tt_only_steering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Pkg; Pkg.activate(@__DIR__); Pkg.instantiate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using PyPlot\n",
    "using ForwardDiff\n",
    "using RobotZoo\n",
    "using RobotDynamics\n",
    "using MatrixCalculus"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Acrobot Dynamics\n",
    "a = RobotZoo.Acrobot()\n",
    "h = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tractor_trailer_qdot (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Parameters of the tractor-trailer\n",
    "g_velocity = 0.5\n",
    "g_tractor_wheelbase = 3.0\n",
    "g_tractor_hitch_offset = 0.5\n",
    "g_trailer_wheelbase = 6.0\n",
    "max_alpha = atan(g_tractor_wheelbase/sqrt((g_trailer_wheelbase^2) - (g_tractor_hitch_offset^2)))\n",
    "\n",
    "function tractor_trailer_qdot(q_current,u)\n",
    "    \n",
    "    # Variable to store the rate of change of state\n",
    "    alpha = u\n",
    "#     gear = 1\n",
    "#     g_velocity = u[2]\n",
    "    \n",
    "    if(alpha!=0)\n",
    "        r1 = g_tractor_wheelbase/tan(alpha);\n",
    "        psi = -1*(alpha/abs(alpha))*atan(g_tractor_hitch_offset/abs(r1));\n",
    "        va = (g_velocity/abs(g_velocity))*abs(((g_velocity*g_tractor_hitch_offset*tan(alpha))/(g_tractor_wheelbase*sin(psi))));\n",
    "        vb = va*abs(cos(psi-q_current[4]));\n",
    "        r2 = g_tractor_hitch_offset/sin(psi);\n",
    "        r3 = g_trailer_wheelbase/sin(psi-q_current[4]);\n",
    "        omega_1 = g_velocity*(1/r1);\n",
    "        omega_2 = g_velocity*((r2)/(r1*r3));\n",
    "        trailer_theta_dot = omega_2;\n",
    "        beta_dot = g_velocity*(((r2)/(r1*r3)) - (1/r1));\n",
    "    end\n",
    "\n",
    "    # Special case when alpha equals zero\n",
    "    if(alpha==0)\n",
    "        va = g_velocity;\n",
    "        psi = 0;\n",
    "        phi = (pi/2) - (abs(q_current[4]) - (pi/2));\n",
    "        hitch_turn_radius_zero_alpha = g_trailer_wheelbase/sin(phi);\n",
    "        trailer_theta_dot = va/hitch_turn_radius_zero_alpha;\n",
    "        beta_dot = trailer_theta_dot;\n",
    "        vb = va*abs(cos(psi-q_current[4]));\n",
    "\n",
    "        if(sin(phi)==0)\n",
    "            beta_dot = 0;\n",
    "            trailer_theta_dot = 0;\n",
    "        end\n",
    "        \n",
    "    end\n",
    "    \n",
    "\n",
    "    q_dot = [vb*cos(q_current[3]); vb*sin(q_current[3]); trailer_theta_dot; beta_dot]\n",
    "\n",
    "    return q_dot;\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dynamics_rk4 (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function dynamics_rk4(x,u)\n",
    "    #RK4 integration with zero-order hold on u\n",
    "    f1 = RobotDynamics.dynamics(a, x, u)\n",
    "    f2 = RobotDynamics.dynamics(a, x + 0.5*h*f1, u)\n",
    "    f3 = RobotDynamics.dynamics(a, x + 0.5*h*f2, u)\n",
    "    f4 = RobotDynamics.dynamics(a, x + h*f3, u)\n",
    "    return x + (h/6.0)*(f1 + 2*f2 + 2*f3 + f4)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dfdu (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function dfdx(x,u)\n",
    "    ForwardDiff.jacobian(dx->dynamics_rk4(dx,u),x)\n",
    "end\n",
    "\n",
    "function dfdu(x,u)\n",
    "    ForwardDiff.derivative(du->dynamics_rk4(x,du),u)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Nx = 4     # number of state\n",
    "Nu = 1     # number of controls\n",
    "Tfinal = 5.0 # final time\n",
    "Nt = Int(Tfinal/h)+1    # number of time steps\n",
    "thist = Array(range(0,h*(Nt-1), step=h));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cost weights\n",
    "Q = Diagonal([1.0*ones(2); 0.1*ones(2)]);\n",
    "R = 50;\n",
    "Qn = Array(100.0*I(Nx));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "stage_cost (generic function with 1 method)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function stage_cost(x,u)\n",
    "    return 0.5*((x-xgoal)'*Q*(x-xgoal)) + 0.5*R*u*u\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "terminal_cost (generic function with 1 method)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function terminal_cost(x)\n",
    "    return 0.5*(x-xgoal)'*Qn*(x-xgoal)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cost (generic function with 1 method)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function cost(xtraj,utraj)\n",
    "    J = 0.0\n",
    "    for k = 1:(Nt-1)\n",
    "        J += stage_cost(xtraj[:,k],utraj[k])\n",
    "    end\n",
    "    J += terminal_cost(xtraj[:,Nt])\n",
    "    return J\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initial guess\n",
    "x0 = [0; 0; pi/2; pi]\n",
    "xgoal = [0; 5; pi/2; pi]\n",
    "xtraj = kron(ones(1,Nt), x0)\n",
    "utraj = randn(Nt-1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4276.540008591817"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Initial Rollout\n",
    "for k = 1:(Nt-1)\n",
    "    xtraj[:,k+1] .= dynamics_rk4(xtraj[:,k],utraj[k])\n",
    "end\n",
    "J = cost(xtraj,utraj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#DDP Algorithm\n",
    "p = zeros(Nx,Nt)\n",
    "P = zeros(Nx,Nx,Nt)\n",
    "d = ones(Nt-1)\n",
    "K = zeros(Nu,Nx,Nt-1)\n",
    "ΔJ = 0.0\n",
    "\n",
    "xn = zeros(Nx,Nt)\n",
    "un = zeros(Nt-1)\n",
    "\n",
    "gx = zeros(Nx)\n",
    "gu = 0.0\n",
    "Gxx = zeros(Nx,Nx)\n",
    "Guu = 0.0\n",
    "Gxu = zeros(Nx)\n",
    "Gux = zeros(Nx)\n",
    "\n",
    "iter = 0\n",
    "while maximum(abs.(d[:])) > 1e-3\n",
    "    iter += 1\n",
    "    \n",
    "    p = zeros(Nx,Nt)\n",
    "    P = zeros(Nx,Nx,Nt)\n",
    "    d = ones(Nt-1)\n",
    "    K = zeros(Nu,Nx,Nt-1)\n",
    "    ΔJ = 0.0\n",
    "\n",
    "    p[:,Nt] = Qn*(xtraj[:,Nt]-xgoal)\n",
    "    P[:,:,Nt] = Qn\n",
    "    \n",
    "    #Backward Pass\n",
    "    for k = (Nt-1):-1:1\n",
    "        #Calculate derivatives\n",
    "        q = Q*(xtraj[:,k]-xgoal)\n",
    "        r = R*utraj[k]\n",
    "    \n",
    "        A = dfdx(xtraj[:,k], utraj[k]) #ForwardDiff.jacobian(dx->dynamics_rk4(dx,utraj[k]),xtraj[:,k])\n",
    "        B = dfdu(xtraj[:,k], utraj[k]) #ForwardDiff.derivative(du->dynamics_rk4(xtraj[:,k],du),utraj[k])\n",
    "    \n",
    "        gx = q + A'*p[:,k+1]\n",
    "        gu = r + B'*p[:,k+1]\n",
    "    \n",
    "        Gxx = Q + A'*P[:,:,k+1]*A \n",
    "        Guu = R + B'*P[:,:,k+1]*B \n",
    "        Gxu = A'*P[:,:,k+1]*B \n",
    "        Gux = B'*P[:,:,k+1]*A\n",
    "        \n",
    "        d[k] = Guu\\gu\n",
    "        K[:,:,k] .= Guu\\Gux\n",
    "    \n",
    "        p[:,k] .= dropdims(gx - K[:,:,k]'*gu + K[:,:,k]'*Guu*d[k] - Gxu*d[k], dims=2)\n",
    "        P[:,:,k] .= Gxx + K[:,:,k]'*Guu*K[:,:,k] - Gxu*K[:,:,k] - K[:,:,k]'*Gux\n",
    "    \n",
    "        ΔJ += gu'*d[k]\n",
    "    end\n",
    "\n",
    "    #Forward rollout with line search\n",
    "    xn[:,1] = xtraj[:,1]\n",
    "    α = 1.0\n",
    "\n",
    "    for k = 1:(Nt-1)\n",
    "        un[k] = utraj[k] - α*d[k] - dot(K[:,:,k],xn[:,k]-xtraj[:,k])\n",
    "        xn[:,k+1] .= dynamics_rk4(xn[:,k],un[k])\n",
    "    end\n",
    "    Jn = cost(xn,un)\n",
    "    \n",
    "    while isnan(Jn) || Jn > (J - 1e-2*α*ΔJ)\n",
    "        α = 0.5*α\n",
    "        for k = 1:(Nt-1)\n",
    "            un[k] = utraj[k] - α*d[k] - dot(K[:,:,k],xn[:,k]-xtraj[:,k])\n",
    "            xn[:,k+1] .= dynamics_rk4(xn[:,k],un[k])\n",
    "        end\n",
    "        Jn = cost(xn,un)\n",
    "    end\n",
    "    #display(α)\n",
    "    \n",
    "    J = Jn\n",
    "    xtraj .= xn\n",
    "    utraj .= un\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1670.0828285738203"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VRASgFYLF2rVr8eCDDyIzMxOBgYE3PO7NN9/EwoUL/3F/awULAFh1OBOvbDgFJwcZ1s8awKl3RH+j1wvYfa4Ayw9kYN/5IsP90f4qTB8Yhgnd28DRgWtiENkzsweLMWPGQKFQYPPmzTc9TuwWC6DhRXPa8iPYd74IwZ5O2BQ7iHssUIvp9ALO5GiQXVoNTXUdvFwViPR1RaiXdW91fj6/HCviMrD+aDaq6xrGVHk4O+DBfiF4+LYw+Ls5ilwhEYnBrMHi4sWLiIiIwPr16zFhwgSzFGZqlytrcddn+5FVUo2BkV74dnpfjregZsksrsLnu1Px+5l8lFy1xfkVHQLUeG5EO4zt7C9CdaZTVlWHNfGZ+O7gRWSXVgMA5FIJxnb2x/SB4egZ4s5uEiI7YtZg8eabb2LZsmXIysqCXG7cKHKxggUAJOdpcPfncaiq1WHGoHC8dkfHVn18sm51Oj3e256C5QfSDetCqB3liPBxhdrJAcUVWiTnlUPXuNf5lL4h+O+kzlb/5luv02PH2Xx8cyADR9JLDPd3C3LDowPDML5LIBRyhnQiW2e2YKHX6xEeHo4pU6bg7bffNlth5rLtVC6eXnkUALB4cjfc3TOo1Wsg61NWXYfYlUexP7Vh/MGQ9j6YOSQCfcI94XBVy9flylp8vT8dn+9OhV4A5o+LxsyhbcUq2+SScsqw4kAGNp7IQW3jLqs+KiUe6heKB/uFwEelFLlCIjIXswWL33//HWPGjEFKSgrat29vtsLM6YPfU/DJn6lQyKX4aWZ/dA1yF6UOsg71Oj0e/OowjqSXwFkhw+LJ3W/ZzfH9oYt47ZfTUDvKcXDBCJtbH6K4QotVhzPx/aGLKChvGEOlkElxR7cAPDYwHJ3buIlcIRGZmt0v6X0zer2AJ75LwM7kAgS4OWLTM4P4nxbd0Du/JWPJ7jS4KuVY8+RtTXrT1OkFDHl3F7JLq7Fieh8Mi/JthUpbX229HttO52L5gQwczyo13D+4nTdiYyLRL5zTVYlshVmW9LYVUqkEHz7QHRE+Lsgtq8GslYmGZl2iqyXnabBkdxoA4J17ujb5P3GZVIKOgQ1/eJklVWarT2wKuRQTurfBL7EDsWHWANzVLRAyqQT7zhfhgS8O4Z4lcdhxJh96PZcNJ7IXdhksAEDt6IAvH+kNlVKO+IzLeGNTEvdMoH/4Ys8FAMD4LgEY3zXAqHNrGqdqOitsqxvkRnqEeODjKT2wa94wPHRbCBRyKY5mluLx7xIw7n/78MuxbNTrGOCJbJ3dBgsAaOvjio+n9IBEAqw+kon3f+dmZfSX3LJqbDqRAwBGD8Cs0+lxOrsMABDqZV/LY4d4OeM/E7tg/8sxmDm0LVyVcqTkl2POj8cR88FufH/ooiF0EZHtsetgAQAx0b74vwmdAQCf7UrD57tTRa6ILMWelELU6wX0CHFHlyDjBiPuP1+Ey1V18HJRoIedbn7nq3LE/HHRODB/OF4cEwUvFwWySqrx2i+nMeidXViyOw3lNXVil0lEJmb3wQIAHrotFAvGRQMA3v0tBd/GZYhbEFmE+IzLAIABbb2MOk+vF7D4j3MAgAnd29j9QmxuTg6IjYnE/peHY+FdndDG3QlFFVq881syBrz9J97bnoyiCu2tfxARWQX7fsW7ylND22L28EgAwBubkrA2IUvkikhsCRcbFoPqHeZp1Hmr4zNxKrsMLgoZZsXYzhoWLeWkkGHagDDsfnEYPrivGyJ9XVFeU4/PdqVh4Nt/4o2Np3Hpsu0OdCWyFwwWV3l+VHs8NrBh99P5P5/ErydzRa6IxCIIArIaZ3N08G/6tOizuRr8e/MZAA3PJ29XTmP+OweZFPf0CsLvc4Zg2cO90C3IDdp6Pb49eBHD3tuNuWuP43x+udhlElEz2cdw9SaSSCR47Y4OqKqtx5r4LDy35hicFFIMj/YTuzRqZZW1OlyZIenm5NCkc2rr9YhddRTaej1ionwMIZWuTyqVYEwnf4zu6Ie4tGIs2Z2G/alFWH80G+uPZmN0Rz/MiolEdzsdo0Jkrdhi8TcSiQRvTeqCCd0DUa8XMPOHo4hLLbr1iWRTKmrqATRsuuXo0LQ/E4VciudHtkc7X1d8MLk7pFIuDNUUEokEAyO98cPj/bAxdiDGdvKHRAL8fiYfEz87gAe/PIT954s4HZzIStjlyptNUafTY9bKo/jjTD6cFTJ8P6MfeoV6iF0WtZK0wgqM+GAPVI5ynHpzjFHn6vQCZAwVLZJaUI6ley40rH3R2HTUNcgNs4a1xeiO/gxtRCLgypst5CCT4pMpPTAo0htVtTo8uvwITl4qFbssaiWujXt7VNXqjF41kqGi5SJ9VXj/vm7Y81IMHh0QBkcHKU5eKsPMH45i1Id7sC4hC3VcbIvIIjFY3ISjgwxfPNILvUM9UF5Tjwe/PHzNttFkuzycFQAaWh80XGtBNG3cnfDmXZ1w4OXheHZ4JFSOcqQVVuLFn05i6Lu78MOhi1yOn8jCMFjcgrNCjhWP9UW/cE9UaOvxyDeHsedcodhlkZkp5FKoHBtaLYora0WuhrxclZg3Ogpx84dj/rho+KiUyCmrwb9+OY2Y93dj9ZFMtmAQWQgGiyZwVcqxYnpfDIvyQU2dHo9/G4/fTnMqqq3zcmlotSgs5+JNlkLl6ICZQ9ti30sxWHhXJ/iqlMgurcaC9acw/IPdWBvPLhIisTFYNJGTQoYvHu6N8V0CUKcTMGvlUfyceEnsssiMwr1dAIBrKlggR4eGxbb2vhSD1+7oCG9XJbJKqvHSzycxcvEe/JR4iRueEYmEwcIICrkUH0/pgft6BUEvAPPWncD3BzPELovM5Mq252dyNSJXQjfi6CDDjEHh2PdSDF69vQO8XBS4WFyFF9adwKgP92LDsUvQcct2olbFYGEkmVSCd+7pikcHhAEAXtuYhCW708QtisyiY0DDxmNnchgsLJ2TQoYnhkRg38sxmD8uGh7ODkgvqsTzP57A6A/3YOPxbAYMolbCYNEMUqkEb9zZEc/ENOwt8s5vyXhvezIX8LExV1oskvPK2axuJZwV8oYxGC837Kjq7uyAtMJKPLfmOMZ+tBdbTuYYPX2YiIzDYNFMEokEL4yJwvzGXVE/25WGhZvP8EXLhoR6OkOllENbr8fZXI6zsCauSjliYyKx76UYzBvVHmpHOc4XVOCZVccw7n/7sO1ULv9WicyEwaKFZg5ti/+b2BkSCbAiLgMvrDvBefU2QiqVoG94w86mB9K4rLs1Ujk64NkR7bB//nDMGdkOKkc5UvLL8fTKoxj/yX5sT8pjSyORiTFYmMDDt4Vi8eRukEklWH8sG4+tiOeiSjZiQKQ3AOAA94uxampHB8wZ2R77XxqO2cMj4aqU42yuBk99n4g7P92PHWfyGTCITITBwkQm9QjCV9N6w1khw/7UIkxeehC5ZdVil0UtNKgxWMRnlEBbrxO5GmopN2cHzB0dhf0vxyA2pi1cFDKcztbg8e8SMOGzA9iVXMCAQdRCDBYmFBPli7VP9YePSonkvHJM+iyOMwqsXHs/V3i7KlFTp8exzFKxyyETcXdW4MUx0dj38nDMHNoWTg4ynLxUhukr4jHp8zjsOVfIgEHUTAwWJta5jRs2zBqASF9X5GlqMHnZQew7zyXArVXDlt5eAMCl3G2Qp4sC88dFY9/LMXhySAQcHaQ4nlWKad8cwb1LD3K7dqJmYLAwgyAPZ/w8cwBui2jYX2T68nisS8gSuyxqpuHRvgCAHWfyRa6EzMXbVYlXbu+AvS/FYMagcCjlUiRevIyHvj6M+5cdwsG0YrFLJLIaDBZm4ubsgG8f64sJ3QNRrxfw4k8n8dGOc/zvxwoNa+8LuVSC8wUVyCiqFLscMiNflSNeu6Mj9jVu166QS3EkowRTvjyEqV8dwomsUrFLJLJ4DBZmpJTL8OHk7pg1rC0A4KMd5/HiTye5SZKVcXN2MEw73XGWrRb2wFftiDfv6oS9L8bgkf6hUMikOJBajAmfHcCslYlIK6wQu0Qii8VgYWZSqQQvjY3GW5M6QyoBfkq8hMdWxKOc01GtyqiOfgCAP9gdYlf83Rzx7wmdsXPeUNzTMwgSCbD1VB5Gf7gX838+yZlfRNfBYNFKpvYLNUxH3Xe+CJM+j2OzuhUZ2aEhWMRnlOByZa3I1VBrC/Z0xgeTu+G354ZgZAc/6PQC1sRnYdh7u7Fo61mUVvE5QXQFg0UrGh7thx+f7A8/tRKpBRWY8NkBLrxkJYI9nRHtr4JeYHeIPYvyV+Grab3x89P90TfME9p6PZbtvYDB7+7CZ7tSUVVbL3aJRKJjsGhlXYLcsPmZQegW7I6y6jo88s0RfBuXwUGdVmBsZ38AwPYkBgt71yvUEz8+dRuWP9oH0f4qlNfU473tKRj63m78cOgix1GRXTM6WGRnZ+Ohhx6Cl5cXnJyc0KVLFyQkJJijNpvlq3bEj0/ehrt7tIFOL+CNTUl4ZcMp7jFi4cZ0aggWe88XolLL/0ztnUQiQUy0L7bOHoyP7u+OYE8nFJZr8a9fTmPk4j3YdII7qZJ9MipYXL58GQMHDoSDgwO2bduGM2fO4IMPPoCHh4e56rNZjg4yfDC5GxaMi4ZEAqw+koWHvjqM4gqt2KXRDUT7qxDq5Yzaej0XyyIDqVSCiT3aYOfcYVh4Vyd4uypwsbgKs1cfw52f7ucqnmR3JIIRz/j58+fjwIED2LdvX7MfUKPRwM3NDWVlZVCr1c3+ObZkV3IBZq8+hnJtPdq4O+HLR3qjYyCvjSX679az+GLvBdzVLRAfT+khdjlkgSq19fhmfzqW7b2AisaWrdsiPPHy2Gj0COE/YWS9mvr+bVSLxaZNm9C7d2/cd9998PX1RY8ePfDll1/e9BytVguNRnPNja4VE+2LDbEDEObljOzSaty7NA6/nc4Vuyy6jjGdGmaH7EouYD86XZeLUo5nR7TD3pdi8PigcChkUhy6UIJJn8fhqe8TkFpQLnaJRGZlVLC4cOEClixZgnbt2mH79u14+umnMXv2bHz77bc3PGfRokVwc3Mz3IKDg1tctC2K9FVhY+wgDIr0RlWtDjN/OIqPdpxjH62F6R7sAS8XBcq19YjPKBG7HLJgni4K/OuOjtj14jDc1ysIUknDwN/RH+7FSz+dQE4p18Ag22RUV4hCoUDv3r0RFxdnuG/27NmIj4/HwYMHr3uOVquFVvvXuAGNRoPg4GB2hdxAvU6Pt7aexfIDGQCAEdG+WDy5O9ycHcQtjAzmrT2Bn49ewuODwvGvOzqKXQ5ZifP55Xhvewp+b1xkTSGXYlr/UMwaFgkPF4XI1RHdmlm6QgICAtCx47UvpB06dEBmZuYNz1EqlVCr1dfc6MbkMineuLMT3r2nKxRyKXYmF+COT/fhdHaZ2KVRoxEdGjYl+zO5QORKyJq081Phi0d6Y/2sAegX7onaej2+3JeOIe/uwic7z3OmEdkMo4LFwIEDkZKScs19586dQ2hoqEmLImByn2Csf3oAgj2dkFVSjbuXxOHH+BsHOGo9g9t5Qy6V4EJRJdK5eioZqWeIB9Y8eRu+fawvOgaoUa6txwd/nMPQ93bju4MZnHZOVs+oYPH888/j0KFD+O9//4vU1FSsWrUKX3zxBWJjY81Vn13r3MYNW54ZjBHRvqit1+Pln0/hxXUnUFOnE7s0u6Zy/GtTsp1chZOaQSKRYGh7H2x5dhA+ntIDoV7OKKrQ4vWNSRi5eA82Hs/m+CqyWkaNsQCALVu2YMGCBTh//jzCw8Mxd+5cPPHEE00+n9NNjafXC1iyJw0f/J4CvQB0CFBj6UM9EerlInZpduvLvRfw1tazGB7ti28e7SN2OWTlauv1+DEhCx/vPI/C8oYxad2C3PDq+I6GEEsktqa+fxsdLFqKwaL5DqQWYfbqYyiurIXKUY4P7uuG0Y2rQVLrOpFVigmfHYDaUY7jr4+GVCoRuySyAVW1DWtgLNmdhsrahpbJMZ388PLYaET4uIpcHdk7swzeJHENjPTGr7MHo2eIO8pr6vHk94l4e1sy6rmeQqvrFKiGs0IGTU09UvK5LgGZhrNCjmeGt8PuF2MwtV/INVNU39yUhBLurEtWgMHCyvi7OWLNk/0xfWAYAGDpnjRM+fIQLl2uErcwOyOXSdErtGEVRa5nQabmo1LirUldsH3OEAyP9kW9XsCKuAwMfW8Xlu1J4zgrsmgMFlZIIW+Ykvrpgz3gqpQjPuMyxv1vH7aczBG7NLvSJ6yh7/tIOoMFmUc7PxW+ebQPVj7eDx0C1CivqceibcmGTc64BwlZIgYLK3ZH10BsnT0Y3YMbukaeWXUML/10gvPhW8mVYJF48bLIlZCtGxjpjS3PDsL793WDv9oRly5XY/bqY5j4eRxbzMjiMFhYuRAvZ6yb2R/PDo+ERAKsTbiEOz7Zj1OXuKCWuV3ZKC63rMaw2RSRucikEtzbKwi7XhiGeaPaw1khw4msUty39CBmfp/INVXIYjBY2AAHmRTzRkdh9RO3IcDNEelFlbh7yQEs25PGufBm5ObkAM/GpZgvFvNFnVqHk0KGZ0e0w+4Xh2FK34YBnr8l5WHU4j1YuDkJlznAk0TGYGFDbovwwrbnBmNcZ3/U6QQs2paMR745ggJNjdil2awwL2cAQEYRB89S6/JVOWLR3V3w25whGBblg3q9gOUHGgZ4frn3ArT1HOBJ4mCwsDHuzgp8PrUn3r67C5wcZNifWoSx/9uHbae4Dbs5hHk3LFKWwRYLEkl7PxVWTO+L72f0RbS/Cpqaery19SxGLt6DLSc5wJNaH4OFDZJIJHigbwg2PzsIHQPUKKmsxdMrjyJ25VEUVWhv/QOoycIbVz9l/zaJbXA7H/w6ezDevbcrfFVKZJVU45lVx3D3kjgkcIAntSIGCxsW6euKDbED8OzwSMikEvx6KhejP9zLaWom5KNSAgD7tckiyKQSTO4djN0vDsPzIxsGeB7LLMW9Sw/i6R8SORaIWgWDhY1TymWYNzoKG2MHokNj68Xs1cfw1PeJKCjn2IuWurKUN2MaWRJnhRzPjWyH3S8MwwN9giGVANtO52Hk4j349+YzKK1iECbzYbCwE53buGFj7EDMGdkOcqkEv5/Jx6jFe7H+6CW2XrTAlR1C9LyGZIF81Y54+56u2PrcYAxp74M6nYBvDqRjyLu78NU+DvAk82CwsCMKuRRzRrbH5mcHoXMbNcqq6zB37Qk8/m0C8srYetEcUkljiwVzBVmwaH81vnusL7597K8Bnv/59SxGLd6L7Ul5/OeCTIrBwg51CFBjw6yBeHFMFBQyKXYmF2Dk4j34at8F1HFDM6M05gq2WJBVGNq+YYDnO/d0gY9KicySKjz1fSIe+eYIznMzPTIRBgs75SCTIjYmEltmD0L3YHdUaBv+gxn3v32ISy0SuzyrUVDeMMvGzclB5EqImkYmleD+PiHY/cIwzBrWFgqZFPvON0xLX7g5CWXVdWKXSFaOwcLOtfdTYf3TA/DOPV3g6aJAakEFHvzqMGJXHUVOabXY5Vm85FwNgIZWICJr4qKU46Wx0fhj7hCM6ugHXeMCWzHv78aqw5nQcdVeaiYGC4K08T+YXfOGYVr/UEglwK8nczHigz34fHcqB3jdRHJeQ/NxtL9K5EqImifUywVfPtIb38/oi0hfV5RU1uKVDadw16f7uXMvNYtEaOVROxqNBm5ubigrK4Nazf/yLNGZHA3e2HQa8RkNu3aGe7vg9Ts6YliUDyRXBhUQtPU6dHp9O+r1AuLmD0egu5PYJRG1SJ1Oj+8PXsSHO86hvKZhY707uwViwbhoPr+pye/fbLGgf+gYqMbap/rjw/u7wUelRHpRJaaviMf9XxziFs1XOZJegnq9AHdnBwS4OYpdDlGLOcikeGxQOHa/0LDBmUQCbD6RgxEf7MHHO8+jpo6tl3RrbLGgmyqvqcOnf6ZieVwGausbZowMi/LBC6Oj0LmNm8jViWvGinjsTC7AtP6hWDihs9jlEJnc6ewyLNycZGi9DPJwwqu3d8DYzv5svbRDTX3/ZrCgJsktq8Ynf6ZibXwW6hsHdY3vEoDnR7VHpK+ryNW1voyiSsR8sBuCAPw5bygifOzvGpB9EAQBm0/mYtHWs8htXO+mf4QX3rirI6L9+RpuTxgsyCwyiirx0Y5z2HgiB4IASCXA3T2DMHt4O4Q0biFuD97clIQVcRmIifLB8ul9xS6HyOyqauuxdHcalu69gNp6PaQS4KHbQjF3VHu4OyvELo9aAYMFmVVKXjk++D0Fv5/JB9AQMMZ08sfjg8PRM8TDpptJD18oxoNfHYZOL+D7GX0xuJ2P2CURtZqskir8d+tZbDudBwBwd3bAvNFReLBvCGRS2/27JwYLaiXHMi/jox3nsedcoeG+7sHueHxwOMZ28odcZlvjg/M1NRj/8X4UVWgxsXsgPry/u02HKKIbiUstwsLNZ5CS/9eU6zfv6oTbIrxErozMhcGCWlVKXjm+2Z+ODcezDYM827g7YfrAMEzuEwy1o/WvTFmn02PKF4eQcPEyov1VWD9rAJwVcrHLIhJNvU6PlYczsfiPc4YVO8d3CcCC26MR5GE/XaP2gsGCRFFUocUPhy7i+4MXUVzZsDWzi0KGsZ0DcE/PNrgtwsuw1bg1KSzX4tnVR3HoQglUjnJsfmYQwrxdxC6LyCJcrqzFB3+kYNXhTOgFQCmXYubQtpg5tC2cFDKxyyMTYbAgUdXU6bDxeDa+2peO8wUVhvsD3BwxoXsb3N2zDdr7WcdqlYkXL2PWykTka7RwUciw5KFeGNKe4yqI/u5MjgYLNyfhcOOKnW3cnfD6nR0xppO/yJWRKTBYkEUQBAGJFy9j/bFsbDmRA03jan4A0DFAjbt7tsHojv4WOaOkUluPFXEZ+GjHOdTpBET6umLpQ73scnotUVMJgoCtp/Lw361nkd2439DIDr54865O7B6xcgwWZHG09TrsSi7A+qPZ2JVSgDrdX0+9cG8XDGnnjaFRPrgtwkvUsQtl1XX4Li4DXx9IR2nVX/3G79zbFa5KjqkgaorqWh0+3XUeX+y9gDqdACcHGZ4b2Q4zBoXDwcYGddsLBguyaJcra7HlZA42n8zF0YuXDYtuAYBCJkXvMA8Mae+DHsHu6BiohsrMgz+19TokZFzGzrMFWJeQhXJtQ8tKuLcLYmMicU/PNpz9QdQM5/PL8eovpw0bmkX5qfDWpM7oHeYpcmVkLAYLshrlNXWISyvGnnOF2HuuEJcu/3O79lAvZ3QKVKNToBs6BqoR7a+Cj6uy2dNZy6rqkHW5CkczL2NPSiHi0opRfdU+CFF+KsQOj8T4LgGcm0/UQoIg4Oej2fjv1rMoaRzU/UCfYLw8NhoeLlxcy1owWJBVEgQBF4oqsfdcw5t9UnYZchqXEf47iQTwclHAR+UIH5USviolfFRKyKUS6AUBegHQCwIEoWGqaG5pDbIuVyGzpMqwc+PVfFRKDG3vg7Gd/DE82tcqZ68QWbLLlbV457dkrInPAgB4uiiwYFw07u0VxBZBK2CWYPHmm29i4cKF19wXFRWF5ORkkxdGdEVJZS3O5GiQlFOGpBwNzuRqkF5UCZ2+ZZnY21WBdr4qDGnvg6HtfdAhQMUXN6JWkJBRglc3nDYsrtU33BNvTeyMdlYyU8xemS1Y/PTTT9ixY4fhPrlcDm9vb5MXRnQzOr2AkspaFJTXoKBci8KrboIgQCKRQCqRQCoBpNKGz/3USoR4OiPY0xlBHk5c3IpIRHU6Pb7Zn46PdpxHdZ0OcqkETw6JwLPD23HtCwvV1Pdvo19Z5XI5/P05J5nEJZNK4NPY9dFJ7GKIyGgOMimeGtoW47sG4M1NSdhxtgCf707DphM5+L8JnRET7St2idRMRo98O3/+PAIDAxEREYGpU6ciMzPzpsdrtVpoNJprbkRERAAQ5OGMr6b1wRcP90KgmyMuXa7G9BXxePqHROSW/XMgN1k+o7pCtm3bhoqKCkRFRSE3NxcLFy5EdnY2Tp8+DZXq+n1j1xuXAYBdIUREdI1KbT0+2nEO3xzIgE4vwEUhw9zRUZjWP9TmNjS0Rq0yK6S0tBShoaFYvHgxZsyYcd1jtFottFrtNYUFBwczWBAR0XWdzdXg1Q2ncDSzFEDDKr3/vbsLuge7i1qXvWtqsGhRBHR3d0f79u2Rmpp6w2OUSiXUavU1NyIiohvpEKDGTzMHYNHdXeDm5IAzuRpM+vwA/vXLKcMuqmS5WhQsKioqkJaWhoCAAFPVQ0REBKlUgil9Q7Bz3lDc3bMNBAH44VAmRnywB5tO5KCVl2AiIxgVLF544QXs2bMHGRkZiIuLw6RJkyCTyTBlyhRz1UdERHbM21WJxZO7Y9UT/RDh44KiCi1mrz6GmT8korBce+sfQK3OqGBx6dIlTJkyBVFRUZg8eTK8vLxw6NAh+PhwC2kiIjKfAW29se25wZgzsh3kUgm2J+Vj9IdsvbBEXNKbiIisSlJOGV5YdxJncxuWLxjbyR//mdQZ3q5KkSuzba0yeJOIiKi1dQp0w8bYgXhuREPrxW9JeRi1eA+2nMwRuzQCgwUREVkhhVyK50e1xy+xAxHtr8Llqjo8s+oYZq1MRFEFx16IicGCiIisVuc2btj0zCDMHh4JmVSCrafyMPrDvfj1ZK7YpdktBgsiIrJqCrkUc0dHYWNj60VJZS1iVx1F7MqjKGbrRatjsCAiIptwpfXi2cbWi19P5WL0h3ux9RRbL1oTgwUREdkMhVyKeaOj8MusgYjyU6G4shazVh5F7KqjKKmsFbs8u8BgQURENqdLkBs2PTsQz8Q0tl6czMWoxXuwja0XZsdgQURENkkpl+GFMVHYMGsA2vu5oriyFk+vPIpnVx9j64UZMVgQEZFN6xrkjs3PDsKsYW0hlQCbT+Rg9Id78NvpPLFLs0kMFkREZPOUchleGhuNDbMGop2vK4oqajHzh0S8sO4EqmrrxS7PpjBYEBGR3egW3NB68XRj68VPiZcw4dMDOJdfLnZpNoPBgoiI7Iqjgwwvj43Gqidug69KifMFFbjr0/1Ym5DFDc1MgMGCiIjs0m0RXtj63GAMbueNmjo9XvrpJOatPYFKLbtGWoLBgoiI7Ja3qxLfTu+LF8dEQSoB1h/Lxl2f7kdKHrtGmovBgoiI7JpUKkFsTCRWP3Eb/NRKpBVW4q5P9+PH+Ex2jTQDgwURERGAfhFe2Dp7MIa094G2Xo+Xfz6F5388zq4RIzFYEBERNfJyVWLFo33w0tgoyKQS/HI8B3d+uh9nczVil2Y1GCyIiIiuIpVKMGtYJNY8eRv81Y64UFiJiZ8dwOoj7BppCgYLIiKi6+gT5omtzw3GsKiGrpEF60/huTXHUcGukZtisCAiIroBTxcFvpnWB/PHRUMmlWDTiRzc+cl+nMlh18iNMFgQERHdhFQqwcyhbfHjk7chwM0R6UWVmPj5Aaw8fJFdI9fBYEFERNQEvcM8sXX2YAyP9kVtvR6vbjiNBetPoU6nF7s0i8JgQURE1EQeLgp89UhvLBgXDakEWBOfhce/TeC4i6swWBARERlBKpXgqaFtsezh3nB0kGLPuULcv+wg8jU1YpdmERgsiIiImmFURz+sebI/vFwUSMrRYNJn3CUVYLAgIiJqtu7B7tgwayAivF2QU1aDe5bEIS6tSOyyRMVgQURE1AIhXs74+ekB6BPmgfKaekz75gg2HLskdlmiYbAgIiJqIQ8XBb6f0Q/juwagTifg+R9P4NM/z9vldFQGCyIiIhNwdJDhkwd64KkhEQCA938/Z5fTURksiIiITEQqlWDB7R3w7wmd7HY6KoMFERGRiT3SP+ya6aiTl9rPdNQWBYu3334bEokEc+bMMVE5REREtmFURz/8+GR/eLsqcCa3YTpqSp7tT0dtdrCIj4/HsmXL0LVrV1PWQ0REZDO6Bbtj/dMDEeHTMB313qVxOJ5VKnZZZtWsYFFRUYGpU6fiyy+/hIeHh6lrIiIishkhXs5Yf9V01OnLjyC1wHZbLpoVLGJjYzF+/HiMHDnylsdqtVpoNJprbkRERPbE3VmB5dP7oluQGy5X1eHhr48gu7Ra7LLMwuhgsWbNGhw9ehSLFi1q0vGLFi2Cm5ub4RYcHGx0kURERNbOVSnH8ul90dbHBbllNXj468MortCKXZbJGRUssrKy8Nxzz2HlypVwdHRs0jkLFixAWVmZ4ZaVldWsQomIiKydZ+NCWoFujrhQWInpK+JtbiqqRDBiWbBffvkFkyZNgkwmM9yn0+kgkUgglUqh1Wqv+d71aDQauLm5oaysDGq1uvmVExERWanUggpMXnYQJZW1GNDWC8un94FSfvP3T7E19f3bqBaLESNG4NSpUzh+/Ljh1rt3b0ydOhXHjx+/ZaggIiIiINLXFSum94GLQoa4tGI8t/o4dHrbWP7bqGChUqnQuXPna24uLi7w8vJC586dzVUjERGRzeka5I4vH+kNhUyK35Ly8OqGUzaxtwhX3iQiIhLJgEhvfDylu2H573e3p4hdUosZNcbCFDjGgoiI6Fo/xmfi5Z9PAQBeuT0aTw5pK3JF/2SWMRZERERkevf3CcH8cdEAgP9uTcbaBOudQclgQUREZAFmDm1r2HJ9wfpTOJp5WeSKmofBgoiIyELMHxeNO7oGQKcXMG/tCVTX6sQuyWgMFkRERBZCIpHgrUld4K92RHpRJd7edlbskozGYEFERGRB3Jwc8N59DTuHf3vwIvafLxK5IuMwWBAREVmYwe188PBtoQCAF386gbLqOpErajoGCyIiIgu04PZohHk5I7esBgs3JYldTpMxWBAREVkgZ4UcH0xuWDxr/bFs/HY6V+ySmoTBgoiIyEL1CvXAzKENi2W9suE0Csstf5t1BgsiIiILNmdke3QIUKOkshavWMF+IgwWREREFkwhl2Lx5G5wkEnwx5l8/JR4SeySborBgoiIyMJ1CFBj7qgoAMDCzWdQVGG5XSIMFkRERFbgySER6NxGjQptPb6LyxC7nBtisCAiIrICMqkEs4ZFAgC+O3QRVbX1Ild0fQwWREREVmJMJ3+EejmjtKoOa+MtcwdUBgsiIiIrIZNK8Pjghh1Qv9qfjnqdXuSK/onBgoiIyIrc1ysIXi4KXLpcja2n88Qu5x8YLIiIiKyIo4MMj/QPAwAs25NmcetaMFgQERFZmUf6h8LJQYakHA3i0orFLucaDBZERERWxsNFgcm9gwAAy/ZeELmaazFYEBERWaHHB0dAKgH2nivEmRyN2OUYMFgQERFZoWBPZ9zeJQAA8MPhiyJX8xcGCyIiIit1T8+G7pB95wtFruQvDBZERERWqm+4J+RSCbJKqpFZXCV2OQAYLIiIiKyWi1KO7sHuAIADaUXiFtOIwYKIiMiKDYj0BgAcSGWwICIiohYa1BgsDqYVQ68Xf7EsBgsiIiIr1j3YHU4OMhRX1iIlv1zschgsiIiIrJlCLkXfcE8AltEdwmBBRERk5QZGegGARSzvzWBBRERk5Qa0bRhncfhCsehbqRsVLJYsWYKuXbtCrVZDrVajf//+2LZtm7lqIyIioiboGKCGg0yCylod8su1otZiVLAICgrC22+/jcTERCQkJGD48OGYMGECkpKSzFUfERER3YJUKoGf2hEAkFdWLW4txhx855134vbbb0e7du3Qvn17vPXWW3B1dcWhQ4fMVR8RERE1QaCbEwAgp7RG1DrkzT1Rp9Nh3bp1qKysRP/+/W94nFarhVb7V7OMRmM5O7ARERHZCn+3Ky0W4gYLowdvnjp1Cq6urlAqlZg5cyY2bNiAjh073vD4RYsWwc3NzXALDg5uUcFERET0TwHuDcEi19qCRVRUFI4fP47Dhw/j6aefxrRp03DmzJkbHr9gwQKUlZUZbllZWS0qmIiIiP4pQH0lWIg7xsLorhCFQoHIyEgAQK9evRAfH4///e9/WLZs2XWPVyqVUCqVLauSiIiIbirAvWGMhdW1WPydXq+/ZgwFERERtb4ANytssViwYAHGjRuHkJAQlJeXY9WqVdi9eze2b99urvqIiIioCQIaZ4UUlGtRr9NDLhNnDUyjgkVBQQEeeeQR5Obmws3NDV27dsX27dsxatQoc9VHRERETeCilAEABAGo0wmQy8Spw6hg8fXXX5urDiIiImoBCSSGz/WCeNunc68QIiIiGyD5K1dAvFjBYEFERGQTpBK2WBAREZGJSK9usRBxg1MGCyIiIhsgYYsFERERmYqUYyyIiIjIVNhiQURERCaj0/8VJq4eyNnaGCyIiIhsQEVNveFzV6XRW4GZDIMFERGRDdDU1AEAHB2kUMjFe3tnsCAiIrIBV4KFytFB1DoYLIiIiGxAeWNXiMpRvG4QgMGCiIjIJvwVLNhiQURERC1U3tgVomaLBREREbWUpvrKGAsGCyIiImqh0sZg4ebErhAiIiJqoXyNFgDgq3IUtQ4GCyIiIhtQoKkBAPipGSyIiIiohfLLrwQLpah1MFgQERHZgCtdIWyxICIiohap1+lRVMFgQURERCZQVFELQQBkUgm8XBSi1sJgQUREZOXyGgdu+qqUkErF2zIdYLAgIiKyetmXqwEAAW7idoMADBZERERWL6O4EgAQ6uUiciUMFkRERFYvs7gKABDi6SxyJQwWREREVu9iyZUWCwYLIiIiaqErLRYMFkRERNQi2nodchtnhYR4cowFERERtUBWSTUEAXBWyODtKu4aFgCDBRERkVVLL/prRohEIu4aFgCDBRERkVVLydMAAKL9VSJX0oDBgoiIyIol55UDAKKsMVgsWrQIffr0gUqlgq+vLyZOnIiUlBRz1UZERES3YNXBYs+ePYiNjcWhQ4fwxx9/oK6uDqNHj0ZlZaW56iMiIqIb0NbrDGMsLKUrRG7Mwb/99ts1X69YsQK+vr5ITEzEkCFDTFoYERER3VxqQQV0egFqRzn8Rd4u/QqjgsXflZWVAQA8PT1veIxWq4VWqzV8rdFoWvKQRERE1CilsRskOkBtETNCgBYM3tTr9ZgzZw4GDhyIzp073/C4RYsWwc3NzXALDg5u7kMSERHRVU5nN/yz3sFCukGAFgSL2NhYnD59GmvWrLnpcQsWLEBZWZnhlpWV1dyHJCIioqskZl4GAPQM9RC5kr80qyvkmWeewZYtW7B3714EBQXd9FilUgmlUtms4oiIiOj6qmt1SMpuGJLQM8RKg4UgCHj22WexYcMG7N69G+Hh4eaqi4iIiG7i5KVS1OsF+KqUCPJwErscA6OCRWxsLFatWoWNGzdCpVIhLy8PAODm5gYnJ8v5pYiIiGzdlW6Q3mEeFjNwEzByjMWSJUtQVlaGYcOGISAgwHD78ccfzVUfERERXUdiRuP4CgvqBgGa0RVCRERE4tLrBRw1tFjceMkHMXCvECIiIitzOqcMl6vq4KKQoWOAWuxyrsFgQUREZGV2ni0AAAxp7wOF3LLeyi2rGiIiIrqlncn5AIDh0b4iV/JPDBZERERWJK+sBqezNZBIgBgGCyIiImqJXSkN3SDdg93h7Wp5C1AyWBAREVmRnWcbukFGdvATuZLrY7AgIiKyEmXVddh3vgiAZY6vABgsiIiIrMam49nQ1usR7a9CtAXtaHo1BgsiIiIrsSa+YYfw+/sEW9Qy3ldjsCAiIrICp7PLkJSjgUIuxaQebcQu54YYLIiIiKzAmvhMAMDYTv5wd1aIXM2NMVgQERFZuOpaHTYeywEAPNAnWORqbo7BgoiIyML9fPQSyrX1CPF0xm0RXmKXc1MMFkRERBZMW6/D57tSAQDTB4ZBKrXMQZtXMFgQERFZsLUJl5BTVgM/tRJT+oaIXc4tMVgQERFZqKtbK2YNi4Sjg0zkim6NwYKIiMhCrY3PQm5ZDfzVjrjfwgdtXsFgQUREZIFq6nT4bFcaACA2pq1VtFYADBZEREQW6at9F5CnqUGAmyMmW0lrBcBgQUREZHEuFFbg4z8bxlbMHxcNpdw6WisABgsiIiKLIggCFqw/hdp6PYa298Fd3QLFLskoDBZEREQWZG1CFg6nl8DJQYb/TOxssZuN3QiDBRERkYUoLNfirV/PAgDmjmqPYE9nkSsyHoMFERGRBRAEAW9uToKmph6d26gxfWCY2CU1C4MFERGRBVh5OBO/nsyFTCrB23d3hVxmnW/R1lk1ERGRDTmeVYp/bz4DAHhpTBQ6t3ETuaLmY7AgIiISUUllLWb9kIhanR5jO/njySERYpfUIgwWREREItHpBcxefQw5ZTWI8HbBe/d1tbpZIH/HYEFERCSSD/84h/2pRXBykGHpw72gcnQQu6QWY7AgIiISwcbj2fi0cefSt+/pgvZ+KpErMg0GCyIiola2K7kA89aeAAA8NjAcE7q3Ebki0zE6WOzduxd33nknAgMDIZFI8Msvv5ihLCIiItuUkFGCp1cmol4v4K5ugfjX+A5il2RSRgeLyspKdOvWDZ999pk56iEiIrJZZ3M1eGxFPGrq9BgW5YMPJneDVGrdgzX/Tm7sCePGjcO4cePMUQsREZHNulhciYe/PgJNTT16h3pgydRecLDSRbBuxuhgYSytVgutVmv4WqPRmPshiYiILEpeWQ0e+vowiiq0iPZX4etH+8BJYT1boRvD7FFp0aJFcHNzM9yCg4PN/ZBEREQWI6OoEvcujUNWSTVCvZzx3Yy+cHOy/mmlN2L2YLFgwQKUlZUZbllZWeZ+SCIiIouQkleO+5YdxKXL1QjzcsbKx/vBV+UodllmZfauEKVSCaVSae6HISIisijHs0rx6PIjKK2qQ7S/Ct/N6GvzoQJohWBBRERkb+LSivDEtwmorNWhR4g7VjzaF27Ottv9cTWjg0VFRQVSU1MNX6enp+P48ePw9PRESEiISYsjIiKyNjvO5GPWqqOorddjQFsvfPlIb7go7ef/eKN/04SEBMTExBi+njt3LgBg2rRpWLFihckKIyIisjarj2TitV9Oo14vYFRHP3wypQccHWxz9seNGB0shg0bBkEQzFELERGRVdLpBSzaehZf7U8HANzdow3euberTa5TcSv20zZDRERkBhXaejy3+hh2JhcAAOaOao9nh0da/fbnzcVgQURE1EzZpdWYsSIeyXnlUMqleP++brizW6DYZYmKwYKIiKgZjmeV4vFvE1BUoYW3qxJfPtILPUI8xC5LdAwWRERERtp8IgcvrDsBbb3esER3G3cnscuyCAwWRERETVSn0+OdbcmGQZojon3xvyk94GpH00lvhVeCiIioCQrKa/DMymM4klECAJg5tC1eHBMFmY1te95SDBZERES3EJ9RgtiVR1FQroWrUo737+uGsZ39xS7LIjFYEBER3YAgCFh+IAP/3XoW9XoB7f1csfShXojwcRW7NIvFYEFERHQdldp6zF9/CptP5AAA7uwWiLfv7mJXy3M3B68OERHR35zPL0fsqqM4l18BuVSCV8d3wKMDwux20StjMFgQERE1EgQBaxOy8MamJNTU6eGrUuKzqT3RJ8xT7NKsBoMFERERgPKaOryy4bSh62NwO28sntwdPiqlyJVZFwYLIiKyeycvleLZ1cdwsbgKMqkEL4yOwlNDIiDlVFKjMVgQEZHdEgQBX+9Pxzu/JaNOJ6CNuxM+ntIDvUK5NHdzMVgQEZFdKqmsxYvrThh2JR3byR/v3NMVbs4OIldm3RgsiIjI7hxILcK8tSeQp6mBQi7Fa3d0xEP9QjjrwwQYLIiIyG7U1Onw3vYUfN2410eEjws+ndITHQPVIldmOxgsiIjILpzN1WDOmuNIyS8HAEztF4JXx3eAs4JvhabEq0lERDZNrxfw1f4LeH/7OdTq9PB2VeDde7tieLSf2KXZJAYLIiKyWTml1Zi39gQOXigGAIzs4Ie37+kCb1euTWEuDBZERGSTNh7Pxr9+OY3ymno4Ocjw+p0d8UCfYA7QNDMGCyIisimXK2vxxqYkbGpcQbN7sDs+vL87wr1dRK7MPjBYEBGRzfjtdC7+9UsSiiq0kEkleHZ4JJ6JiYRcJhW7NLvBYEFERFavuEKL1zcl4deTuQCASF9XvHdvV/QI4QqarY3BgoiIrJYgCNh8MhdvbkpCSWUtZFIJZg6NwOwR7aCUy8Quzy4xWBARkVUqKK/Bvzacxu9n8gEA0f4qvH9fN3Ru4yZyZfaNwYKIiKyKIAjYcCwbCzefQVl1HeRSCZ4ZHolZwyKhkHMshdgYLIiIyGrkllXj1Q2n8WfjxmGd26jx3r3d0CGAS3JbCgYLIiKyeHU6PVYcyMBHO86hslYHhUyK50a2w1NDIjjjw8IwWBARkUWLSyvCGxuTcL6gAgDQI8Qd797TFe38VCJXRtfDYEFERBYpt6wab/16Flsap5B6uigwf2w07u0VBKmUq2daqma1H3322WcICwuDo6Mj+vXrhyNHjpi6LiIislO19Xos3ZOGER/swZaTuZBKgEf6h2LXvGGY3CeYocLCGd1i8eOPP2Lu3LlYunQp+vXrh48++ghjxoxBSkoKfH19zVEjERHZif3ni/DGptNIK6wEAPQMcce/J3TmFFIrIhEEQTDmhH79+qFPnz749NNPAQB6vR7BwcF49tlnMX/+/Fuer9Fo4ObmhrKyMqjVHMVLREQNu5D+59cz2HoqDwDg7arA/HEdcHePNmyhsBBNff82qsWitrYWiYmJWLBggeE+qVSKkSNH4uDBg9c9R6vVQqvVXlMYERERAGjrdfhqXzo+/TMV1XW6xm6PMDw/qj3cnBzELo+awahgUVRUBJ1OBz8/v2vu9/PzQ3Jy8nXPWbRoERYuXNj8ComIyGadyCrDe9tTAAB9wjyw8K7O6BjI1mxrZvZZIQsWLMDcuXMNX2s0GgQHB5v7YYmIyAr0DffEowPC0DXIDZN6tIFEwm4Pa2dUsPD29oZMJkN+fv419+fn58Pf3/+65yiVSiiVyuZXSERENu3NuzqJXQKZkFHTTRUKBXr16oWdO3ca7tPr9di5cyf69+9v8uKIiIjIuhjdFTJ37lxMmzYNvXv3Rt++ffHRRx+hsrIS06dPN0d9REREZEWMDhb3338/CgsL8frrryMvLw/du3fHb7/99o8BnURERGR/jF7HoqW4jgUREZH1aer7N7eEIyIiIpNhsCAiIiKTYbAgIiIik2GwICIiIpNhsCAiIiKTYbAgIiIik2GwICIiIpNhsCAiIiKTYbAgIiIikzH7tul/d2WhT41G09oPTURERM105X37Vgt2t3qwKC8vBwAEBwe39kMTERFRC5WXl8PNze2G32/1vUL0ej1ycnKgUqkgkUhuebxGo0FwcDCysrK4t8gt8FoZh9fLOLxeTcdrZRxeL+OIdb0EQUB5eTkCAwMhld54JEWrt1hIpVIEBQUZfZ5areYTrol4rYzD62UcXq+m47UyDq+XccS4XjdrqbiCgzeJiIjIZBgsiIiIyGQsPlgolUq88cYbUCqVYpdi8XitjMPrZRxer6bjtTIOr5dxLP16tfrgTSIiIrJdFt9iQURERNaDwYKIiIhMhsGCiIiITIbBgoiIiEzGooJFRkYGZsyYgfDwcDg5OaFt27Z44403UFtbe9Pzhg0bBolEcs1t5syZrVS1eJp7vWpqahAbGwsvLy+4urrinnvuQX5+fitVLa633noLAwYMgLOzM9zd3Zt0zqOPPvqP59fYsWPNW6gFaM61EgQBr7/+OgICAuDk5ISRI0fi/Pnz5i3UQpSUlGDq1KlQq9Vwd3fHjBkzUFFRcdNz7Om167PPPkNYWBgcHR3Rr18/HDly5KbHr1u3DtHR0XB0dESXLl2wdevWVqrUMhhzvVasWPGP55Gjo2MrVnstiwoWycnJ0Ov1WLZsGZKSkvDhhx9i6dKleOWVV2557hNPPIHc3FzD7d13322FisXV3Ov1/PPPY/PmzVi3bh327NmDnJwc3H333a1Utbhqa2tx33334emnnzbqvLFjx17z/Fq9erWZKrQczblW7777Lj7++GMsXboUhw8fhouLC8aMGYOamhozVmoZpk6diqSkJPzxxx/YsmUL9u7diyeffPKW59nDa9ePP/6IuXPn4o033sDRo0fRrVs3jBkzBgUFBdc9Pi4uDlOmTMGMGTNw7NgxTJw4ERMnTsTp06dbuXJxGHu9gIZVOK9+Hl28eLEVK/4bwcK9++67Qnh4+E2PGTp0qPDcc8+1TkEW7lbXq7S0VHBwcBDWrVtnuO/s2bMCAOHgwYOtUaJFWL58ueDm5takY6dNmyZMmDDBrPVYsqZeK71eL/j7+wvvvfee4b7S0lJBqVQKq1evNmOF4jtz5owAQIiPjzfct23bNkEikQjZ2dk3PM9eXrv69u0rxMbGGr7W6XRCYGCgsGjRouseP3nyZGH8+PHX3NevXz/hqaeeMmudlsLY62XM61lrsKgWi+spKyuDp6fnLY9buXIlvL290blzZyxYsABVVVWtUJ3ludX1SkxMRF1dHUaOHGm4Lzo6GiEhITh48GBrlGiVdu/eDV9fX0RFReHpp59GcXGx2CVZnPT0dOTl5V3z3HJzc0O/fv1s/rl18OBBuLu7o3fv3ob7Ro4cCalUisOHD9/0XFt/7aqtrUViYuI1zwupVIqRI0fe8Hlx8ODBa44HgDFjxtj88who3vUCgIqKCoSGhiI4OBgTJkxAUlJSa5R7Xa2+CZkxUlNT8cknn+D999+/6XEPPvggQkNDERgYiJMnT+Lll19GSkoK1q9f30qVWoamXK+8vDwoFIp/9Jn7+fkhLy/PzBVap7Fjx+Luu+9GeHg40tLS8Morr2DcuHE4ePAgZDKZ2OVZjCvPHz8/v2vut4fnVl5eHnx9fa+5Ty6Xw9PT86a/uz28dhUVFUGn0133eZGcnHzdc/Ly8uzyeQQ073pFRUXhm2++QdeuXVFWVob3338fAwYMQFJSUrM2/WypVmmxmD9//j8Glvz99vcLlp2djbFjx+K+++7DE088cdOf/+STT2LMmDHo0qULpk6diu+++w4bNmxAWlqaOX8tszH39bI1zblexnjggQdw1113oUuXLpg4cSK2bNmC+Ph47N6923S/RCsx97WyNea+Xrb22kXi6N+/Px555BF0794dQ4cOxfr16+Hj44Nly5aJUk+rtFjMmzcPjz766E2PiYiIMHyek5ODmJgYDBgwAF988YXRj9evXz8ADf/Bt23b1ujzxWbO6+Xv74/a2lqUlpZe02qRn58Pf3//lpQtGmOvV0tFRETA29sbqampGDFihMl+bmsw57W68vzJz89HQECA4f78/Hx07969WT9TbE29Xv7+/v8YWFdfX4+SkhKj/q6s/bXrery9vSGTyf4x8+xmrzn+/v5GHW9LmnO9/s7BwQE9evRAamqqOUq8pVYJFj4+PvDx8WnSsdnZ2YiJiUGvXr2wfPlySKXGN6ocP34cAK55cbMm5rxevXr1goODA3bu3Il77rkHAJCSkoLMzEz079+/xbWLwZjrZQqXLl1CcXGxVT6/zHmtwsPD4e/vj507dxqChEajweHDh42ehWMpmnq9+vfvj9LSUiQmJqJXr14AgD///BN6vd4QFprC2l+7rkehUKBXr17YuXMnJk6cCADQ6/XYuXMnnnnmmeue079/f+zcuRNz5swx3PfHH39Y7WuUMZpzvf5Op9Ph1KlTuP32281Y6U2IPXr0apcuXRIiIyOFESNGCJcuXRJyc3MNt6uPiYqKEg4fPiwIgiCkpqYK//73v4WEhAQhPT1d2LhxoxARESEMGTJErF+j1TTnegmCIMycOVMICQkR/vzzTyEhIUHo37+/0L9/fzF+hVZ38eJF4dixY8LChQsFV1dX4dixY8KxY8eE8vJywzFRUVHC+vXrBUEQhPLycuGFF14QDh48KKSnpws7duwQevbsKbRr106oqakR69doFcZeK0EQhLfffltwd3cXNm7cKJw8eVKYMGGCEB4eLlRXV4vxK7SqsWPHCj169BAOHz4s7N+/X2jXrp0wZcoUw/ft+bVrzZo1glKpFFasWCGcOXNGePLJJwV3d3chLy9PEARBePjhh4X58+cbjj9w4IAgl8uF999/Xzh79qzwxhtvCA4ODsKpU6fE+hValbHXa+HChcL27duFtLQ0ITExUXjggQcER0dHISkpSZT6LSpYLF++XABw3dsV6enpAgBh165dgiAIQmZmpjBkyBDB09NTUCqVQmRkpPDiiy8KZWVlIv0Wrac510sQBKG6ulqYNWuW4OHhITg7OwuTJk26JozYsmnTpl33el19fQAIy5cvFwRBEKqqqoTRo0cLPj4+goODgxAaGio88cQThj9wW2bstRKEhimnr732muDn5ycolUphxIgRQkpKSusXL4Li4mJhypQpgqurq6BWq4Xp06dfE8Ls/bXrk08+EUJCQgSFQiH07dtXOHTokOF7Q4cOFaZNm3bN8WvXrhXat28vKBQKoVOnTsKvv/7ayhWLy5jrNWfOHMOxfn5+wu233y4cPXpUhKobcNt0IiIiMhmLX8eCiIiIrAeDBREREZkMgwURERGZDIMFERERmQyDBREREZkMgwURERGZDIMFERERmQyDBREREZkMgwURERGZDIMFERERmQyDBREREZkMgwURERGZzP8DdQ1nqoRZ2ugAAAAASUVORK5CYII=",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Vector{PyCall.PyObject}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f32bd057550>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot(thist,xtraj[1,:])\n",
    "# plot(thist,xtraj[2,:])\n",
    "plot(xtraj[1,:],xtraj[2,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Vector{PyCall.PyObject}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2f396eda50>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(thist,xtraj[3,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Vector{PyCall.PyObject}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x7f2f4dac14b0>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(thist[1:Nt-1],utraj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "    <div style=\"height: 500px; width: 100%; overflow-x: auto; overflow-y: hidden; resize: both\">\n",
       "    <iframe src=\"http://127.0.0.1:8701\" style=\"width: 100%; height: 100%; border: none\"></iframe>\n",
       "    </div>\n"
      ],
      "text/plain": [
       "MeshCat.DisplayedVisualizer(MeshCat.CoreVisualizer(MeshCat.SceneTrees.SceneNode(nothing, nothing, Dict{String, Vector{UInt8}}(), nothing, Dict{String, MeshCat.SceneTrees.SceneNode}()), Set{Any}(), ip\"127.0.0.1\", 8701))"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using TrajOptPlots\n",
    "using MeshCat\n",
    "using StaticArrays\n",
    "\n",
    "vis = Visualizer()\n",
    "render(vis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MeshCat Visualizer with path /meshcat/robot/link1/joint at http://127.0.0.1:8701"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "TrajOptPlots.set_mesh!(vis, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = [SVector{4}(x) for x in eachcol(xtraj)];\n",
    "visualize!(vis, a, thist[end], X1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.8.5",
   "language": "julia",
   "name": "julia-1.8"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}