
    "Np = q_waypoints.shape[0]-1       # Number of phase (dersired waypoints: N+1)\n",
    "T = Np*Ntp   # Number of total collocation points / optimization variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Initial Guesses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[DM([0, 0]), DM([0, 0]), DM([0.97005, -0.0481143])]\n",
      "[array([-1.16032013, -0.90533559]), array([-1.15599666, -0.90145092]), array([-1.14584668, -0.89233339]), array([-1.12995076, -0.87806074]), array([-1.1083848 , -0.85870926]), array([-1.08124901, -0.83437926]), array([-1.04866737, -0.805194  ]), array([-1.01078612, -0.77129755]), array([-0.96777235, -0.73285267]), array([-0.9198126 , -0.69003858]), array([-0.86711179, -0.64304896]), array([-0.80989248, -0.59209014]), array([-0.74839447, -0.5373795 ]), array([-0.68287472, -0.47914405]), array([-0.61360771, -0.41761912]), array([-0.54088598, -0.35304701]), array([-0.46502105, -0.28567538]), array([-0.38634467, -0.21575521]), array([-0.30521041, -0.14353796]), array([-0.22199602, -0.06927141]), array([-0.13710688,  0.00680651]), array([-0.05098148,  0.08447709]), array([0.03589937, 0.1635556 ]), array([0.12299654, 0.2439153 ]), array([0.20968362, 0.32552842]), array([0.29519176, 0.40854044]), array([0.37849857, 0.49341522]), array([0.45808513, 0.58124572]), array([0.5313414 , 0.67450609]), array([0.59285328, 0.77920662]), array([0.62803455, 0.91288857]), array([0.57526498, 1.15212769]), array([-0.77205161,  3.00991302]), array([1.52145275, 0.29415024]), array([1.33528421, 0.68242155]), array([1.33742766, 0.82716866]), array([1.37689656, 0.91729846]), array([1.42909238, 0.98321839]), array([1.4867274 , 1.03367708]), array([1.54723129, 1.07156467]), array([1.60988983, 1.09750242]), array([1.67493406, 1.1109814 ]), array([1.74311326, 1.11088583]), array([1.81529411, 1.09596969]), array([1.89184122, 1.06558911]), array([1.97164154, 1.02086748]), array([2.05088566, 0.96617446]), array([2.12222802, 0.91018045]), array([2.17545919, 0.86509651]), array([2.20034349, 0.84320141]), array([1.85301332, 1.23477678]), array([1.85612401, 1.23231508]), array([1.86340838, 1.22652291]), array([1.8747647, 1.2174156]), array([1.89007148, 1.20499054]), array([1.90916891, 1.18924624]), array([1.93186232, 1.17018528]), array([1.95792681, 1.14781718]), array([1.98711228, 1.12216143]), array([2.01914859, 1.09325053]), array([2.0537507 , 1.06113276]), array([2.09062341, 1.0258748 ]), array([2.12946581, 0.9875637 ]), array([2.16997516, 0.94630841]), array([2.21185032, 0.90224066]), array([2.25479462, 0.85551511]), array([2.29851829, 0.8063089 ]), array([2.34274049, 0.75482049]), array([2.38719095, 0.70126801]), array([2.43161142, 0.64588704]), array([2.47575687, 0.58892802]), array([2.51939653, 0.53065342]), array([2.56231484, 0.4713347 ]), array([2.60431231, 0.41124926]), array([2.64520628, 0.3506775 ]), array([2.68483163, 0.28989999]), array([2.72304134, 0.22919492]), array([2.759707  , 0.16883594]), array([2.79471911, 0.10909024]), array([2.82798727, 0.05021712]), array([ 2.85944012, -0.00753315]), array([ 2.8890251 , -0.06392009]), array([ 2.91670795, -0.11871349]), array([ 2.94247192, -0.17169364]), array([ 2.96631683, -0.22265136]), array([ 2.98825774, -0.27138799]), array([ 3.00832349, -0.31771529]), array([ 3.02655492, -0.36145532]), array([ 3.04300298, -0.40244046]), array([ 3.05772661, -0.44051349]), array([ 3.07079049, -0.47552779]), array([ 3.08226281, -0.50734768]), array([ 3.09221285, -0.53584886]), array([ 3.10070875, -0.56091894]), array([ 3.10781527, -0.58245815]), array([ 3.1135917 , -0.60037988]), array([ 3.11808996, -0.61461144]), array([ 3.12135297, -0.6250945 ]), array([ 3.12341311, -0.63178513]), array([ 3.1242851 , -0.63463432])]\n"
     ]
    }
   ],
   "source": [
    "t_initial = 2\n",
    "ini_collo_pts = t_initial/2 * (LGL_Pts+1)\n",
    "\n",
    "ini_p = np.full((Ntp, ndof), 0.0)\n",
    "ini_q = np.full((Ntp, ngc), 0.0)\n",
    "y_waypoints = [None]* (Np+1)\n",
    "ini_x = [None] * T\n",
    "ini_y = [None] * T\n",
    "ini_u = [None] * T\n",
    "\n",
    "q0_basis_list = [None] * Np\n",
    "\n",
    "for k in range(Np):\n",
    "    for j in range(Ntp):\n",
    "\n",
    "        q0_ = q_waypoints[k]\n",
    "        qT_ = q_waypoints[k+1]\n",
    "        q0_basis = local_basis(q0_, J_holonomic)   # basis of tangent space at q0_\n",
    "        q0_basis_list[k] = q0_basis\n",
    "\n",
    "        y_waypoints[k] = q_manifold_to_local(q0_, q0_, q0_basis)\n",
    "        y_waypoints[k+1] = q_manifold_to_local(qT_, q0_, q0_basis)\n",
    "\n",
    "        ini_p[j,:] = np.squeeze(y_waypoints[k] + ini_collo_pts[j]/t_initial*(y_waypoints[k+1]-y_waypoints[k]))\n",
    "        ini_q[j,:] = q_local_to_manifold(q0_, q0_basis, ini_p[j,:], F_holonomic)\n",
    "\n",
    "    ini_dp = np.array([np.squeeze(LocalDiff(casadi.vertcat(*ini_p), t_initial, DL[i,:])) for i in range(Ntp)])\n",
    "    ini_ddp = np.array([np.squeeze(LocalDiff(casadi.vertcat(*ini_dp), t_initial, DL[i,:])) for i in range(Ntp)])\n",
    "    ini_dq = np.array([np.squeeze(dq_local_to_manifold(ini_dp[i,:], ini_q[i,:], q0_basis)) for i in range(Ntp)])\n",
    "    ini_ddq = np.array([np.squeeze(ddq_local_to_manifold(ini_dp[i,:], ini_ddp[i,:], ini_q[i,:], ini_dq[i,:], q0_basis)) for i in range(Ntp)])\n",
    "    ini_dyn = np.array([pin.rnea(FiveBar, data, ini_q[i], ini_dq[i], ini_ddq[i]) for i in range(Ntp)])  # M@ddq + C@dq + G\n",
    "\n",
    "    # Lagrange multiplier of constraint force\n",
    "    multiplier = np.array([np.linalg.inv(J_holonomic(ini_q[i]).T[1:4,:]) @ -ini_dyn[i,1:4] for i in range(Ntp)])\n",
    "    ini_U = np.array([np.squeeze(ini_dyn[i] + J_holonomic(ini_q[i]).T @ multiplier[i]) for i in range(Ntp)])\n",
    "\n",
    "    for j in range(Ntp):\n",
    "        t = k*Ntp + j\n",
    "        ini_x[t] =  np.concatenate([ini_q[j],ini_dq[j]])\n",
    "        ini_y[t] = np.concatenate([ini_p[j],ini_dp[j]])\n",
    "        ini_u[t] = np.array([ini_U[j][0],ini_U[j][-1]])\n",
    "\n",
    "print(y_waypoints)\n",
    "print(ini_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Should be zero: [0, 6.93889e-18, -4.16334e-17]\n",
      " Should be equal: [0.00636985, -0.0115623, 0] == [0.00636985, -0.0115623, 1.71057e-49] \n",
      " Should be equal: [ 0.06456188 -0.03411386  0.01057762  0.0488022  -0.08982784] == [0.0645619, -0.0341139, 0.0105776, 0.0488022, -0.0898278] \n",
      " Should be equal: [-2.41846e-13, 1.15255e-14] == [-2.41966e-13, 1.15658e-14] \n"
     ]
    }
   ],
   "source": [
    "# Verify kinematic constraint of initial guess\n",
    "j = 6\n",
    "print(f\" Should be zero: {J_holonomic(ini_q[j]) @ ini_dq[j]}\")\n",
    "xi = casadi.Function(\"xi\", [q,dq], [-dJq_dt@dq])\n",
    "print(f\" Should be equal: {J_holonomic(ini_q[j]) @ ini_ddq[j]} == {xi(ini_q[j], ini_dq[j])} \")\n",
    "\n",
    "# Verify constrained dynamics of initial guess\n",
    "print(f\" Should be equal: {ini_ddq[j]} == {F_ConstrAcc(ini_q[j], ini_dq[j], ini_u[k*Ntp + j])[ngc:]} \")\n",
    "\n",
    "print(f\" Should be equal: {q0_basis_list[k].T[nhc:,:] @ ini_ddq[j]} == {LocalDiff(casadi.vertcat(*ini_dp), t_initial, DL[j,:])} \")\n",
    "\n",
    "\n",
    "#print(F_LocalAcc(ini_q[j], ini_dq[j], ini_u[k*Ntp + j], q0_basis_list[k]))  # q0_basis.T[nhc:,:] @ F_ConstrAcc(q, dq, u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Nonlinear Optimization Problem (NLP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "opti = casadi.Opti()\n",
    "# Optimization variables\n",
    "var_xs = [opti.variable(2*ngc) for _ in range(T)]\n",
    "var_ys = [opti.variable(2*ndof) for _ in range(T)]\n",
    "var_us = [opti.variable(ndof) for _ in range(T)]\n",
    "var_deltaT = [opti.variable(1) for _ in range(Np)]\n",
    "\n",
    "for i in range(Np):\n",
    "    opti.subject_to(var_deltaT[i] > 0.0)\n",
    "\n",
    "    for tp in range(Ntp):\n",
    "        t = i*Ntp + tp\n",
    "\n",
    "        # constriants   solve x = H^(-1)(y) <-> y = H(x) and F(x) = 0\n",
    "        opti.subject_to(F_holonomic(var_xs[t][:ngc]) == 0)\n",
    "        opti.subject_to(q_manifold_to_local(var_xs[t][:ngc], q_waypoints[i], q0_basis_list[i]) == var_ys[t][:ndof])\n",
    "\n",
    "        opti.subject_to(J_holonomic(var_xs[t][:ngc]) @ var_xs[t][ngc:] == 0)\n",
    "        opti.subject_to(dq_manifold_to_local(var_xs[t][ngc:], q0_basis_list[i]) == var_ys[t][ndof:])\n",
    "\n",
    "        #dynamics\n",
    "        opti.subject_to(LocalsDiff(casadi.vertcat(*var_ys[i*Ntp: (i+1)*Ntp]), var_deltaT[i], DL[tp,:]) \n",
    "                        == F_LocalAcc(var_xs[t][:ngc], var_xs[t][ngc:], var_us[t], q0_basis_list[i]))\n",
    "        \n",
    "        # joint constraints\n",
    "        opti.subject_to(var_xs[t][:ngc] <= upperPositionLimit)\n",
    "        opti.subject_to(var_xs[t][:ngc] >= lowerPositionLimit)\n",
    "        # joint velocity constraints\n",
    "        opti.subject_to(var_xs[t][ngc:] <= upperVelocityLimit)\n",
    "        opti.subject_to(var_xs[t][ngc:] >= lowerVelocityLimit)\n",
    "        # torque constraints\n",
    "        opti.subject_to(var_us[t] <= upperTorqueLimit)\n",
    "        opti.subject_to(var_us[t] >= lowerTorqueLimit)\n",
    "\n",
    "# waypoint constraints\n",
    "for i in range(1, Np):\n",
    "    opti.subject_to(var_ys[i*Ntp][:ndof] == y_waypoints[i])\n",
    "\n",
    "# continuity constraints\n",
    "for i in range(1, Np):\n",
    "    opti.subject_to(var_xs[i*Ntp-1] == var_xs[i*Ntp])\n",
    "    opti.subject_to(var_us[i*Ntp-1] == var_us[i*Ntp])\n",
    "\n",
    "# boundary conditions\n",
    "opti.subject_to(var_ys[0] == ini_y[0])\n",
    "opti.subject_to(var_ys[-1] == ini_y[-1])\n",
    "\n",
    "#Objective\n",
    "total_cost = 0\n",
    "for i in range(Np):\n",
    "    for tp in range(Ntp):\n",
    "        total_cost += var_deltaT[i]/2 * LGL_Wts[tp] * var_us[i*Ntp+tp].T @ var_us[i*Ntp+tp]\n",
    "    total_cost += var_deltaT[i]\n",
    "\n",
    "opti.minimize(total_cost)\n",
    "opti.solver(\"ipopt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "for t in var_deltaT:\n",
    "    opti.set_initial(t, t_initial)\n",
    "for t in range(T):\n",
    "    opti.set_initial(var_xs[t], ini_x[t])\n",
    "    opti.set_initial(var_ys[t], ini_y[t])\n",
    "    opti.set_initial(var_us[t], ini_u[t])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\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 3.14.16, running with linear solver MUMPS 5.7.2.\n",
      "\n",
      "Number of nonzeros in equality constraint Jacobian...:    30134\n",
      "Number of nonzeros in inequality constraint Jacobian.:     2402\n",
      "Number of nonzeros in Lagrangian Hessian.............:     7302\n",
      "\n",
      "Total number of variables............................:     1602\n",
      "                     variables with only lower bounds:        0\n",
      "                variables with lower and upper bounds:        0\n",
      "                     variables with only upper bounds:        0\n",
      "Total number of equality constraints.................:     1422\n",
      "Total number of inequality constraints...............:     2402\n",
      "        inequality constraints with only lower bounds:     1202\n",
      "   inequality constraints with lower and upper bounds:        0\n",
      "        inequality constraints with only upper bounds:     1200\n",
      "\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "   0  2.1858577e+01 6.16e-01 8.33e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0\n",
      "   1  5.2852218e+00 2.73e+03 7.17e+04  -1.0 2.00e+00    -  7.50e-01 9.88e-01f  1\n",
      "   2  5.3744399e+00 1.29e+03 3.59e+04  -1.0 1.72e+00    -  7.42e-01 1.00e+00h  1\n",
      "   3  5.7748834e+00 1.05e+03 2.98e+04  -1.0 1.29e+01    -  3.89e-01 2.09e-01h  1\n",
      "   4  6.0285910e+00 8.80e+02 2.51e+04  -1.0 8.74e+00    -  5.61e-01 1.85e-01h  1\n",
      "   5  6.3368453e+00 6.42e+02 1.89e+04  -1.0 6.98e+00    -  4.63e-01 3.30e-01h  1\n",
      "   6  6.6835499e+00 4.68e+02 1.41e+04  -1.0 6.93e+00    -  3.70e-01 3.32e-01h  1\n",
      "   7  6.9823582e+00 3.59e+02 1.10e+04  -1.0 9.05e+00    -  2.87e-01 2.79e-01h  1\n",
      "   8  7.2133544e+00 2.91e+02 9.02e+03  -1.0 9.21e+00    -  1.83e-01 2.20e-01h  1\n",
      "   9  7.5021162e+00 2.30e+02 7.19e+03  -1.0 8.27e+00    -  3.10e-01 2.49e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  10  7.8792245e+00 1.68e+02 5.30e+03  -1.0 8.52e+00    -  2.14e-01 3.46e-01h  1\n",
      "  11  8.3033058e+00 1.19e+02 3.68e+03  -1.0 6.21e+00    -  2.36e-01 4.13e-01h  1\n",
      "  12  8.5566198e+00 9.38e+01 2.73e+03  -1.0 4.91e+00    -  2.38e-01 3.17e-01h  1\n",
      "  13  9.4294710e+00 7.11e+01 1.15e+03  -1.0 4.34e+00    -  4.42e-01 9.70e-01h  1\n",
      "  14  9.7045470e+00 1.97e+01 3.02e+02  -1.0 2.49e+00    -  5.42e-01 1.00e+00h  1\n",
      "  15  9.6860636e+00 3.72e+00 3.23e+01  -1.0 2.09e+00    -  4.93e-01 1.00e+00h  1\n",
      "  16  9.7113443e+00 4.28e+00 3.69e+00  -1.0 2.28e+00    -  6.55e-01 1.00e+00f  1\n",
      "  17  1.0190455e+01 8.49e+00 1.13e+00  -1.0 1.45e+00    -  7.75e-01 1.00e+00f  1\n",
      "  18  1.1736132e+01 1.09e+01 9.57e-01  -1.0 1.19e+00    -  1.00e+00 1.00e+00h  1\n",
      "  19  1.2188714e+01 6.39e-01 8.39e-02  -1.0 2.61e-01    -  1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  20  9.3748044e+00 4.36e+00 8.14e-01  -1.7 7.35e-01    -  1.00e+00 1.00e+00h  1\n",
      "  21  8.2631400e+00 1.26e+01 7.27e-01  -1.7 9.27e-01    -  1.00e+00 8.67e-01h  1\n",
      "  22  8.1372180e+00 3.96e+00 1.15e-01  -1.7 4.98e-01    -  1.00e+00 1.00e+00h  1\n",
      "  23  8.1810451e+00 1.68e-01 1.26e-02  -1.7 2.16e-01    -  1.00e+00 1.00e+00h  1\n",
      "  24  6.7759968e+00 9.22e+00 3.63e-01  -2.5 4.48e-01    -  1.00e+00 1.00e+00f  1\n",
      "  25  6.3458478e+00 2.61e+00 3.76e-01  -2.5 5.43e-01    -  1.00e+00 1.00e+00h  1\n",
      "  26  6.3763620e+00 5.77e-02 9.57e-03  -2.5 6.52e-02    -  1.00e+00 1.00e+00h  1\n",
      "  27  6.3753939e+00 2.36e-04 1.45e-05  -2.5 4.71e-03    -  1.00e+00 1.00e+00h  1\n",
      "  28  6.0673114e+00 1.92e+00 2.75e-01  -3.8 4.50e-01    -  9.52e-01 8.76e-01f  1\n",
      "  29  6.0442407e+00 1.59e-01 2.53e-02  -3.8 3.42e-01    -  9.72e-01 9.33e-01h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  30  6.0441258e+00 3.22e-02 3.60e-04  -3.8 8.25e-02    -  1.00e+00 1.00e+00h  1\n",
      "  31  6.0438081e+00 2.71e-04 9.14e-06  -3.8 7.20e-03    -  1.00e+00 1.00e+00h  1\n",
      "  32  6.0312019e+00 1.59e-02 1.98e-03  -5.7 9.69e-02    -  8.88e-01 8.47e-01h  1\n",
      "  33  6.0293126e+00 1.27e-02 5.44e-04  -5.7 5.51e-02    -  9.93e-01 8.94e-01h  1\n",
      "  34  6.0290628e+00 2.42e-03 2.52e-05  -5.7 3.14e-02    -  1.00e+00 1.00e+00h  1\n",
      "  35  6.0290510e+00 6.07e-05 3.63e-06  -5.7 1.19e-02    -  1.00e+00 1.00e+00h  1\n",
      "  36  6.0290506e+00 6.33e-07 4.65e-08  -5.7 9.28e-04    -  1.00e+00 1.00e+00h  1\n",
      "  37  6.0288916e+00 8.42e-05 5.98e-05  -8.6 1.07e-02    -  9.93e-01 9.26e-01h  1\n",
      "  38  6.0288795e+00 7.48e-06 1.08e-05  -8.6 4.75e-03    -  9.46e-01 9.25e-01h  1\n",
      "  39  6.0288786e+00 1.41e-06 1.39e-07  -8.6 6.07e-04    -  1.00e+00 1.00e+00h  1\n",
      "iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls\n",
      "  40  6.0288786e+00 1.30e-07 7.56e-09  -8.6 1.76e-04    -  1.00e+00 1.00e+00h  1\n",
      "  41  6.0288786e+00 2.21e-09 1.30e-10  -8.6 2.28e-05    -  1.00e+00 1.00e+00h  1\n",
      "\n",
      "Number of Iterations....: 41\n",
      "\n",
      "                                   (scaled)                 (unscaled)\n",
      "Objective...............:   6.0288785612010738e+00    6.0288785612010738e+00\n",
      "Dual infeasibility......:   1.2956754601688572e-10    1.2956754601688572e-10\n",
      "Constraint violation....:   9.8805024208614532e-10    2.2051082487761775e-09\n",
      "Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00\n",
      "Complementarity.........:   2.5477106483691852e-09    2.5477106483691852e-09\n",
      "Overall NLP error.......:   2.5477106483691852e-09    2.5477106483691852e-09\n",
      "\n",
      "\n",
      "Number of objective function evaluations             = 42\n",
      "Number of objective gradient evaluations             = 42\n",
      "Number of equality constraint evaluations            = 42\n",
      "Number of inequality constraint evaluations          = 42\n",
      "Number of equality constraint Jacobian evaluations   = 42\n",
      "Number of inequality constraint Jacobian evaluations = 42\n",
      "Number of Lagrangian Hessian evaluations             = 41\n",
      "Total seconds in IPOPT                               = 6.522\n",
      "\n",
      "EXIT: Optimal Solution Found.\n",
      "      solver  :   t_proc      (avg)   t_wall      (avg)    n_eval\n",
      "       nlp_f  |  39.53ms (941.19us)   3.12ms ( 74.40us)        42\n",
      "       nlp_g  |   1.22 s ( 29.10ms) 107.26ms (  2.55ms)        42\n",
      "  nlp_grad_f  |  74.07ms (  1.72ms)   5.94ms (138.24us)        43\n",
      "  nlp_hess_l  |  22.77 s (555.26ms)   3.03 s ( 73.91ms)        41\n",
      "   nlp_jac_g  |  24.08 s (560.00ms)   2.12 s ( 49.25ms)        43\n",
      "       total  |  58.66 s ( 58.66 s)   6.53 s (  6.53 s)         1\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    sol = opti.solve_limited()\n",
    "    sol_xs = [opti.value(var_x) for var_x in var_xs]\n",
    "    sol_ys = [opti.value(var_y) for var_y in var_ys]\n",
    "    sol_us = [opti.value(var_u) for var_u in var_us]\n",
    "    sol_T = [opti.value(var_t) for var_t in var_deltaT]\n",
    "except:\n",
    "    print(\"ERROR in convergence, plotting debug info.\")\n",
    "    sol_xs = [opti.debug.value(var_x) for var_x in var_xs]\n",
    "    sol_us = [opti.debug.value(var_u) for var_u in var_us]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0803131496638454, 0.45644609838617867]\n",
      "Total time: 1.536759248050024\n",
      "[DM([-4.16334e-17, 2.77556e-17, -2.44929e-16]), DM([-2.77556e-16, 5.55112e-17, -2.44929e-16]), DM([8.32667e-17, -2.77556e-17, 6.43249e-16]), DM([1.52656e-16, -2.77556e-17, 6.43249e-16]), DM([1.11022e-16, 0, 6.43249e-16]), DM([1.80411e-16, 2.77556e-17, 6.43249e-16]), DM([2.77556e-16, 2.77556e-17, 1.53143e-15]), DM([1.11022e-16, 2.77556e-17, 6.43249e-16]), DM([0, 2.77556e-17, -2.44929e-16]), DM([1.94289e-16, -2.77556e-17, 6.43249e-16]), DM([-1.38778e-16, -2.77556e-17, -2.44929e-16]), DM([-1.38778e-16, 5.55112e-17, -2.44929e-16]), DM([-2.77556e-17, -1.38778e-16, -2.44929e-16]), DM([0, 2.77556e-17, -2.44929e-16]), DM([2.35922e-16, -2.77556e-17, 6.43249e-16]), DM([-1.11022e-16, 5.55112e-17, -2.44929e-16]), DM([3.05311e-16, -5.55112e-17, 6.43249e-16]), DM([-2.91434e-16, -2.77556e-17, -1.13311e-15]), DM([2.35922e-16, 0, -2.44929e-16]), DM([-2.08167e-16, -1.11022e-16, -2.44929e-16]), DM([2.77556e-17, 1.11022e-16, 6.43249e-16]), DM([9.71445e-17, -2.77556e-16, 6.43249e-16]), DM([2.63678e-16, -2.77556e-17, 6.43249e-16]), DM([0, -3.60822e-16, -2.44929e-16]), DM([2.35922e-16, 8.32667e-17, 6.43249e-16]), DM([-1.11022e-16, -4.996e-16, -2.44929e-16]), DM([2.63678e-16, -1.94289e-16, -2.44929e-16]), DM([6.93889e-16, -8.32667e-17, -1.13311e-15]), DM([6.50868e-15, 5.30131e-15, 6.43249e-16]), DM([1.33227e-15, -4.13558e-15, -2.44929e-16]), DM([5.82867e-16, -1.11022e-15, 6.43249e-16]), DM([-1.08247e-15, 8.54872e-15, -2.44929e-16]), DM([-1.11022e-16, -3.60822e-15, -2.44929e-16]), DM([0, 3.41394e-15, 6.43249e-16]), DM([-1.66533e-16, -2.2482e-15, -1.13311e-15]), DM([1.11022e-16, 1.94289e-15, -2.44929e-16]), DM([1.66533e-16, -2.44249e-15, -2.44929e-16]), DM([-2.22045e-16, 1.22125e-15, -2.44929e-16]), DM([8.32667e-17, -2.9976e-15, -2.44929e-16]), DM([9.71445e-17, 1.4988e-15, 1.53143e-15]), DM([1.249e-16, -2.38698e-15, -2.44929e-16]), DM([1.52656e-16, 1.60982e-15, 1.53143e-15]), DM([8.32667e-17, -1.66533e-16, -2.44929e-16]), DM([-3.60822e-16, 1.05471e-15, -2.44929e-16]), DM([-2.77556e-17, 2.80331e-15, -2.44929e-16]), DM([1.66533e-16, -6.66134e-16, -2.44929e-16]), DM([-2.63678e-16, 5.2458e-15, 6.43249e-16]), DM([5.55112e-16, -3.9968e-15, -2.44929e-16]), DM([-1.11022e-15, 1.02973e-14, 1.53143e-15]), DM([8.88178e-16, -7.43849e-15, -2.44929e-16]), DM([-2.35922e-16, -7.24421e-15, -2.02129e-15]), DM([1.94289e-16, 1.66533e-16, -2.44929e-16]), DM([1.66533e-16, 0, -2.44929e-16]), DM([-4.16334e-17, 5.55112e-17, -2.44929e-16]), DM([5.55112e-17, 0, -2.44929e-16]), DM([-8.32667e-17, -2.77556e-17, -2.44929e-16]), DM([1.38778e-16, -2.77556e-17, 6.43249e-16]), DM([2.77556e-17, 2.77556e-17, -2.44929e-16]), DM([1.52656e-16, -2.77556e-17, -2.44929e-16]), DM([5.55112e-17, 5.55112e-17, -2.44929e-16]), DM([-1.66533e-16, 2.77556e-17, -2.44929e-16]), DM([-1.66533e-16, 0, -2.44929e-16]), DM([-4.16334e-17, -1.38778e-16, 6.43249e-16]), DM([-3.46945e-16, 0, -1.13311e-15]), DM([2.08167e-16, -8.32667e-17, 6.43249e-16]), DM([-8.32667e-17, -8.32667e-17, -2.44929e-16]), DM([6.93889e-17, -1.94289e-16, -2.44929e-16]), DM([2.22045e-16, -1.11022e-16, 6.43249e-16]), DM([1.38778e-16, -1.11022e-16, -2.44929e-16]), DM([-1.80411e-16, -8.32667e-17, -2.44929e-16]), DM([-2.77556e-17, -1.11022e-16, 6.43249e-16]), DM([1.52656e-16, -5.55112e-17, 1.53143e-15]), DM([-1.38778e-17, -8.32667e-17, 6.43249e-16]), DM([1.52656e-16, -8.32667e-17, 6.43249e-16]), DM([1.94289e-16, 0, 6.43249e-16]), DM([-3.05311e-16, -5.55112e-17, -2.44929e-16]), DM([-1.38778e-16, 0, -2.44929e-16]), DM([2.22045e-16, -5.55112e-17, 6.43249e-16]), DM([2.77556e-17, 5.55112e-17, 6.43249e-16]), DM([2.22045e-16, 2.77556e-17, 6.43249e-16]), DM([-1.11022e-16, 0, -2.44929e-16]), DM([3.33067e-16, 8.32667e-17, 6.43249e-16]), DM([-6.93889e-17, 5.55112e-17, -1.13311e-15]), DM([5.55112e-17, -5.55112e-17, 6.43249e-16]), DM([-1.66533e-16, -5.55112e-17, -2.44929e-16]), DM([-1.11022e-16, 0, -2.44929e-16]), DM([0, 0, -2.44929e-16]), DM([-1.38778e-16, 0, -2.44929e-16]), DM([8.32667e-17, 1.38778e-16, -2.44929e-16]), DM([1.38778e-16, -2.77556e-17, 6.43249e-16]), DM([-8.32667e-17, 1.11022e-16, -2.44929e-16]), DM([-1.249e-16, 0, -2.44929e-16]), DM([-8.32667e-17, -2.77556e-17, -2.44929e-16]), DM([6.93889e-17, 8.32667e-17, -2.44929e-16]), DM([1.38778e-17, 0, -2.44929e-16]), DM([1.249e-16, 8.32667e-17, 6.43249e-16]), DM([-2.77556e-17, -1.11022e-16, -2.44929e-16]), DM([-1.94289e-16, -2.77556e-17, -1.13311e-15]), DM([1.52656e-16, 2.77556e-17, 6.43249e-16]), DM([5.55112e-17, 0, 6.43249e-16])]\n"
     ]
    }
   ],
   "source": [
    "print(sol_T)\n",
    "print(f\"Total time: {sum(sol_T)}\")\n",
    "\n",
    "T_List = [0] + [sum(sol_T[:i+1]) for i in range(Np)]\n",
    "\n",
    "# verify kinematic loop\n",
    "sol_F = [F_holonomic(var_x[:ngc]) for var_x in sol_xs]\n",
    "print(sol_F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nsample = 200\n",
    "fig, axs = plt.subplots(ndof,1)\n",
    "for i in range(Np):\n",
    "    sample_t = np.linspace(T_List[i], T_List[i+1], nsample)\n",
    "    collo_pts = sol_T[i]/2 * (LGL_Pts+1) + T_List[i]\n",
    "    t = casadi.SX.sym(\"t\")\n",
    "\n",
    "    inter_ys = casadi.Function(\n",
    "        \"yt\", \n",
    "        [t], [LagrangeInterpolation(t, collo_pts, sol_ys[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "    inter_us = casadi.Function(\n",
    "        \"ut\", \n",
    "        [t], [LagrangeInterpolation(t, collo_pts, sol_us[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "    inter_dys = casadi.Function(\n",
    "        \"dyt\", \n",
    "        [t], [DiffLangrangeInterpolation(t, collo_pts, sol_ys[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "\n",
    "    sample_p = np.array([np.squeeze(inter_ys(t))[:ndof] for t in sample_t])\n",
    "    sample_dp = np.array([np.squeeze(inter_ys(t))[ndof:] for t in sample_t])\n",
    "    sample_ddp = np.array([np.squeeze(inter_dys(t))[ndof:] for t in sample_t])\n",
    "\n",
    "    # Interpolated control input\n",
    "    sample_u = np.array([np.squeeze(inter_us(t)) for t in sample_t])\n",
    "\n",
    "    # Inverse dynamics from interpolated trajectory\n",
    "    sample_q = np.array([q_local_to_manifold(q_waypoints[i], q0_basis_list[i], sample_p[k,:], F_holonomic) for k in range(nsample)])\n",
    "    sample_dq = np.array([np.squeeze(dq_local_to_manifold(sample_dp[k,:], sample_q[k,:], q0_basis_list[i])) for k in range(nsample)])\n",
    "    sample_ddq = np.array([np.squeeze(ddq_local_to_manifold(sample_dp[k,:], sample_ddp[k,:], sample_q[k,:], sample_dq[k,:], q0_basis_list[i])) for k in range(nsample)])\n",
    "    sample_U = np.zeros((nsample, ndof))\n",
    "    for k in range(nsample):\n",
    "        dyn_i = pin.rnea(FiveBar, data, sample_q[k], sample_dq[k], sample_ddq[k])\n",
    "        multiplier_i = np.linalg.inv(J_holonomic(sample_q[k]).T[1:4,:]) @ -dyn_i[1:4]\n",
    "        temp = np.squeeze(dyn_i + J_holonomic(sample_q[k]).T @ multiplier_i)\n",
    "        sample_U[k,0] = temp[0]\n",
    "        sample_U[k,-1] = temp[-1]\n",
    "\n",
    "    # Inverse dynamics at collocation points\n",
    "    collo_u = np.zeros((Ntp, ngc))\n",
    "    for j in range(Ntp):\n",
    "        t = i*Ntp + j\n",
    "        collo_ddq = np.squeeze(ddq_local_to_manifold(sol_ys[t][ndof:], inter_dys(collo_pts[j])[ndof:], sol_xs[t][:ngc], sol_xs[t][ngc:], q0_basis_list[i]))\n",
    "        collo_dyn = pin.rnea(FiveBar, data, sol_xs[t][:ngc], sol_xs[t][ngc:], collo_ddq)\n",
    "        collo_multiplier = np.linalg.inv(J_holonomic(sol_xs[t][:ngc]).T[1:4,:]) @ -collo_dyn[1:4]\n",
    "        collo_u[j,:] = np.squeeze(collo_dyn + J_holonomic(sol_xs[t][:ngc]).T @ collo_multiplier)\n",
    "\n",
    "    for k in range(ndof):\n",
    "        axs[k].plot(sample_t, sample_u[:,k], label=f'u{k}',color='blue')\n",
    "        if k == 0:\n",
    "            axs[k].plot(sample_t, sample_U[:,0], label=f'tau{k}',color='orange',linestyle='dashed')\n",
    "            for j, col in enumerate(collo_pts):\n",
    "                t = i*Ntp + j\n",
    "                axs[k].plot(col, sol_us[t][0], color='red', marker='o', markersize=2)\n",
    "                axs[k].plot(col, collo_u[j,0], color='green', marker='o', markersize=2)\n",
    "        else:\n",
    "            axs[k].plot(sample_t, sample_U[:,-1], label=f'tau{i}',color='orange',linestyle='dashed') \n",
    "            for j, col in enumerate(collo_pts):\n",
    "                t = i*Ntp + j\n",
    "                axs[k].plot(col, sol_us[t][-1], color='red', marker='o',markersize=2)\n",
    "                axs[k].plot(col, collo_u[j,-1], color='green', marker='o',markersize=2)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# plot trajectories local coordinates\\nfig, axs = plt.subplots(3,1)\\n\\naxs[0].plot(sample_t, sample_p[:,0], label=f'p{i}') # blue\\naxs[0].plot(sample_t, sample_p[:,1], label=f'dp{i}') # orange\\n    #axs[i].plot(sample_t, sample_dp[:,i], label=f'dp{i}')\\n\\naxs[1].plot(sample_t, sample_dp[:,0], label=f'dp{i}')\\naxs[1].plot(sample_t, sample_dp[:,1], label=f'dp{i}')\\n\\naxs[2].plot(sample_t, sample_ddp[:,0], label=f'ddp{i}')\\naxs[2].plot(sample_t, sample_ddp[:,1], label=f'ddp{i}')\\nplt.show()\\n\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "# plot trajectories local coordinates\n",
    "fig, axs = plt.subplots(3,1)\n",
    "\n",
    "axs[0].plot(sample_t, sample_p[:,0], label=f'p{i}') # blue\n",
    "axs[0].plot(sample_t, sample_p[:,1], label=f'dp{i}') # orange\n",
    "    #axs[i].plot(sample_t, sample_dp[:,i], label=f'dp{i}')\n",
    "\n",
    "axs[1].plot(sample_t, sample_dp[:,0], label=f'dp{i}')\n",
    "axs[1].plot(sample_t, sample_dp[:,1], label=f'dp{i}')\n",
    "\n",
    "axs[2].plot(sample_t, sample_ddp[:,0], label=f'ddp{i}')\n",
    "axs[2].plot(sample_t, sample_ddp[:,1], label=f'ddp{i}')\n",
    "plt.show()\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\n# plot trajectories joint variables\\nfig, axs = plt.subplots(3,1)\\n\\nfor i in range(ngc):\\n    axs[0].plot(sample_t, sample_q[:,i], label=f'q{i}')\\n\\nfor i in range(ngc):\\n    axs[1].plot(sample_t, sample_dq[:,i], label=f'dq{i}')\\n\\nfor i in range(ngc):\\n    axs[2].plot(sample_t, sample_ddq[:,i], label=f'ddq{i}')\\n\\nplt.show()\\n\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "# plot trajectories joint variables\n",
    "fig, axs = plt.subplots(3,1)\n",
    "\n",
    "for i in range(ngc):\n",
    "    axs[0].plot(sample_t, sample_q[:,i], label=f'q{i}')\n",
    "\n",
    "for i in range(ngc):\n",
    "    axs[1].plot(sample_t, sample_dq[:,i], label=f'dq{i}')\n",
    "\n",
    "for i in range(ngc):\n",
    "    axs[2].plot(sample_t, sample_ddq[:,i], label=f'ddq{i}')\n",
    "\n",
    "plt.show()\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ForwardDynamics(y, t, q0, q0_basis, inter_us):  # local coordinates\n",
    "    q = q_local_to_manifold(q0, q0_basis, y[:ndof], F_holonomic)\n",
    "    dq = dq_local_to_manifold(y[ndof:], q, q0_basis)\n",
    "    u = inter_us(t)\n",
    "    dy = np.squeeze(np.array([F_LocalAcc(q, dq, u, q0_basis)]))\n",
    "    return dy\n",
    "\n",
    "\n",
    "y_forward = [None]*Np\n",
    "for i in range(Np):\n",
    "    time_grid = np.linspace(T_List[i], T_List[i+1], nsample)\n",
    "    collo_pts = sol_T[i]/2 * (LGL_Pts+1) + T_List[i]\n",
    "    t = casadi.SX.sym(\"t\")\n",
    "    inter_us = casadi.Function(\n",
    "        \"ut\", \n",
    "        [t], [LagrangeInterpolation(t, collo_pts, sol_us[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "    y0 = sol_ys[i*Ntp]   # initial condition\n",
    "    y_forward[i] = scipy.integrate.odeint(ForwardDynamics, y0, time_grid, args = (q_waypoints[i], q0_basis_list[i], inter_us))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1, axs1 = plt.subplots(ngc, 1)  # joint positions\n",
    "fig2, axs2 = plt.subplots(ngc, 1)  # joint velocities\n",
    "fig3, axs3 = plt.subplots(ngc, 1)  # joint accelerations\n",
    "\n",
    "\n",
    "for i in range(Np):\n",
    "    time_grid = np.linspace(T_List[i], T_List[i+1], nsample)\n",
    "    collo_pts = sol_T[i]/2 * (LGL_Pts+1) + T_List[i]\n",
    "\n",
    "    inter_ys = casadi.Function(\n",
    "        \"yt\", \n",
    "        [t], [LagrangeInterpolation(t, collo_pts, sol_ys[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "    inter_us = casadi.Function(\n",
    "        \"ut\", \n",
    "        [t], [LagrangeInterpolation(t, collo_pts, sol_us[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "\n",
    "    inter_dys = casadi.Function(\n",
    "        \"dyt\", \n",
    "        [t], [DiffLangrangeInterpolation(t, collo_pts, sol_ys[i*Ntp: (i+1)*Ntp])]\n",
    "    )\n",
    "\n",
    "    q_forward = np.array([q_local_to_manifold(q_waypoints[i], q0_basis_list[i], y_forward[i][k,:ndof], F_holonomic) for k in range(nsample)])\n",
    "    dq_forward = np.array([np.squeeze(dq_local_to_manifold(y_forward[i][k,ndof:], q_forward[k,:], q0_basis_list[i])) for k in range(nsample)])\n",
    "    ddq_forward = np.array([np.squeeze(ddq_local_to_manifold(y_forward[i][k,ndof:], \n",
    "                                                            F_LocalAcc(q_forward[k,:], dq_forward[k,:], inter_us(time_grid[k]), q0_basis_list[i])[ndof:], \n",
    "                                                            q_forward[k,:], dq_forward[k,:], q0_basis_list[i])) \n",
    "                                                            for k in range(nsample)])\n",
    "\n",
    "    sample_p = np.array([np.squeeze(inter_ys(t))[:ndof] for t in time_grid])\n",
    "    sample_dp = np.array([np.squeeze(inter_ys(t))[ndof:] for t in time_grid])\n",
    "    sample_ddp = np.array([np.squeeze(inter_dys(t))[ndof:] for t in time_grid])\n",
    "\n",
    "    # Interpolated trajectory\n",
    "    sample_q = np.array([q_local_to_manifold(q_waypoints[i], q0_basis_list[i], sample_p[k,:], F_holonomic) for k in range(nsample)])\n",
    "    sample_dq = np.array([np.squeeze(dq_local_to_manifold(sample_dp[k,:], sample_q[k,:], q0_basis_list[i])) for k in range(nsample)])\n",
    "    sample_ddq = np.array([np.squeeze(ddq_local_to_manifold(sample_dp[k,:], sample_ddp[k,:], sample_q[k,:], sample_dq[k,:], q0_basis_list[i])) for k in range(nsample)])\n",
    "\n",
    "    for j in range(ngc):\n",
    "        axs1[j].plot(time_grid, q_forward[:,j]-sample_q[:,j], label=f'Integrate_q{j}',color='blue')\n",
    "\n",
    "    for j in range(ngc):\n",
    "        axs2[j].plot(time_grid, dq_forward[:,j], label=f'Integrate_dq{j}',color='blue')\n",
    "        axs2[j].plot(time_grid, sample_dq[:,j], label=f'Nominal_dq{j}',color='orange',linestyle='dashed')\n",
    "\n",
    "    for j in range(ngc):\n",
    "        axs3[j].plot(time_grid, ddq_forward[:,j], label=f'Integrate_ddq{j}',color='blue')   # blue\n",
    "        axs3[j].plot(time_grid, sample_ddq[:,j], label=f'Nominal_ddq{j}', color='orange',linestyle='dashed')      # orange\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "jnrh-2023",
   "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": "3.9.19"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}