Raw File
{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Dynamic optimization of walking on uneven terrain\n",
        "\n",
        "A simple walking model is optimized to walk over uneven terrain. The\n",
        "objective is to minimize energy expenditure, quantified by the push-off\n",
        "work performed with each step. The optimization here seeks to traverse a\n",
        "stretch of terrain, starting and ending at level walking, and taking the\n",
        "same amount of time as level walking.\n",
        "\n",
        "## Walk over a single upward step\n",
        "\n",
        "The optimal compensation for a single upward step is to speed up\n",
        "beforehand, lose speed stepping upward, and then speed up again\n",
        "afterward. The optimal speed-ups both occur over several steps but have\n",
        "different shapes: the first one increases nearly exponentially with\n",
        "time, and the second one resembles a saturating exponential. The\n",
        "optimization is described by Darici et al. (2020), and tested with human\n",
        "subjects experiment (Darici and Kuo 2022)."
      ],
      "id": "bc47b3f0-6a1a-4017-a054-eb1c3bed5791"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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ecePGJScn6+5k/FJRUVE//PBD+/btT548+euvv1bY2+vvv/8eNWpUSEiIUqlM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          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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s7+9vXQtGRMeOHWvevHlERIRWq7VYLLc/AoCLcMI3nazQogtAfjjGHPUp22AwcBxnl9Pr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\n0wVB4DguNDSU47h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rHF8SANiHrwdZGBkt5IMWXXAH1kncav9NK6GrBmadvhX/2zaIGxHF\nadUU4cfhCq12dzOPfXx8xo0bJ95mjK1cubKiomLo0KFhYWFXr1795ZdfGGP9+vWTrk4AqI8wXy4P\nLbqUrUKwMcYV/3uphHEcaX05nd+f/+0cQrH+vFZNYb4cjz8cJ7qZx/7+/gsWLBBvL1y4sHnz5lu2\nbNFobjbLMBgMDz74YH5+vjQ1AkB9oUWXAl0z0tECdvQ6O1bAjl5nV/VekRqLVk3hai7cj7RqrkNj\n0qr5SD9q6ou+vC7ExvzxF198sWzZMmsYE5Gvr+/cuXMnTZr09ttvO7E2AGgotOhSghw9O1LAUgvp\ndCE7UsCKKqhTCLUN4oZHca934pt5Gqsez8Fl2cjjwsLC8vLyahv1en1RUZFTSgIAu8ESa1kSA1j8\n3x/XGMdR5xCucwg3LpZ7v7sqzPcvO5eVSVQl1JGNPO7Vq9e//vWvDh06tG7dWtxy8eLFOXPm9O7d\n27m1AUBDabHEWhaqBvDv+cyTvxnAT7Xiv+nN47I08mAjj5ctWzZgwIB27dq1adMmLCwsPz//1KlT\n4eHhn376qfPrA4CGQIsud2QW6FzxnwF8qpCFqzkxgF/qwN8bwvnhm6pyZOP/1ejo6JMnT65YseLo\n0aPZ2dldu3Z98sknp0yZ4u+PNSEAbgYtutxCpUDnqwRwyg0W4XczgMfF8J1DOF8EsALY/j/Zz89v\n+vTpTi4FAOwO88euqaySjl9nqUVMXIF1toi1CuTaBnFtArlxMXzXJne87C7IGD50AcgZ5o9dR1EF\nrboo7LvKjhWw6ybWMZjrFMz1COWeacM3b4Rv+sKtPM7Pz2/VqtWwYcNWrlw5bNiwgwcP3r5r586d\nd+zY4dzyAKBB1B5kYWSyEMZbEjpVyD45Lfx8WRjVjB8Xw83vwqNDC9zuZh77+fnNnj27ZcuWRDRp\n0qSePXvevqtOp3NqaQBgD2G+XC5adElBYLQ5S1h2WkgvpSfj+dSxnsHeUtcELuzPPH755ZfF25Mn\nT5auHgCwM7Tocr6iClp+Xlh6WohrRE+14kdH8yp8HIK7wfwxgMyhRZczHS1gX5wVNlwWHmzGb3pA\n1SYQLzvUlu08/vXXX9esWXPlyhWTyWTdGB8f/8knnzirMACwDyyxdoIKgTZcFr48K2SW0eMt+bPj\nPANx+SOoI9v9QJ5//vnmzZu3atUqKCjIur1Ro0ZOLAwA7ANLrB0qz0DLzwufnhFaBtBzbfnhUVgo\nDfVkI48//vjjGTNmLFu2jOPwdwXg9rRo0eUYRwrY0lPC1ivCw3F88jAVVsxBA9nI45KSksGDByOM\nAeRBp+Zy9WjRZTcmC/2YJnx4SuCInm7Nf97TU411OGAPNv6OEhIS9u7dO2LECOdXAwB2p1NTjl7q\nImQhu5x9dU748qzQsym/qJtqYDgGLWBPNvL4ww8/HDNmzOzZs4cMGRIYGGjd7ufn16pVKyfWBgB2\ngPnjhtuXx5adFg7ks8nNuUMPekT6IYnB/mzkcWlpqclkWrx48eLFi6tu79at26FDh5xVGADYh9qD\nzAIZLeSDFl11VFpJ318SPj4teKvoqVb8ir4qvIbgODby+IknnsjMzExMTIyPj/fx+fO6mn5+fk4s\nDADsRqvmrhpYMw1GdbV1oZglnheWnxd6hfFf9lL1CMVLBw5nI48PHz78ySefPPLII86vBgAcQZxC\nbqaRug6XJzD6LYctPW05dp2eiOdSxniG+Nz9pwDswkYeR0RE8Dzv/FIAwEHQouuuiivov+eFpacF\nnZqeb8f/PJD3wFEQnMvGX9xrr722ePHigoIC51cDAI6AFl01OFvEnj9oiV9TmVrENg5W7RvhMS4G\nYQwSsDE+Pn36dEFBQVxcXNeuXRs3bmzd3rx58/fee8+JtQGAfWCJ9e3MAv2UIXySKuQb6Jk2/Pnx\nno08pa4JlM32+mrxwotEVFhYaN1eUlLipKIAwK7Qoqsao4XG/Wo2mOnVjqrBEWh+BC7BRh4vWbLE\n+XUAgOOgRVdVejON2mGO9uc+v1+FZtPgOjBJAiB/WrTouqW4ggZvNbcI4L7oiTAG14I8BpA/HeaP\niYio0EQP/GLuGcb9+/9UyGJwNchjAPmztuhSsqsG6rvZnBDBL+iKJlvgipDHAIogtuiSugrJZJWz\nPpvMj7XkX++Egx64KPxpAiiCkqeQM0rZgC2W2R34me1wxAPXhb9OAEVQ7BTy2SLWd7Pl1Y781Hgc\n7sCl4TraAIqgzKsgH7/Ohm+3LOvBj45GGIOrQx4DKIICW3T9UcAe2mFJ7KV6IAKLqcEN4DMjgCIo\nbf54bx4bud383z4IY3AbGB8DKIKiWnT9coVN3WP5aaAHrlsMbgR5DKAIyhkfb8pkzxywbH5A1TEY\nYQzuBOerARRBIeurf7gk/GM/whjcEvIYQBGU0KJr5UXhX38Ivw1TtQtCGIP7QR4DKIW8W3R9dkZ4\n77iwe7iqeSOEMbgl5DGAUsh4CnnhCeGT08KvQ1WRfghjcFdYzwWgFLemkOWWWAtPCKvTheThHiE+\nUpcC0ADIYwClkN/4mBG9+LvlcAH7bahHgJfU1QA0DPIYQClk1qKLET13wJJSyLY84OHvKXU1AA2G\n+WMApdCpKVcu42MLo8eSLWmlbCvCGOQC42MApdCpuRxZtOiqEOjhXRYVR+sHeXhiTAFygb9lAKWQ\nx/yxyULjfrV487SqrwphDHLiqPFxRUXFvn37OI7r2bOnp+cdTyedOXPGx8cnJiZGvJuRkXHmzJmQ\nkJDOnTvzPE9EZrP5xIkT1v1jY2ODgoIcVDOAvMmgRVe5mUbtMMf5c5/er+Lltk4clM4heVxaWtqr\nV6/Q0FDGWGFhYXJysp+f3+27/f7773369Bk3bty3335LRDNnzkxKSurUqdOFCxd8fHx27typ0WhK\nSkq6det27733ij8yf/78QYMGOaJmANkTW3SZLOStkrqUeimqoKG/mHuGcQu7qZDFID8OOd2TmJgY\nHh6+ffv27du3BwcHr1ix4vZ9TCbTc889N2XKFOuWZ5999sKFC2vWrDl69ChjTAxpIvL19f3jFoQx\nQENo1Vyee7boumGiwVvNvbXc+whjkCmH5PGWLVvGjBlDRBzHjR49esuWLbfv8+abb06aNMl6ppqI\n4uLixHPUPM+HhIRUVlaK2wVBSEpK2rZtW3FxsSOqBVAON51CzjNQ383mEVH8gq7uObQHqAWHnK/O\nzs7WarXibZ1Ol52dXW2H48ePJycn79mz5/3337/9x5OTk//4449vvvlGvNu2bdv169fn5OQcPXo0\nKSmpW7dud3re4uLit99+W6PRiHcHDhzYt2/fhv86bs1kMnEcJ37QAXsRBMFkMqlU7pcNTb25zGJL\npwCp67gDk8l0+3KTrHIaupOf1pLNaG0xmSSpy73ZfFWhgcxms9ls5rjanqzhOM7L6y49axySxyqV\nirGb58QEQah22DKbzdOmTfv8889tHs5OnTr1yCOPfPvtt6GhoUTUuHHjw4cPi/+0YMGC2bNnJycn\n1/C8gYGB/v7+4l2NRoMc4m+RuhC5cdNXVedHeUbOZQu//VXNKKOEHfRSB/p7c05+nT6dw03/Vl1c\nXQ+ttUluh+Rx1TFxdna2Tqer+q9Hjx49ffr0k08+SUR5eXkGg2HChAk//vgjEZ07d27o0KGfffaZ\nzXnivn37Llu2rIbn1Wg0zz77bLWnUzhPT09PT0+8G+1LEASLxeKOY45wjZBvZJ6eLjqyF/9crXfP\nFLEh2yzvduEnN8cfcP1Ve1XBLjiO4zjOvi+sQ/7KR44cuXr1asaYIAhr164dOXIkEZWWliYlJRHR\nPffcc/LkydWrV69evfrhhx/u1avXBx98QEQXL14cPHjwokWLRowYYX2okpIS61B73bp17du3d0TB\nAArhRi26jhawQVstS3sgjEEpHDI+njJlyrffftuzZ09BELy8vB5++GEiunz58siRIxlj3t7esbGx\n4p5BQUEajSYiIoKIZs+eXVxcvGjRokWLFhHRxIkTZ82a9f333y9cuLBNmzZZWVkmk+nnn392RMEA\nCqF1kxZdh6+x0Tst3/RWDQrHOWpQCs46+rQvQRCOHj3Kcdy9995r7eyRl5cnRq9VUVFRRUWFOFWc\nl5en1//50T0gICA4OJiIMjIyMjMzg4ODW7VqVfMKmhYtWiQnJ+N8dVV6vd7Hxwfnq+1LEASj0ahW\nq6UupM4ulrAxOy0nRrtoo9yysjKNRpOcyybtMq/q59FPizC2A/FVlboKuRHXc/n42PMan456W/I8\n36VLl788k4dHtTAmosDAQOvtsLAwmw8VHR0dHR1t7wIBlEin5nJcu0XX1iz2xF7LzwM9uocijEFZ\nMGwCUBBriy7XtCWbf3q/ZesQFcIYFAh5DKAsYa7aouu7S8KLRzy3PKDq0BhhDEqEPAZQFtdcYv3l\nWeG1P4Qt/SvaBiGMQaFcdFkHADiI9uYUsgvF3veXhI9OCXuGqwIcs7wUwC1gfAygLK42PhYYvXlU\nWNFXFe7nQh8RAJwPeQygLFoXW2K94bIQ7kddQhDGoHTIYwBlcbXx8eIUYXYHF+3fCeBMyGMAZXGp\n8fH/rrGSCnogAoNjAOQxgMK41Ph4/nFhdgceaQxAyGMApdGpuVzXGB+fL2ZHCtjEOByFAIiQxwBK\no/agStdo0fVBivBcO94LByEAIkIeAyiQK7ToyjfQ+svCk/E4BAHchDcDgOK4whTyx6mWKS34AC+J\nywBwHejPBaA4krfo0psp8Zxw6EEcfwD+hPExgOJIPj5OPCcMCucj0ZALoAp8PgVQHK2kS6wtjJad\nFtYMQA8QgL/A+BhAcXRqypFufLw2XWjeiDoGY3AM8BfIYwDFkbZF14en0CATwAbkMYDiSDh/vCuX\nGc3UT4fBMUB1yGMAxZGwRdeik5a596BBJoANyGMAxZGqRdeZIna2iMbG4LADYAPeGABKJEmLroUn\nhJnteA8cdQBswTsDQImcP4WcXc5+uSI83hLHHADb8N4AUCLnL7Feelp4Ip7XeDrzOQHcCfqBACiR\nk8fHpZW04oJw7CGkMcAdYXwMoERObtH15VlhZDNeq3baEwK4H+QxgBJpfZ3XoqtSoI9PCy+0w9EG\noCZ4hwAokc7PeePjH9KEjsFc60B86xigJshjACVyZgvrJSnC7A441ADcBd4kAErktBZd264wL57u\nb4rBMcBdII8BlMhpLbrEBpkOfxoA94f3CYBCham5qw5u0XXiBssoo5HNcJwBuDu8TwAUyglTyAtP\nCLPa8yqcqwaoBeQxgEI5ukVXVjlLzmVTWuAgA1AreKsAKJSjW3R9kCJMa837ogcgQO3gvQKgUA5t\n0VVoou8vCafHoEEmQG1hfAygUA5t0fXZGWFcDB/i46jHB5AfjI8BFErnx+XqBUc8sslCn50Rdg1T\nOeLBAeQK42MAhXLc+HjlRaFHKNe8EdZVA9QB8hhAocId08KaEX2YIvyzPY4tAHWD9wyAQjmoRVfS\nZaGJL90XisExQN0gjwGUyxEtuhalCLM7YOYYoM6QxwDKZfcp5MPXWIGREiIwOAaoM+QxgHLZ/SrI\nC04IczrwPOIYoO6QxwDKZd8W1mml7Pd8NikORxWA+sA7B0C57Nuia/FJ4bm2vA/mjgHqBXkMoFx2\nnD++bqKfM4RprXFIAagnvHkAlMuO88cfn7Y83JwP9LLLgwEoEfplAiiXvcbHejN9eVb4fSSOJwD1\nh/ExgHLZq0XXf88LA3R8lAbrqgHqD3kMoFxii66Khl1UwsLoo9NokAnQUHgLAShamJrLa9gQ+ecM\nIUZD9wZjcAzQIMhjAEVr+BTyBynCLDTIBGgw5DGAojVwifWePKY308BwDI4BGgp5DKBoDRwfLzpp\nmdMB/TEB7AB5DKBoDWnRda6YnbxB42NxGAGwA7yRABRNp6bc+o6P3z8hzGzHe+IoAmAPeCcBKJrO\nj8up1/j4qoE2ZQmPt8QxBMA+8F4CULR6zx9/dMryeEs+AA0yAewE/e0AFK1+LbrKzbT8gvDHKBxA\nAOwG42MARVN7UEXdW3R9eVZIiOB1aiysBrAb5DGA0mnr2KLLLNAyNMgEsDe8owCUrq5TyD+mCe2C\nqG0QBscA9oQ8BlC6urbo+iBFmI0GmQD2hjwGULo6jY93ZDMPnnqHYXAMYGfIYwClq1OLrsUnLXM6\n4LgBYH94XwEoXe1bdKXcYBdL6KFoHDcA7A/vKwCl06pr26Lr/ZPCi+15Fc5VAzgA8hhA6Wo5Pr5S\nznZmC1PQIBPAMfDWAlC68Nq1sP7wlDCtNe+HllwAjoH3FoDSWVt0ed3583lJJa26KJwY7enEugCU\nBeNjAKAw37u06PosVRgdzTf1dVpFAIqDPAaAu0whVwr02RnhhXY4XAA4EN5gAHCXqyB/e1HoHMK1\nCMC6agAHQh4DQE0tuhjRBynCLPQAAXAwvMcAoKYWXVuyWJA39QjF4BjAsZDHAFDT/PGik5bZuLQi\ngOPhbQYAd2zR9UcBy9PT8CgcKAAcDm8zALjj+Pj9E8KsDjyPc9UAjoc8BgDb4+P0Urb/KpvcHEcJ\nAGfAOw0ASON5s0VXVR+kCM+04X1UEtUEoDDIYwAguq1F1w0TrUkXprXGIQLASfBmAwCi26aQP0kV\nJsXxwd7SFQSgMLieBAAQ/TmFzBGR0UJfnhX2DMepagDnwfgYAIj+Oj7+73mhdxgX64911QDOg/Ex\nABCJLboMjIgERstOC9/2xeAYwKkwPgYAIiKdmnLKiYg2XBZ0auoUgsExgFM5JI8ZY19++eWIESOe\neuqptLS0O+2WlZU1bdq0PXv2WLd8//33o0aN+vvf/56SkmLdeOjQoUceeWTMmDGbNm1yRLUAQFW+\ngrw4RZjdAYNjAGdzSB5/9dVXH3/88axZs2JiYgYMGFBRUWFzt+nTp2/ZsiU1NVW8u2HDhpdffnnG\njBndu3cfMGBAUVEREWVlZSUkJDzwwANTp0594okn9u3b54iCAUCcP95/lZVW0uAIDI4BnM0hebxs\n2bL58+f36dPn5ZdfbtKkycaNG2/f57///W90dHSHDh2q/tRrr702cODA6dOnd+/efdWqVUSUmJg4\ncuTIRx99dOjQof/85z///e9/O6JgABDHx4tOCrM7oD8mgATsn8dms/nMmTNdu3YV73bt2vXkyZPV\n9snLy1u8ePE777xTdWNKSkrVnzpx4gQRnTx50rqxS5cutz8UANiF2KLr2HU2IRbLSgAkYP/11dev\nXxcEoVGjRuLdwMDAa9euVdvnmWeeeffddwMDA61bGGPXr18PCAgQxIHLEgAAC7hJREFU7wYEBBw7\ndoyICgoKrBttPlRVubm5bdq04bibH+5feOGFf/7zn/b4ndyYXq83m808jyOsPQmCYDQaBUG4+65u\nJdTba0qcpUJvtD3D5Hjl5eUSPbOc4VV1BPMttdyf53m1Wl3zPvbP46CgII7jysrKfH19iaikpCQ4\nOLjqDhs3bszJyYmIiDhy5EhxcXFmZmZmZmZUVFRAQEBpaam4j/WngoKCqm5s3LhxDU8dFhaWlJQU\nFhYm3g0ICEAO8Tzv4+OD18G+BEHw8PC467vL7SzsLgwM5zWeUtag0WikfHqZwqtqd2IY+/j42PEx\n7X+Y9vLyio6OPnXqlHg3JSWlZcuWVXcwmUwajWbu3Llz5849d+7czz//vH79eiKKj4+3Lqs+deqU\n+FMtW7a0PpR1451wHBcQEBB0C0IIoE4eiub9JQ1jAEVjDvDee+/17ds3MzPzhx9+aNKkSVlZGWNs\n8+bNc+bMqbbn0KFDP/vsM/H2119/fc8991y6dGnr1q2BgYE5OTmMsdTU1MaNG+/du/fMmTNxcXEb\nN26s4XmbN2+enZ3tiN/IfZWXl1ssFqmrkBuLxVJeXi51FTJUWloqdQkyhFfVESorKw0Gg30f0yH9\nuWbNmlVcXDxkyBCdTrdp0yY/Pz8isk7rVtWxY8eIiAjx9uOPP3716tVRo0YFBgauXr1aq9USUevW\nrb/66qvZs2cbjcaZM2eOGDHCEQUDAABIi2Os+kXI3VeLFi2Sk5N1Op3UhbgQvV6P+WO7E9dzyW/+\nWHJlZWWY6bQ7vKqO4B7zxwAAAFBXyGOZ++WXX65cuSJ1FXKTkZGxc+dOqauQG8bYN998I3UVMpSU\nlFTzN0WhHs6fP7937177PibyWOZ+/PHHo0ePSl2F3Bw+fHjNmjVSVyE3lZWVr732mtRVyNDy5cut\n31IBe9m3b9+GDRvs+5jIYwAAAOkhjwEAAKSHPAYAAJCerL7vFBoaWllZafOLzoplMBg8PT09PBzy\nRXPFMpvNlZWVYkdYsKPS0lJ/f3+pq5AbvV7v7e2tUuGa1vZUWVlpsVhq/30nb2/vc+fOWa/sYJOs\n8hgAAMBN4Xw1AACA9JDHAAAA0kMeAwAASA95DAAAID3kMQAAgPTwNRjZOn36dGpqqnjb19d3+PDh\n0tbj1srLy48dO5abmzt27NiqX6jbvXv38ePHO3To0L9/fwnLc1OMsYsXL546dapt27YtW7YUN54/\nf/7EiRPibZVKNXr0aOkKdEuVlZV79+49ffp0cHDw8OHDrV+wEQQhKSkpPT29T58+9957r7RFuqO0\ntLQ9e/bo9foePXpYX8AjR46kpaWJt4OCggYOHNiQp8D4WLbWrFkzf/78nTt37ty50+59zxUlPz+/\nadOmzzzzzPjx4wVBsG5fsGDB9OnTS0pKnn322XfeeUfCCt3Uo48+Onjw4KeffjopKcm6cfPmzW+8\n8Yb4d7tr1y4Jy3NTM2bMePfdd7Ozs9evX9+qVSvr5WQee+yxRYsWFRUVjRgxYu3atdIW6XZOnz7d\nq1ev33///fLly0OHDl2yZIm4/Ysvvli6dKn453ro0KGGPg0DmXr99ddfeeUVqauQA4vFUlFRkZOT\nQ0Rms1ncWF5eHhQUlJqayhi7ePFiQEBAaWmppGW6H6PRyBgbP3784sWLrRuXLFnyj3/8Q7qi3F5x\ncbH19rBhwxYsWMAYu3DhgvVPNCkpqV27dpLV554MBoPJZBJvb9++XavVireffPLJjz/+2F7PgvGx\nnB07dmz+/Pk//vhjRUWF1LW4MZ7nPT09q208ceKEv79/69atiSguLi40NBTX0aorb29vm9vPnDkz\nf/78VatWGQwGJ5ckA1U7QFVWVqrVaiLas2fPfffdp9FoiGjQoEGpqakFBQWSleiGfHx8vLy8xNuV\nlZV+fn7Wf9q3b9/ChQvXr19f9eRZ/SCPZSsqKqpt27aCIHz66ac9evQwGo1SVyQrubm5TZo0sd4N\nDQ3Nzc2VsB7Z0Ol0HTt2ZIytWLGiU6dOJSUlUlfkrtavX5+amvroo4/SX/9cvb29AwIC8OdaP+Xl\n5bNnz3755ZfFu/Hx8bGxsRUVFW+//faQIUMaGMlYzyVbjz/+uHhj7ty5nTp1Wrt27eTJk6UtSU58\nfHwqKyutd00mU+072UINJkyYMGHCBCJ6+eWXe/fuvWLFihkzZkhdlPvZs2fPM888k5SUFBAQQPhz\ntROj0Thq1KgBAwZYj64vvviieGPWrFktWrTYvXt3Q5Z2YnwsfyqVqlWrVvg4bF+RkZFZWVkWi4WI\nBEHIzMyMioqSuihZ4TiuTZs2+Luth4MHD06aNGnt2rWdOnUSt0RGRmZkZIi38/PzTSaTTqeTrD73\nZDKZRo8eHRMTs3Tp0tv/1dfXNyYmpoF/rshj2Tp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          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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rqIF7alx0rWAApbGSx6WlpaWlpXFxcenp6SEhIS3HY2JiXn31VQfW5qJ0wvWO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\n61BxUwHfi17rW2DwGMApWLn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AHgPIoM0h5OwKnorBYwBXgjwGkMHdIayongrqb9tExuAx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\n"
          }
        }
      ],
      "source": [
        "using DynLoco, Plots; \n",
        "\n",
        "wstar4s = findgait(WalkRW2l(α=0.4102,safety=true), target=:speed=>0.4789, varying=:P)\n",
        "nsteps = 15\n",
        "bumpHeightDimless = 0.075\n",
        "B  = asin(bumpHeightDimless / (2*sin(wstar4s.α)))\n",
        "δs = zeros(nsteps); δs[Int((nsteps+1)/2)] = B # one bump\n",
        "upstepresult = optwalk(wstar4s, nsteps, boundarywork=false, δs=δs)\n",
        "\n",
        "p = multistepplot(upstepresult, boundarywork=false, legend=false) # plot speed, push-off, terrain heights\n",
        "display(p)\n",
        "\n",
        "p = plot(cumsum(upstepresult.steps.tf), upstepresult.steps.vm,xlabel=\"time\",ylabel=\"midstance speed\",legend=false)\n",
        "display(p)\n",
        "\n",
        "# step timings, per step\n",
        "plot(cumsum(upstepresult.steps.tf),upstepresult.steps.tf, xlabel=\"time\",ylabel=\"step time\", legend=false)"
      ],
      "id": "28e159fd-24f0-4f48-b855-05882afd0268"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The optimization is performed with `optwalk`, which computes the\n",
        "minimum-work trajectory for `nsteps` of walking. A terrain may be\n",
        "provided by an array of height/angle changes `δs`.\n",
        "\n",
        "All quantities are plotted in dimensionless form, with base units of\n",
        "body mass $M$, leg length $L$, and gravitational acceleration $g$. Thus\n",
        "speed is normalized by $\\sqrt(gL)$ and time by $\\sqrt(L/g)$. For a\n",
        "typical leg length of $L = 1\\,\\mathrm{m}$, the equivalent dimensional\n",
        "speed is about 1.25 m/s, and step time about 0.55 s.\n",
        "\n",
        "## Use varying step lengths to walk over a single upward step\n",
        "\n",
        "The model above uses fixed step lengths, whereas humans adjust step\n",
        "length with speed. The model can also be constrained to step at the\n",
        "preferred step length vs speed relationship of human, resulting in a\n",
        "different amplitude of speed fluctuations, but a similarly-shaped speed\n",
        "profile."
      ],
      "id": "56466aac-65ab-4f6c-9978-1f544af985c9"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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kFeVcesxxPBa1GvU5Oh1LJqKb3z3upY5HJtrLUr4uGlziCQOeAPIjQx5zHMfz\nw7f39PQYDIZRHjQej3/961+vqqpavHjxe++9d6Tdtm3btmLFitdffz398k9/+tOKT9x446c9SJ96\n6qk5c+bU1tbef//9oywAQK7FjMXffrPt+srYV+p4IkomE6Hu1jr3cS5FfFSRD9/Rz1goWAtzcXDR\nVZFussYUXQB5lOH58eLFi//6179eeOGFQ/VjWZYfeeSRpUuXjvKgDz74YEtLy86dOz/44IOrrrqq\nubnZah0+l5AkSd/4xjeCwWBHx2Bfkqamprq6upUrVxKRTjc4BHLXrl3f+9733n33XbvdvmLFiunT\np19xxRXH8XcCZNFmL7tsrf6/v1hTK7X5mxnH8wZeWTy1vKCgICfnYyy87n/tX/lhTg5OJDrdUm+H\ngciu43yoHwPkSYY8vueee84888xzzz137ty54XD4kUceeeaZZ7Zt27Zu3bpRHvSxxx575plnbDbb\nF7/4xfnz569atWqon/aQ+++//9JLL127du2hG8vKyhYuXHjolieeeOK666476aSTiOib3/zm448/\njjyG/Hq3i920Vv772cKyEhuRLZVKKYqi1Wb5se6h4h9/KFiLNOW1OTq+xlUR27WRBuvHyGOA/MjQ\nXr148eLVq1eHw+H/+Z//6ezs/OY3v5lIJN5+++3FixeP5ojxeLy9vX327Nnpl7Nnz25qahq2z969\ne//5z39+97vfHbb9N7/5TXFx8WmnnfbOO++ktzQ1NY18qEMpitLa2tr8iXgcTW+QZX87oNy0Vv7f\nzwvLSgZbj0RRzGkYE1FozcuWsy7L3fFFpzvV20Hp/lyJ3J0HAEaSeT6QM844o76+3u/3+/1+m83m\ncrlGf8RgMEhERqMx/dJkMvX39x+6gyzLK1eu/N3vfqfRaA7dftNNN9155502m+3ll1++4oortm/f\nXltbGwwGTSZTegez2RwIBEY4tcfjueaaa4YmZLjttttuv/32EfaPRCKj/7tgUjqma+BPTcIjDcLr\nZ0tTdCwczl2hPkPubZP6elOVs8M5OyUz2CRvZzgU0qd4X0ybuxOpEz4HIBqNMpbbliGe54di8UhG\nWj/VaDRGo9FjCmMistvtgiAEAoF0/6/+/v5hR3j66acTicSWLVu2bNnS1ta2fv36OXPmLF26dNas\nWekdrr322ieffPLdd9+tra11Op1DGdzf3+90Okc4dUlJydq1a8vKykZfWnUxGI8AACAASURBVLPZ\nfEx/HUw+o7wGHtyhPNOsrLtIKDfltjY8TP9rb1nPusxsseT0LBGz1aAkTYX2AUk6AW+KE/BPhkNx\nHDdU8cujzPNzPfnkk3V1dSaTacWKFekt119//eOPPz6aI4qiOHfu3Pr6+vTL+vr6BQsWHLrDlClT\nVqxYkW5SjkajPp/P5/MNO4jP50v/68yfP3/Tpk1HOhTAOGBE390k/7NdWX+RWG4a17kylHAgtudD\n46Jzc30i0elO9bZzRGYNhaVcnw0AMshQP3766advueWW2267rbi4+LnnnktvPOmkk5588smbb755\nNAf9zne+c9ddd4miuGHDhnA4fMEFF6QP+8orr6xatWr58uXLly9P77lr166LLrro0ksvJaLvfve7\nCxcutFqtL730ktfrvfDCC4lo5cqVc+bMefTRRx0Ox69//es33ngjK382wCglFfrKGjmaorfOEw0j\nNSflRHj966bF5/L6ozRzjZ3GWSF5OnTT5qeHIJs1mKILYLxlqB//6le/uvPOOx999NGzzz57aOOC\nBQv27t07yoPeeOON995773PPPZdMJtesWSOKIhFNnz79/PPPH7bnlVdeOVTlnTt37tq1a1944YVp\n06Zt3brVZrMRUWlp6Zo1a3bv3v3222+/8MILo+xTBpAVkRRd8k5Kw9Oqc4XxDONEItHf3x/s8w9s\n+GeO5gAZRnR+OgQZU1gD5EWGz5iWlpZzzjln2Ear1TqsW9bIrr322muvvfbQLYsXLz48TQ8dB3Xz\nzTdnrH/PnTv397///ehPDZAV/Qm68J3UKQ7u16cK/HhVFxVFaWtpGejpMOs0kb0fBQSbidfmZBKQ\nzxJd7tjOD4jIoefQxRogLzLUjx0OR0tLy7CNW7ZsqaioGJciAeRfV5Sd9UZqRTn38GnjF8ZE1NnW\nqvT1THeXVriKi9t2zDnnovaPd0Wj0VyfV+NyS73tlF5SAkOQAfIhQx5fdtll9913X2Nj49D8XFu2\nbPn5z39+5ZVXjm/ZAPJjX4AtfU2+fRZ/z8k5XMz4cIwxf3dHmdPBcVyyrZF4wVRVV2wxent6cn1q\n3lzAknGWiNkxBBkgTzK0V//sZz9bv3797Nmzq6ure3p65s+fv3v37nnz5v3sZz8b//IBjLOPfOyy\nf8m/PpW/sibz6IPckWVZIOJ5PtmxP7T6H+alFxKRXqcLx3NeP6b0I2Rvl11X40P9GCAfMuSx1Wp9\n//33n3rqqbfeequkpKSoqOiWW25ZuXLl6NeTAJig3utmN7wnP3mmsKI8Dx2MBUFIRsLBfz6V6jlo\nOftKbc0sIkokk1pz0TicXeOskDztdnNN2/DhhwAwHjL3GdXpdF/96le/+tWvjnNpAPLolVbl2xuV\n1z4vnOzIx2gfxqIb32Sv/dE765TaG3/MCSIRpVKyZyBcO2XmOJxfdFakPB0OO9qrAfLjiGM49uzZ\ns2XLlu7u7pKSkgULFqRXdACYrJ5sVH6+XfnX+cI0Wx7CONnWGHjxEd5SeNLdf2jvH2jq6jVpRYWx\ncEopnzZrfGYOEp3u2NY19gWcP66Mw+kAYJgMeRyNRm+66abnn3+eiARBkGWZiC655JJnnnkGs8rB\npPTgDuWpJmXNBULF+E6/RURKNDTw1jPxvR8VXPY1/axFRFTrKI1VVEajUUEQqszm9PD9caBxVgx4\nOuw61I8B8iNDj5W77rrr9ddf/93vfufz+VKpVF9f31/+8pf33nvv29/+9viXDyCnGNH36+WXDipr\nLxTHO4wZi25e3fuL/+CNFtddv0+HcZrBYLDb7QUFBeMWxkQkOEplf49dh/lAAPIjw93+4osvPvDA\nA//xH/+RfllYWLhy5UrG2B133PHYY4+Nb/EAciil0NfrxZ4ke/eLollz9P2zKNneGHjhUd5SUPzN\nX4n2knE99xFwgsjbimxRb39iHCYgAYDhMuQxY2xoqaUhs2bNUhQ8VYLJI5qiq95NmXnun18QNeM4\nsunTBupLb9XPXjJ+Jx4FjbNC8baLfGFCJt24Dr0GgEzt1RdddNE//vGPYRuff/759AIPABORoii9\nvZ7G5oOt7Z3hcDiQpM+/maqxcH8+VRq/ME43UD/4NU6jc931e7WFMX2yylORjvMnMAQZYLxlqB9f\nf/31N95443nnnXfVVVe5XC6v1/vyyy9v3rz54YcfXr16dXqfs88+WxDw/Rkmhng8/tGepojWpjPa\n5Fjqg9a2n39suHhB5f9bJITD41QGqWN//wuPcDp98df/n+hyj9NZj5HorJDaGh168sepLOdrSgHA\nZ2TI43vuuaejo6Ojo+Ptt98+dPs111wz9HM4HFbD6s0Ao7GvuS1VUOGwFRBRZ5T9qL3g4uL9P5oW\nJrKNw9mVaHjgradjuzbavviVcVjJeCw0Lnf0o3ftU9HFGiAPMuTxc889F48fpYel0YgvzzAxyLLs\nCcXtzgIi2tPP7vpQuWMuv8jo8vYF0mt65hBj0Y/eDb7+hGHe0pIf/pHTqX2GO9HlTnk67HM4X5wR\nYQlkgHGVIY/LysrGvxwAOaIoSooT3+pQXjrIeqL0s5P5xcVcJCQk5dz2T5Q6DvS/+Ain0Tm+/oDG\nVZnTc2ULbzAzWS7lI/4EZhoAGG8Z8rijoyMSiUyfPp2Iksnkww8/vGfPnnPPPfeGG24Y9+IBjElj\nkD3ewP3p3fjUGdLVtZrPlfLpxRMTsYitQJ+VU0iSJEmSTqcb6lExgRqoD6dxuWsSnf749HwXBOCE\nkyGPv/a1r82YMeNXv/oVEf30pz/95S9/OWfOnGeffTYajd56663jXkKAY5aQ6X/blD/tUxoCdP1U\n7u2rS32BtqLiap7jiSgUDOiifte0sU4KHY/HDzY1SKGgyHMJmdnL3eXuyvjW9yZQA/XhRGdFRbSz\nMTEt3wUBOOFkyOMdO3akc1eW5ccee+zuu+++5557/vu///uRRx5BHoPKNQbZ443Kk43K3CLu1hn8\n5dW8wBFRaa9H3Ne2L8EEjikuq37anLoxTn0ly3Ljzu0lJk2Bu5SIGGNtH3+09bGfV5U4HP/xgKZk\nYjRQH050Vji6Ovzj0dENAD4jw0fSwMCA3W4noi1btvh8vnS36rPOOuvuu+8e79IBjM6wCvHmS0X3\nZye/dDmLXc5iSZIEQeD5LIw47u/vt/BKgdVKREoiGvngn8b9O/tqFhd8+XaNZnzn+soqjctt2/cO\nxh8DjL8MeVxSUtLQ0HDGGWe8+OKL5eXlM2bMIKKBgYHxnEoXYJQaguyJDBXizLKVlCwRCx3YQ237\nwo1hud8jdbXoZy1x3PSTiC+QSCQmdB6LTrehr91Xnu9yAJx4MkTsVVdddeedd65du3bVqlXf+MY3\nOI4joq1bt06ZMmXciweQ2VErxMPIsuzzeaOhAVHUFNgdFotl9OdSwkGppzXl6ZB621K97VJvO0vG\no4Yi3mQrrJ6irZhqOedq3mQlIklWJvrXVrHIJQ54A3F5hMVYASAXMtxyP/vZz3ie/+CDD2699daf\n/vSn6Y1r1qy55JJLxrdscIJKJBJ9fX2SJBUVFR2+xGe6Qvx0EzvZQUetEKfFYrGm3TusvGI26OWY\n0tbVZi51V9Vk/n4pB/2p3raUr1vqaZV62lI9B1lKEl1VmtIqjavSMHuJYC8R7aVF8Xjjlg+1ZU5R\nHOxWPRAOM71Rr89Ot+284Xmh0Kkf6CWaqI/AASaoDHms0WjuvffeYRtfe+21cSkP5Eo8Ho9GoxzH\nmc3mrDSoMsY8nl5Pe2sqkRB1Oqe7yul0pVtTxqL5wIEPN2wUBFEQxHA0PKW29rQzThcEYahC3Bqm\nldP4rZcJrlF3Xm5pbCgz66yfRHuhzdrc2REsslvNJqW/N966W+ppS/l7pO7WVE8rb7SIJZWakipN\nSZVh/nJt+ZSM3aT1en3ZtBlNTQ0FOlEjCrFkMsprp86aO8Y/Xw00Lrc71C6zyqN+0YHcSSQSoVBI\nURSj0ZithedTqVRPd1csNCBqtQX24sLC7CzkxRiLRqPJZFKv1xsME29MgXqgSWryY4wdbD4Q7u20\n6LQKY61JuXRKnatkrGv8HWw+IHm7apwOraYoKUldLY3RcLimdupYjun1ejeuW1c7c57BaCIiprDG\nfXtWrdm81broqSZlqYv/wUnCOeXHkPlMTkmRcLy7zVRql3r7WDIpD/hlf6/QcXD/S4+WijJfVJIq\nq9K4KvUzFlrOvExwlHLCaG8KR7HTaisIBALJRLzAaKopLMxKT7G807gqZvd39ifIMcGr+uNJluUs\nTunf1dHua2ux6kSB43wJSVtUPKVu+hivrkgksn/ndrtBdBgMqWS4Z193n72kdtpYB5pHo9HmfR+L\nUlwr8DEppbEV1dRNn9BdKPLoBM3jVCrV2tra1dVdXOyorKxU1fSfgUCgq6srkUgWFRVWVVWN/YCd\n7W2Kv2daRWm68irL8oED+wxGo9VqPe5jxuPxcG/ndPfgVG5ajaa6vLShvTNeXjGWBtumhgaHqyId\nxqmktMuX3Dxg37Vu4w2XFW6bG7MJEvPGo+1RlkqyRIzFY0yWlHiUJeIslVRiESYlKZVUomGWSjIp\nwRJxTqdPCbpwIBIsK+ZELafR8tYi0V5imXcGX1xVtvC0cDg8lsqHVqt1Op3H/XZ1Ep3uabu2+xPM\noUcF+SgURenu7PB2tPFMUTje6a4uKSsbY3AGAoFAW/O08pL0cVxEnb2ejrbWyuqasRz2YFODu9Bs\nNg1+1tksluaOrkDAVVBQcNzHlGW5aed2d4HJbBocIefrDxzY9/GMufPGUtQ0j8fT3d1NHDmLnaWl\npWM/YLYoitLS0hIIBE0mY0VFRbZaL+jEzGOfz/fW2+9oNXpBED0e/6aNHy4/c6lKeqtt3759+7Zd\ntoJCQRD37Wv6cPOWC7543hi/Lvi7O6e5HEMtyTxTig0az8ED5tpaJR5Jb2TxKFMUIkpHGhExRWHx\naPq3SjxKipz+LUsliagvMMD3tIdbrESkJGPEGBGxQKhjx78LDdrBE6ckJfnJugSMsU/O9ckBB6er\nZFIifUzGKNnbX2vkRa1e4kWZ0Smi4XStpjE1cMruTkGvj+gMvM7AiVpOb+S0Ok5vFAwmTqPjNFrO\nYOI0Wk6j4w0mTtRyWj2vNxAvpM/ct2m9taR46EEvEQU8XnN59Vj+VScx0VVRHX/dF6fpGIV8NAca\nG8RQ34yyYp7nZVnu6jrYEo2MsdLp7+1xFlp5nmdSkskpInJZjHv37y2zZPimq0QzrVCWSjIp+ZkN\nspxo2qUpMn26UIggmuNJz5agwe0mIhK1nEY79EtOo+MOqeNyWj0nHPJSp083IwUCAbPAhjKeiByF\nBf0dPfF4fCzfyxVFef/9dW2tHQWFRUS0a+fe4uKic875nBo6SwYCgTf/+Q7P8yazRUomN2368NRT\nF6dHIY1d/v+88fevd/5dUVFTWGRPXzSJeHzNmvVOpzOLX3OOT29v77ZtO+fNXyR8khyd7a1r3193\n/nlfGOFdSjzCohElFlKiYSU2+AOLhpVYWImF5Ui4r+lAwKZh8agiJThBIKJESulJ8ubiAiLi9AaO\nF4iIRA2n0RERx/OcfvAG43VGEgQi4j75LXEcbzDxgsC0OsVkiUTiSZ4TRY2lsFBrihhLKow2K6c3\ncp9UETitnj5pAeZEDafVEZGsUHuEGpOmxiA1BVljkO2M6A1asaJj3VyrPL3KXWKkKjNnFCksy73b\nPyr+8vXH3RjIcVxJ9dTWlobKUpdGFImoLzgwIPMVjuLjO+Ckp3G6S6OdjVhS4mgikUiy31tVMVh1\nEwTBXepqbO+OuSuHHqMq0TBLxlkyriRiLBZRknGWjLN4VIlHB7fHoyweZcm4koyzWERJxLq7ezkd\nF2cKp9HyusE7MegNejc4OI5I1PBa3eGF4fQmOuxJDieKnFZPRMmUHOvsjhd/piqcjCfCKRZqth4a\n3iwZJzk19FJJxEiWD3k5+NU8raevn1eYx2bhBJ6I43VGTm+IReXubW8XFNl5g5kzmHmDiTeYeYOJ\nM5h5o3nwZ+1Iab13376uzp55Jy8a2tKw9+OPtmw9dcniEd41Plav/nexs6TYNfi8T0omN274sKSk\nZCzNDENOuDz2+XyyLBcW2YkoFo3FwiEiEhj7cPO2mtra/JZt+5aPzHrjQKCPiDQcWeRYNR/bse2j\nAZPEJaNKOmKjIRaLKNGwEgulW2h5vZE3mjmDhTeaeYOJN1p4g5k3WYTiMt5g5g1mi7tR67J3D8QC\nCYXnOYfFZDbqy8yFJVOPf05EvSQd/Pc7fpkTih1arS4lpQ4GPbLRfObpnz/80VFYooYg2xdge3tZ\nQ5D2BlhbmNVYuOk2bkYBLa3hVtq4GQWcUaTe3llv/vOdOY5SjVZDRIyx5gP7a2pqxvhkrqS0VNSI\n+w/s52RJZmRxOKfPq1HDd2114nQGxosDwQGiLHzETGKxWMwgRZPNuyVPp9zXo8QiTEpI/mDr63+w\n8gpLxonjeJ2e0+p5g5nT6TmtntPqeaOF0+h4rZ7TGwRLIafVczo9rzdyemN6h0hnt4lJhYWf/uNL\nqZTDFyxddOpYSuvZtMHoKtQcctlHer0VlbUOp+u4j6nz+wdaGpyuYiJicooloiwe7z3YWlBVrWMS\ni0WUaEgO+KTug0os/MkHV1iJRVgyzml1/CdpzQ1+cA3+3Lptd11Jpeg5mBANAwpPREUFBVs2f+Qq\nrRjLv8AIYrHYaHqihcNhT3e3w+7q93kFXrAWFWm02qJC+8GDB+fPnz/2YpxwH0mJREKjHWyWib//\nimugjYjKI9H4Ft53LGNSc4H395eYtGatlohigq6LM8ZEQ5un71mhWWstEoxFWlOVqcxstZosNovD\nZi4utJgM2qMe1iprV3+4uaputqXYxBjrDfRv3vbxeRdfPJaiCoLgJaMsy6UcTxyvEOtj+pRokGXZ\nJ2n2BlhDkO0NsH0B1hCkiMRmFHAzC7jpBdz/mcbNsFG1hcvYd9flcp2yZGF9/RajxSqKmtBA0Okq\nXnpaFr4UOxzFDkdxKpUSBGHsncAnvYGCCtnTjjweTlEkb4fU2Sx1HpA6Dnj2743KzFI3TSyu0E1b\nkE5WUzBir5tT6HTx+uNcId6lNTXv2GIym7QaDRHJstze43HVjLXjVdmU2pamvZUuh16nY4z5+gIh\nXuO2O8ZyTJvN1iGxonjcoNdzgsgZrf0SE6tmFs5fcNT3smRiMJtjISUWUWJhKRrp7g/1dXW3NjYr\nHp8oJ41yzKpEOUZEVNTb52v/cCylHakwRJGj70XRpFQWGrC1bSCilCDGLrvDYDRodLqjrlA8Sidc\nHttstlhs8LFo4XnX8Xo9Efn37Dxl0YLafNePP/poS1enxzqllohMRCaiWFJu2Vw/79Iv+5OcN04t\nUfLEmDdG3X7mjZM3zqIpyWXgXAYq1nMlBnIZqNjAuQzkMnBOPbkMXKGOBiQm1MzrCPRZItGUokQV\nMkxfPBCOpmdFPaqwRJJCjCiQZEQUlymWomg43Kxxi3bnPm9nJBLxKsZuXV2LN/i1x/yFDtd0G80q\n5OYUclfW8DMLuOJjeZA0Z9asmqqq3t7eRFKyFxVmt7cU6sSjlCys4HwdRJNh+NYQRVH8Pl80FOJF\noaDIPpo5YZicSnk7pfamZHtTsn1/qvugUGAXS6o0JVXm5Rdbrr1j3969ptJPuyZIqVRM8tnKKvkx\nXGlms9k9c25zU4OOZJ7jIinFWVk79gERxU6XqNG2tRxIxfqI523OkhmVVWNseRJFccqck/Zt3yqF\ngsQUThBMxSXT58wazXtlUbefaXfHCnf3sz39tLufdUfZNBs3p5rTxSqUYvPsSqdNN/jVORwa0HS3\nLbri8rGUdgSRSMRkOvr3p3g8/ve/PV+1cDHP80M1oXAoXFOdnQntTriPJ7PZXFrq2t+4b8onrbU9\nXZ2ykspKT+YxmjFj+u5de2yFheleDHJKbmnYdfqCWaeWHPGeSSmUDubuKHnizBujtjDb7CVvXOmJ\nkidOwSTTd0ccU+cVCUlLNKoVBUVrinkkvqFVLE2lGMkKDUhERLEUxWUiokCSMSJJobhMFg0RkVHk\ndDwRUYGOOCItT7qkNBDkrCUmkZumsZDbRMssdHFp9AulXI17rBeVyWRSSfe6E5bicOt6O/NdimxK\nJpMNu3aYlKTZqJdlpb2z1eAqP3x4nhKPSF0HpfamZEdTqqct1dcrFrnEkkptRZ1h/nKtu+7QTk9E\nVDZ12v79DQ6TXq/TxeJxXyReMWP22L/2FRYV2RYticVi6fHH2RpJVVhYWFh4CmMsi01EoUi0T1MY\nd5YTESmyjSXTy48O240RtYTY7j62J0C7+9ieftYcYrVWblYBN7eI+0odzS7kayyDxequm//2m//S\nlplJZyKiRDx+oKnh9NOXZKvMx02v11fXVDU17K2bPjPd+93b25OUorVTs1OX4xibPBPH19XVrV27\ntqysbOTdksnkBx9saG5u4QWRI7I7is5cvmwsg3+yyOPxvLfm/UQsIWo0iURs9pzZpyw8eYzDJ15Z\nv10qmxuQuP4EkxnxHLFkrCDcObVumklDWp44ogIdEZFeIIPAEZFVSyPPBSFJ0nvb9hXVzD70xva3\n7T+truSYpqLMuzGOd5qs1q//KLzutfN+9F/5LkjWNO392CLHimyf3ubNHd3O6XNsAgvt38V7O6Se\n1lRPqzzQL7oqte6pWnedxl2ncVUe3klqmFgs5vP0JmJRvdHkcLom/ARtxyIej7+/c39h1Qz+k28M\n8ViUeZqXLpzbEWF7+mlXP/u4n+3uZ41BVmbk5hRyswu52YU0p5CbauXEI3+wNR9o3rBhE3E8x3Ep\nObl48aKZWerDnNEo68dElEql6jfVNzTu1+v0SUmyFVjPXL60qKgoK8U4EfM4LR6P9/T0OBwOFX4c\nDwwMxOPxgoICrfboj4ePak/jAQ9XYC389Irx93TMsWvKSsfUAtZ8sK2xXyoscYsajaIo/Z4ulxCb\nN3OCrZuLPM5o24He1GM/WnT/4/kuSHYwxnZsXDfLXUpEykBfsr1J8nT2tTf7O9ury0u5kipj1XRN\nea2mvFawZmfKKtWKxWLxeFyr1RqNxrHXknt6e3f5FYujxBtnnRFqCbH9A9TQ0NilLyuymGYXcrML\naG4RN6uQm1nAaY+xWqEoSiAQUBSlqKgo1zPtjD6P05LJZCAQyOLUaWknXHv1EL1er84wJiKr1ZrF\n+vrUqoq+3U39UsJgsTHGIv0+hxAvcY01OGuq3EaDt6mjMZiSNTxNL3G4y8c0OReoR2FxcTIRZHJq\n9LOVqZmiKOmP89jODyIb39TWzBKdFbbKGYqtvGTBKSfIdzJJkvbub+mJyJzORKmEhZfmTq0afQgp\njHpirC1MHRHWHqG2MGuP0IH2RFtMjBtSJQauxEi1Fm5uEX1ujuaqeYKzYKxXDs/z2ap3Zl2OJgKa\nDDcbjEyn050+f2Znd69/oEsU+KklFpezauxfjTmOK3E5S1zO7D6OAjWwG/h6vavG16VxTYZVJQRB\nYHLK99If+Hik8JrvCAUOIgr7/CbHZJtbbQS7Gw/0iUX26sFh97Fo5KO9zUsXzBr2cDqWou4Yax6g\n5hDrirLuKDWHWFeEuqLMIFKZkZti4aZYqdrMne4iR6Wpuz84fcqnOcIY62uOFplPoEb7LEIenxAE\nQaisKMvRJyvCePKxaOiAtuJ0T8fkyONE4zb+9d93ls+cecVNgk5HRMFQyB+XZ7rG2ml5oojH494Y\nGwrjpEJ9ZNwbtu7e4g/rHEPR2xRkAk9TLFypcTB6zy2nUgNfZqIqc4YxiowVfbijJ+D3FtiLiUiR\nZX93e52rAAMZjg/+1QAggy5jeaSr3TjBRzwxKTnw1jOxHeumf+2ekMV14EATr/TLimKwFU6bf3JW\n+mfkSHpBNkEQTCbTWOKtM8IOhGhXV/yDFo3fq3REWEeUiRw5DVxhUjfDnJhZTWeVcpVm3m2iMuNI\nfawOx3HcybOn7T/Y3nGghwSNwKQ55cXlY+uYciJDHgNABn5LRaxne75LMSZST1vf0w9qyqpdd/6O\n0xnsRHaHQ5IkQRDUvBKXoij7W9oO+iOcwUJMFhKtc2vKix1HmS0gpVBbZLCduTk0+ENDkFk0NLuQ\nq9JpjCw5r5zKjXx6Jloi8vdIJ5cYHI4x/VNoNJqZdVNmMCZJkpq/30wIyGMAyCBU4E61T9hVzxmL\nbHxz4O1nbZd81XjyWYf+Rv1LAba2d7ZEeXvNzPSToJQkbW1uXGrQD/W9SsjUGf1M9O7pZwfDrMTA\nTbHSFAs3xcJdNYWmWPhZBZxh8DNe3LKbDxmCFttgB/JEPCbG+gsKsrNuEsdxCOOxQx4DQAbJIrew\nfUJOCSKH+vv//hBLSc47/kewjWoSOlVp8fQXVQ2O7B9IUmdUbEq43l3nDZr16fQNJlm1ZbBf1RQL\nd27ZYAcrfsSOHHOnTdnV2OwP+khrJFkypMKLZmAWd3XBfwYAZGA1aiWtQQ71C5aJNCQ3tmtD4MVH\nzcsvsXzuqqNO5aFCsix3Rml/B232Kpu9ChG5TVypoKuW+8+q41ZO52utnD3D8k5Hp9VqF86ZEQqF\nEomERmOxWKrU3Gh/YkIeA0AGdh0FrRWp3o6JksdMSgZfeyzRuM1x672a8jzPRX+sPDFa26Os7mTr\ne5inSZ53krLExd8+S3AZOCIa6JcqNfra6izEp8VimVgz6J1QkMcAkIFdz3ks7pSnXTd1AvSxTrY3\n9j39C93Uk5x3/JbLtDywCoUl2uRhq7uU1Z2sM8KWlfDnlnM/nMfTIkfjQLej1J3eTU6lkv09JbOr\n81pYGA/IYwDIwK6jTmO55OnId0GOhrHw+6+G3nux8Opv6Wflf736kUVTtKGXre5S1vewjwNsoYM7\nt4z/41L+ZMenbeuKqTzZ3Nra8jHpLaTIYjJ88pSyY5rNESYo5DEAQ8bwbwAAIABJREFUZODQc5t0\n7pRnc74LMhK539P37C85Ueu847d5mXo6mUy2tHd6AhGe50oKLVUVZYf3kEoptKOPre5kq7uUrT52\nsoM7t4x/+DR+gT1zDyye56dPran6dPyxG72uThD4bwaADOx6atCUpXrVWz+ObV8XePkPls9dZV5+\nSV66bsVisU179pOt1FzhZowdDPZ17dh36knTNRqNzGi7n63vYR/0sne7lBoLd24594OThGUlnG50\nayfq9foTaqkoIOQxAGRk19F+siuxEJOSwxb9zTslHg2sejTV0178jQdFZ0W+inGgvZMKyq0Fg/Xy\nArtzb5S9v65zB3Ov6VYqzdy55dyX67i/LNdY1T7mGVQBeQwAGdj1nD9OoqMs5evSlFbnuzifSh7c\n1/fML/SzFhV/56H8Lj/lDUYt1VOI6P0e5a0O2uJVCgTrQub78jLuz8s0NnV9h4EJAHkMABkUaimQ\nZKLLneptV0seK/LAO3+Pbl5deN0duqkn5bs0RMQaguw3u5W4QtfXct+fK1o4hbz8qZUY1wvHA3kM\nABnwHGl5Yo4KqbfdMO5nVxQlFosxxgwGQ3pBwJS/p++ZXwhWu/N7v+WN+R9B2xVlvz9gfH/Av/Jk\n+6VVfLpnVr+vv7Yg/2WDCQp5DACZ2fVcrLCCa9g4zuft8/s79jfoSCGiuMJcVbXWzo+Drz9h/cKX\nTKd/cZwLc7hoin67R/nNbnllbdkt1CxYSJZsKWLRYL8h5q+onZ7vAsJEhTwGgMwcegrY3FrP8+N5\n0lAo1Llv95TSYq1GQ0RSOLTnT/9lFtm0b/5SdJSNZ0kOx4hebFF+8KGy1MVtu1xTYtBI0oy2zm6v\n18cTN9VurZg2M12bBzgOyGMAyMyu47ym8iJvFzE2bgOKvD3dJYWWdBgn2xoG3n62avoiT93peQ/j\nTR52xybZKNLLK4R5RYP/GhqNpra6coJNzglqhTwGgMzsevImhZlmmxz0CwWO8TlpPBIutuiIKNG4\nLbz+NdtFKzUlVZ2tXeNz9ozawuwnHykfetn/PYW/qgZ9tSBXcG0BQGZ2HfkTJLrcKU/7uJ1U1Gol\nKUVEkS3vWc69VlNSJcuykKcB0IEk/XCzfNr/yrMLuZ1XiAhjyClcXgCQWXoIssZZMZ6zWDtcpb39\ngZS/h0VCWncdEXV7/Y6y8nErQFpKoT/tU+asSsVStOdK8QfzeC0+LCHH0F4NAJk5dPRxgInOCqn7\n4LidtMhuj5ZXb//H74rcs1P+vmAsYSguKS0f10m4Vney726Sqy209gKh1jrxFlGGCQp5DACZ2fXk\nj5NY6Y5tXzee5y0vL0/1H9Rf/n95s63GbB7PpY32Btj36+XeGD16hrC8BEkM4wp5DACZ2XWcL6Fo\nnG6pd/yeHxNRbMd6y9TZ9tpp43lSX5z+7zb5lVb2n/P5W6bzGVdeAsgpPBIBgMwcevLHiTfbmJRg\nidi4nTey8S3TqeeP2+liKXpwhzJ3lWQQac8V4q0zEMaQH6gfA0Bmdj3nTxARic6KlLdTUzF1HE6a\n8vekfF36GQuzfuRgMDgQjogCb7VY0m3g6fk97tqkXVbKtl6mKTVm/ZwAxwB5DACZ2XXkjzMiSjdZ\nj08eRza+aVryeeKz2XQny/LuxgM9MU4w2YgpcntrrcPkN1XeUS/reHp2qXS6G4sxQf4hjwEgMw1P\njEhSSHRWpMZnyJMiRz961/mth7J71LaOLo9iclQOzvDVa3Le9u/9rXLvA2c7r6rhw+F4dk8HcHzw\n/BgAjqhIx/UPTgkyHnkc21OvKa0WipzZPWybt7/A4SKisEQP71ZuXCvPrS55bkkI83uAqqB+DABH\nZNeRL8GKnBUD4zJFV2TjW6bTst+TS5IVXhCSCn19gzy3kHv+c6KBdLI3lfUTAYwFvh4CwBENDkF2\nlMr+XmIsp+eSAz6p84B+9pKsH9mk0ySTiQd3KDNs3J0n8VYtxaIRm0mf9RMBjAXyGACOyKHn/AlG\nvMDb7Kl+T07PFal/23jK5zgh+412de6Sv9W37PUnvzeXJ6JkIi71dblLs9wqDjBGyGMAOCK7jvxx\nIiKNsyKV01lBGIvWv2Na/PlcHLtZKXqxt+C/ypoiHY3+g/sUT/OS6e7xnPYLYDTw/BgAjujTIcjp\nVZ5mnpKjE8UbtgpFLtHlzvqRPTG6+l35rxeVrCgricfjPM/rdLqsnwVg7FA/BoAjGhqCLOZ4lafI\nxjdNp52X9cPKjG5Yk7p9Nv/5co7jOIPB8P/bu/e4qOr8f+DvM/dhhusZBuQmohhoKipeKo0MEjNx\nLb5El+9D92uauW2t28N61G67v9Z2H9nFXR/VPtqHrrtWmmFmCkYbXRQXFTU1RUUykYtc5TbAwFzP\n+f0xNCIgzIEZTjCv518zxzOfeYOfc958PudzQTKGny3kYwC4JVZJDV391ZGe66/mjK2W0gvqKXe5\nveQXTtg1Msbx2BjgZw791QBwS13juYhkIR5cEsR4PE89/W5G4eaW62dlXG4lf/wXMixHDSMC/mwE\ngFtiVeTIxxK1lnie62z3xLcYj+dp5qS6t8xLLfyvj3J7U6R+cvcWDOApyMcAcEvO8dXksSay+cci\nicpHHh7jxjLbrJT+tf3tOyTxAWgbw4iBfAwAt8SqmAZT1zIgMr1HVs00Fn7h3jW5eKJf5tsfGsek\nYzlMGFFQXwHgljQyMtnJkZA9McSa62w3XTrtM/1uN5b55zNcq5V/ZYbUjWUCDAPkYwDoj5+CMViI\nPDPEuuPkN+opdzBKtbsK/KqK3/4Dt2uBTIqOahhpkI8BoD+skhxd1rKQCJu7d5UwHs9zY2d1eTu/\n8rB9d7JUh6WpYQRCPgaA/uhUXUO6ZEGh9pYG4uzuKtlSUUI8p4ia6JbSTHZK/9q+YaZkpg5NYxiR\nkI8BoD+ssmvJTGIYaaDe1ljrrpKNR905kmvtEfsdeub/JuKeBiMV6i4A9Mc5BZmcq1i7A2/u7Dxf\n6DPzXreU9s4F7lILv2kuxnDBCIZ8DAD9cS6ZSUTykEhrnXuGWHecyVfFz5T4aIde1LF6/s1z3J5k\nqQL3MxjJUH8BoD+simm8MQXZbUO6jEe/0Mx1wwYSdZ306Lf2HQuk4Ro8NoaRDfkYAPqjU1HX8+Ou\nfOyG9rG1powzGZUxtw+1HI4e/sb23BTJ3aFIxjDiIR8DQH9YJeNcMlOuj7S6Ywqy8dgXmrmLiBlq\nEn2u0B6uYZ6djPsYjAaoxwDQH1Z5YzwXo1QzcgVnbB1KgbzV0nnmsGZ2yhAD++gKd7iW3zofY7hg\nlEA+BoD+sKob47nIHY+QO88WKMbfLtEGDKWQc038Cye4vSlSDfaMhdHCU3XZYrEUFBQwDDNv3jy5\n/JYbnhUXF6tUqnHjxjnelpWVFRcX63S6mTNnSiQSIrLZbGfPnnWeHxMTExgY6KGYAaA3nYpxPj+m\nri7ra4pxkwddoLHwC9+UR4YSUrOZ/ucb+5Z50vF+eGwMo4dH8nFbW9v8+fP1ej3P883Nzfn5+RqN\npvdphYWFSUlJGRkZO3bsIKJ169bl5OTMmDHj8uXLKpXq66+/1mq1ra2ts2fPnj59uuMjr7322n33\n3eeJmAGgT/4KMlh459shto9t16tsjXWqidMHXQLH0/8esv3vBMniSCRjGFU80l+9bdu28PDwvLy8\nvLw8lmU/+OCD3ueYzeZnn312xYoVziPPPPPM5cuXP/nkk9OnT/M870jSRKRWq7/7CZIxwDBjiNRS\nMtq63sqGNgW5aySXZPB3nldO2yUMvZyAZ20w2nikTufm5qanpxMRwzAPPfRQbm5u73P+9Kc/Pfro\no86eaiIaP368o49aIpHodDqr1eo4znFcTk7Ol19+aTAYPBEtAPRP120KsnwIS3TxdlvHqYNDGcmV\nU8FllfIf3iOToG0Mo45H+qurqqrGjBnjeB0WFlZVVdXjhO+//z4/P//w4cNvvPFG74/n5+d/9913\n//73vx1vJ0+evG/fvurq6tOnT+fk5MyePftW32swGF599VWttmvFn5SUlHvuuaefOM1mcz/PtsEb\noA64IlDB1LTZQxy/J5Uv124wGdsZmeDfm7noiDQsxubjbzObBz67lx9bafVhZn8yr+btgyrgFlGh\nDng9s9ksk3l2ZCDDMAqFov9zPBKBVCrl+a6/pjmOk0pvmpBgs9nWrFnzj3/8o8dxh/Pnzz/++OM7\nduzQ6/VEFBQUdPLkScc/bdy48fnnn8/Pz+/newMCAnx9fR1vtVqtpN9uMYlE0v8JMOqhDriCVVKT\nhXH+niRBIXxzvTQkUmg55pNf+9z5wOB+4UYbZebTa4k0w93bN6EOwDDUAcaF2fYeycfd28RVVVVh\nYWHd//X06dMXLlxYvXo1EdXW1nZ2dmZmZmZlZRFRSUnJ4sWL33vvvT6fE99zzz1vv/12P9+r1Wqf\neeaZHl/XD7lcjr+LvRzqgCuC1XaDjZHLu25YitAoaqqVR8QIKsTect1WW665fQ4jHcxt56n/2lMj\n6f/i3D/bGHUAfiZ1wCN/ESxdunT37t08z3Mct2fPnqVLlxJRW1tbTk4OEU2bNu3cuXO7d+/evXv3\nY489Nn/+/E2bNhHRjz/+uHDhwjfffDMtLc1ZVGtrq7OpvXfv3ilTpngiYADoR/clM2mwQ6yNx/7j\nM/u+wSXjTUVcpZHfOAtLf8Bo5pF8vGLFCqPROG/evLvuustutz/22GNEVF5e7kjMSqUy5ieBgYFa\nrTYiIoKInn/+eYPB8OabbyYmJiYmJr711ltEtGvXrvHjxy9ZsmTatGnZ2dmbN2/2RMAA0A/25inI\nMn2EVegq1jxvPPmVZs7CQXz7kTr+7QvcJ8lSOTqVYVTzSH+1RqMpKCg4ffo0wzDTp0939MvHxcVV\nVvb8m3rt2rUWi8Xx+r333uvo6HD+k7+/PxGtWbMmNTW1oqKCZdm4uLg+HzkDgEexSjrXdGMKslwf\n2X7oM0ElmIpPynThMp2rz5KcajrosYP2nfdIw3wwohpGOU+NKJNIJImJiTd9k0zmaAd3FxBwY828\n0NDQPouKjo6Ojo52d4AA4Ko+lsy8Lqx9bDz2H80dru6uyHGcxWJRKBR2kmR8Y3tpmmQetm8CL4C1\nXwFgAKySaTRzzreMXCFRaeytzVI/lxavtbc2W8qLg1a8NOCZNputtPxaeWMrSRW81fzvSt/ooPCn\n4nGbAq+Aig4AA9CpqNF00xFZSKStvtLFfNxxIs9nxgJX5iufu/RjkywgcFwUwzCfV9hPttTsiCsn\nmji4sAFGFgyQAIABsMqbxnMRkUwfaXNxI2SeNx7P85mbOuCJ7e3tDWZJoC6EYZgfDPzfi+lvqeGt\nFs5oNA4qaoARBvkYAAYQpKQmM9/9iNzlIdbmy2cl2gB56NgBzzSZTKT0ISIbRy+c4P7fdEmYD0MK\njclkGvCzAKMA8jEADEAmIYbIwnU7EhJpcy0fGwu/0Lo2kksqlRJnI6Jj9XyUhuboGSIizubphQwB\nfiaQjwFgYKyKaRK+JAhnbDX9cFadcLcrX+Hn5yczt1ktlq+q+PsiGCKyWMxyS5tzRXqA0Q35GAAG\nxiqpwXSjy1rqF8R1GnnLALs6dJz82mfaPEahdOUrpFLp9AmRLRU/HC2pmqluaayr7qy6PGPiWKw6\nAF4C+RgABsb2HmKtC7M1VPf/KWPhl65POyaiwMAAAzvxjhDZZLVxKiu7e3q8Y10gAG+ABzMAMDCd\nkmk080Q31uWQhUTa6irlYeNu9RHL1YuMXCGPmCDoi/ZUyJYnhsZEo6kAXgeVHgAG1rt9LNdHWPt9\nhGw89oVmroDGMRG1WelQDbckCvcl8Eao9wAwMFbJNPSYgtzvEGvO1NF54bh6RpKgb9lfzqWES7Ti\nb3wHIALkYwAYGKuiRtNNU5Bl+kjrrZcE6Tx1UH37XIla2NDorFIuMwZLVYOXQj4GgIGxSuq5RFdw\nmL2hhni+z/PbhXdWN5upsJ5fFIGbEngpVH0AGJhOxfR4fsxIZRLfALuhoffJ1uqrvNWsiI4X9BWf\nlnFLoiQqTG4Cb4V8DAADY1XUaO7ZFL5Vl7XxyOfaOxcTI6znOauUy4zBHQm8F2o/AAyMVd60BbKD\nPCSi95Au3mrpPHfEZ+a9gsq/bqLzTXxyGB4eg/dCPgaAgbFKpsd4LupaNbNnPu44k6+MnSrRClvH\nI6uUWxYtkeOGBF4M1R8ABqaWkYUj7uaM3Gd/tfHYfzR33C+0fHRWA+ACAACXBCiYZstNR+QhkT12\nlbDVVXKtTcoJ0wSVXGnkS1tpfig6q8GrIR8DgEt0vaYgSzR+vNXCmzudR9qPfaG5Y5HwkVz8wzGM\nFOkYvBvyMQC4hFX1nIJMji7rnx4h83Zb5+lDPrNShJacdQWd1QDIxwDgGlbZcwoydQ2x7uqy7jx3\nRDE2TurPCir2Sit/3URz9Ggdg7dDPgYAl7Cqm7ZAdpDpb6xibXR0Vgu06wr/6HiBHdwAoxHyMQC4\nRNdryUwikodEOPqrbY21tvoqVVyi0GIxshrAAZcBALiEVfU5BTnSVldJRMbC/2jmLCSJsFtKcQtv\n5SiBRfMYAPkYAFzTe0sJIjKrfGuulVdXVNQVfKGZkyq0zI+ucI+MRzIGIEI+BgAXsSqmez7meb68\n9MrVojNSH9+OQ7ubpJortdftdrugMrNK+YfRWQ1ARMjHAOAiVnnTeK7GhgZTfdXEyLDQyGh18bHJ\nCxYpOg1VlRWuF/hdA6+R0aQAtI8BiJCPAcBFOhV1n+/UWF+rDwwgImmgnogU46eEsEHNtTWuF4hp\nxwDdycQOAABGBlbFdN9y0WaxyNVqIlJETZT4aBmpTErE2W0ulsYT7Snjv12MfAzQBfkYAFziJ6dW\nC/FEjv5ltVbb0dmukMsVY+MUY+OIyGQ2y9U+LpZ2pJYPVdM4X3RWA3TBH6cA4CpfObVbu16HhEXU\ntrSbzF1DvKw2W2V9w5ioaBeLwrRjgB7QPgYAVzmmIPvKGSLSaDRjb08oKymWcS1EvJUkYybEszqd\nK+VwPH1Wzh9finwMcAPyMQC4yjEFOdq3662/v/+UWXMsFgvHcSqVinF51ctvq/lYPwrXoLMa4Abk\nYwBwFatiGm7eUoJhGKVSKbQcdFYD9IZLAgBcpVNR9yHWg2PlKLuCeygaNx+Am+CSAABXsUrqveWi\nUF9e42ewjF7tjoAARhHkYwBwVY8pyIODzmqAPuGqAABXDb19bLJTXhW3DJ3VAL3gqgAAV7FKaui1\nxZMgByq4O/WSAIWbAgIYRZCPAcBVur62QBYkq5TPjME0J4A+IB8DgKtYVR9bILuuzUqHarglUbjt\nAPQBFwYAuIpVMkN5fry/nEsJl2jl7gsIYBRBPgYAVwUqqXkI46uzSjl0VgPcCvIxALhKypBMQib7\nYD7bbKbCen5RBO45AH3DtQEAArAqpmlQTeRPy7glURKV1O0RAYwSyMcAIACrpIZBPULGMiAA/cPl\nAQAC6AY1xPq6ic438clheHgMcEvIxwAgAKsczBTkrFJuWbREjvsNwK3h+gAAAQY3BRmd1QADwhUC\nAAKwyp5bIA+o0siXttL8UHRWA/QH+RgABGBVJLS/OquUfziGkSIdA/QL+RgABNApBfdXZ11BZzXA\nwHCRAIAArMAtJa608tdNNEeP1jHAAJCPAUAAVmD7eNcV/tHxDLIxwICQjwFAAFYlbD2QrFLukfG4\nzwAMDNcJAAigE7JeZnELb+NpWhCaxwADQz4GAAEUErJxZONcOvmjK9wjGMkF4BpcKgAgTKCSaba4\ndKZjppOHwwEYJZCPAUAYnWtTkL9r4LUyig9APgZwCfIxAAjj4hBrTDsGEARXCwAIw6qYhoHaxzzR\nnjI+E53VAC5DPgYAYVxpHx+p5ceoKdoX+RjAVcjHACAMq6LGgaYgY0MnAKFwwQCAMDoV09jvFGQ7\nT5+Wcf8zDo1jAAGQjwFAGFY5QPv4YDUf58+Ea5CPAQRAPgYAYVjVAFsgZ5VymVgjE0AgXDMAIAyr\npH76q60cZVdwD47FvQVAGFwzACCMrt/xXF9e42fqGL16GAMCGBWQjwFAGFbZ33gujKwGGBxcNgAg\njFZORhv1mZBNdsqr4pahsxpAOFw2ACCYn5xp7WtLiQMV3F0hEn/FsAcEMPIhHwOAYKyq7yFdWaVY\nIxNgkJCPAUAwVkm9pzy1WelQDbckCncVgMHAlQMAgrEqpvcQ6/3l3H3hEo1MjIAARj7kYwAQTNfX\nFOSsUg6d1QCDhnwMAIL13lKi2UyF9XxqBG4pAIOEiwcABOs9BfnTMi4tSqKSihURwIiHfAwAgrGq\nnuO5sAwIwBDh+gEAwVgl02i+8fa6ic438clheHgMMHjIxwAgmE5FjaYb/dVZpdyD0RIZbicAQ4AL\nCAAEY5XUvX2MzmqAocMlBACCdd8CudLIX22jeaHorAYYEuRjABAsQEEtlq7+6qxS/uFxjBTpGGBo\nkI8BQDAJQyopddqIiLKuoLMawA2wtB0ADAarZBrMvKWDmsw0W4/WMcBQIR8DwGDoVNRoogMVfGYM\ng2wMMHQe6WXieX7Lli1paWlPPvlkaWnprU6rrKxcs2bN4cOHnUd27dq1bNmyX/7yl0VFRc6Dx48f\nf/zxx9PT0w8cOOCJaAFgEFgV02imrFIuczw6qwHcwCMX0tatW995553169ePGzcuOTnZYulr43Ki\ntWvX5ubmXrx40fF2//79L7300q9//es5c+YkJye3tLQQUWVl5f3335+amvrEE0+sWrWqoKDAEwED\ngOs4jqu4Vs1XX9pVcKGjrjxeaxU7IoDRwCP5+O23337ttdeSkpJeeuml4ODg7Ozs3uds3749Ojp6\n6tSp3T/1hz/8ISUlZe3atXPmzNm5cycRbdu2benSpcuXL1+8ePFzzz3397//3RMBA4CL7Hb7ibMX\nf2jlfcPG7euImRetLThb0tHRIXZcACOe+/OxzWYrLi6eNWuW4+2sWbPOnTvX45za2tq33nrrz3/+\nc/eDRUVF3T919uxZIjp37pzzYGJiYu+iAGA41dTVtykCA/VhQRplo02eFh8s00X9UHZN7LgARjz3\nj+dqbGzkOM7Pz8/xNiAg4Pr16z3Oefrpp//yl78EBAQ4j/A839jY6O/v73jr7+9/5swZImpoaHAe\n7LOo7mpqaiZNmsT8NLjkt7/97XPPPdfP+UajUcAPBqMR6oBQFdXXyXdMR0eHDyON9ZOESDuJZBV1\njROi2sUObZBQB6Cjo4Pne+7n7V4SicTHx6f/c9yfjwMDAxmGaW9vV6vVRNTa2sqybPcTsrOzq6ur\nIyIiTp06ZTAYKioqKioqoqKi/P3929raHOc4PxUYGNj9YFBQUD9fHRoampOTExoa6njr7+8vkQzQ\nAaDVagf1U8LogTogiMpHRRqNUqWeH85PCCIfHzkRmdTqEf1rHNHBw9AxDKPRaMSOwgP91QqFIjo6\n+vz58463RUVFEydO7H6C2WzWarUvvvjiiy++WFJS8tlnn+3bt4+IbrvtNuew6vPnzzs+NXHiRGdR\nzoO3wjCMv79/4E8GTMYAIFSwv9bY2kJEY3yYGSxDRB3tbayvWuy4AEY8j8w/Xr169YYNGyZMmHD0\n6NGLFy+mp6cTUW5ubn5+/uuvv56RkZGRkeE484EHHkhLS3vqqaeIaNWqVa+//vqcOXN++OGHvLy8\nzZs3E9HKlSvnzZv36KOP6nS6zZs3/+1vf/NEwADgojEh+mvXS5qvM74BrEQiaW9rtTddmzF5vNhx\nAYx4HsnH69evNxgMixYtCgsLO3DggKMfgOlrzYCEhISIiAjH65UrV9bV1S1btiwgIGD37t1jxowh\novj4+K1btz7//PMmk2ndunVpaWmeCBgAXCSTyWZPiausqqmuvWzhuBA/n5ipE1UqldhxAYx4jKcf\nYg+n2NjY/Pz8sLAwF89vb2/HcyMvhzoAqANgNBpH5/NjAAAAEMqr8/GHH35otWJpIa+2a9curGXh\n5T799FODwSB2FCCmnJyc+vp6saPw7nz8xhtvNDY2ih0FiOndd9+9dg1rWXi1rVu3Xr58WewoQEwf\nfvhh900TxOLV+RgAAOBnAvkYAABAfMjHAAAA4htV8530er3Vau1zonOf2tratFqt6+fD6NPe3u7j\n44Ol3LyZ0WhUq9WoA96so6NDqVRKpVLPfYVSqSwpKXHu7NCnUZWPAQAARij8SQgAACA+5GMAAADx\nIR8DAACID/kYAABAfMjHAAAA4vPIfosjwokTJ44ePRobG7t48WJMefIeV69ePXfu3Lhx46ZOneo8\n2NzcvHfvXpvN9uCDD+r1ehHDA08zm835+fklJSXBwcFpaWnOXX1sNlt2dnZFRUVycvKUKVPEDRI8\nqqWl5fDhw2VlZb6+vqmpqc4tATmOy87OLisrS0pKmj59+vAH5qXt4/fffz8jI6OlpWXDhg1PP/20\n2OHAMFm/fv38+fOffvrpnTt3Og82NzdPnz69sLDwwoULCQkJ1dXVIkYInrZy5cpNmzZVV1d//PHH\nkydPdu4ikJmZ+e677zY3Ny9cuDA3N1fcIMGjvvrqq48++qihoeHo0aOTJ0/+7rvvHMdXrFixadOm\n5ubmJUuW7N27V4TIeO9jt9tjYmK++eYbnuebmpq0Wm1lZaXYQcFwMJlMPM8/++yzL7zwgvPgpk2b\nli1b5ni9atWql19+WZzgYFgYDAbn67vvvvudd97hef7MmTPBwcGdnZ08z+/atWvu3LmixQfD61e/\n+tW6det4nr906VJAQEB7ezvP8/v37586derwB+ON7eOKioqqqqqkpCQiCgwMnDFjRkFBgdhBwXBQ\nKpW9Dx46dCg1NdXxeuHChQcPHhzeoGBYdV8gyWazOfqr8/Pzk5KSVCoVEaWmphYWFnZ2dooWIgyX\ntra2oqKi22+/nYgOHz585513OurDwoULi4qKmpqahjkeb8x3jVigAAAFtElEQVTHtbW1QUFBzqXR\nQkJCampqxA0JRFRbWxscHOx4rdfrURm8xI4dO+rq6jIzM+nmOhAYGCiXy2tra0WNDjzr1KlTQUFB\nQUFBISEhK1euJKKamhpnHVCpVH5+fsN/K/DGfKxSqaxWq/Ot2Wx2/F0M3kmpVFosFsdrs9msVqvF\njQeGwZdffvniiy/u37/fx8eHiJRKpfOeYLfb7XY77gmj28yZM5uamkpKSurr61999VXqlRcsFsvw\n1wFvzMcREREtLS0Gg8HxtqysLCoqStyQQERRUVFlZWWO1+Xl5ZGRkaKGAx737bffPvHEEzk5OZMn\nT3YciYyM7F4H5HI5htl7g5iYmCeffDIvL49urgO1tbVWq9U57nrYeGM+1ul0SUlJ//rXv4iosLCw\nqqoqOTlZ7KBANBkZGTt37uzo6LBardu3b3/44YfFjgg86MiRI8uXL//ss8+6T2j5xS9+ceLEiUuX\nLhHR1q1b09PTPbrVD4irpKTEbrcTkdls3rdvn+P58eLFiy9cuHD27Fki2rJly5IlS0ToKhv+IWQ/\nB0VFRbGxsZMmTQoNDd27d6/Y4cAwee+997pX/u3bt/M8b7fbV61aNWbMmMjIyMzMTIvFInaY4EGL\nFi3qXgfWr1/vOP7Pf/4zODg4Li5u6tSpZWVl4gYJHvW73/1Op9PFxcUFBgYuW7asqanJcXzHjh16\nvT4+Pn7SpEmXL18e/sC8d79FjuNqa2t1Op1CoRA7FhBfS0sLx3FBQUFiBwKiMZvNjY2Nw99LCcPP\n8X/d+/7vOD5mzBhRFony3nwMAADw8+GNz48BAAB+bpCPAQAAxId8DAAAID7kYwAAAPEhHwMAAIgP\n+RgAAEB8yMcA3mvjxo1vvfWW2FEAABHyMYD3WL58+ZYtW7ofyc/P/+9//ytWPADQnUzsAABgmBw5\nciQ0NLT7kQ8++ECUdYgAoDfkYwCvcODAAaPRWFJS8sknnxBRQkJCbGxsSUmJRCLR6XRE9OOPP37/\n/ffp6emff/75yZMnw8LCHn/8ca1WW1dXt3v3boPBkJKSMnfu3O5lXr169cCBA9XV1TExMRkZGQEB\nAeL8bACjAtbLBPAKjzzySHZ2tl6vj42NJaK1a9c+9NBD999/v0Kh2L9/PxG9++67v/nNb5544omD\nBw9GR0cfO3bstttu27Zt25IlS2JjYxsbGy9evPjRRx8597/atm3b2rVrY2NjJ0yYcPr0abvd/u23\n38bFxYn5QwKMZGgfA3iFjz/+ePz48enp6W+88catzuE4zmw2X7p0SSqVHjx48N577124cGFubm5i\nYiLP8w888MCGDRsc+fj8+fNPPfXUH//4x5dffplhmI6OjpSUlDVr1uTn5w/jzwQwqmA8FwDc8Mor\nrzi2/l2wYIGfn9+CBQsSExOJiGGYtLS0kpISm81GRO+//76/v//vf/97x+NnHx+fdevWFRQUdHZ2\nihs/wMiF9jEAdGEYZuzYsc63AQEB0dHR3d/abLa2trbAwMDi4mKTyTR79mznv7a3t3McV1ZWFh8f\nP5wxA4wayMcA0IVhGInkpj4zR1u5T+Hh4Rs3buxxMCIiwiORAXgB5GMAbyGXyx29zUM3ZcqUgwcP\nzpo1y9/f3y0FAgCeHwN4i6ioqFOnTnV0dAy9qNWrVzMMs3LlypaWFscRg8GwZ8+eoZcM4LWQjwG8\nxQsvvFBUVKTRaBiG2bx581CKiomJ2bt375EjR8LDwxMSEm677Ta9Xv/Xv/7VXaECeCHMPwbwImaz\n+erVq0ajMTIyUq/XX758mWGYCRMmEFF9fX1lZeXMmTOdJxcVFQUFBYWHhzveNjU1Xb16NSEhwflQ\nubOz89ChQ5WVlb6+vvHx8dOmTcNqXwCDhnwMAAAgPvRXAwAAiA/5GAAAQHzIxwAAAOJDPgYAABAf\n8jEAAID4kI8BAADEh3wMAAAgvv8PIR8/QxdMUCcAAAAASUVORK5CYII=\n"
          }
        }
      ],
      "source": [
        "# WalkRW2ls has varying step lengths according to preferred human\n",
        "wstar4ls = findgait(WalkRW2ls(α=0.4102,safety=true), target=:speed=>0.4789, varying=:P, cstep=0.35, vmstar=wstar4s.vm)\n",
        "varyingresult = optwalk(wstar4ls, nsteps, boundarywork=false,δs=δs)\n",
        "plotvees(upstepresult,boundaryvels=upstepresult.boundaryvels, speedtype=:midstance)\n",
        "plotvees!(varyingresult,boundaryvels=upstepresult.boundaryvels, speedtype=:midstance)"
      ],
      "id": "52596ab3-778d-4bb6-ae11-9d0f3ac24acc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Walk over a bunch of terrains\n",
        "\n",
        "The terrain is specified as a series of angle/height changes each step.\n",
        "The task is to start and end with nominal level walking, and to traverse\n",
        "the terrain in minimum energy, in the same amount of time as for level\n",
        "walking.\n",
        "\n",
        "Note that terrain profile is not plotted to scale."
      ],
      "id": "e12d3cbc-ce49-4f8a-acfa-78553d6de0b6"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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CaNiwYS5PJIPbop14nJiY+Prrr48cOdJ+2aXX61999dV77rnH/e3+9NNPBw8e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\nmICAgICAYOr5fwqyTkHGS/WvAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "## plot bumps and speed trajectories of all 8 terrains\n",
        "numStepsBefore = 6; numStepsAfter = 6\n",
        "# all terrain trajectories\n",
        "wstar4s = findgait(WalkRW2l(α=0.4102,safety=true), target=:speed=>0.4789, varying=:P)\n",
        "\n",
        "δs = ( # terrain defined a sequence of height or angle changes from previous step\n",
        "    \"level\" =>[zeros(numStepsBefore); [0] .* B; zeros(numStepsAfter)], # level   \n",
        "    \"U\" =>    [zeros(numStepsBefore); [1] .* B; zeros(numStepsAfter)], # Up\n",
        "    \"D\" =>    [zeros(numStepsBefore); [-1] .* B; zeros(numStepsAfter)], # Down\n",
        "    \"UD\" =>   [zeros(numStepsBefore); [1, -1] .* B; zeros(numStepsAfter)], # Up-Down\n",
        "    \"DnUD\" => [zeros(numStepsBefore); [-1, 0, 5/3, -5/3] .* B; zeros(numStepsAfter)] , # Down & Up-Down\n",
        "    \"P\" =>    [zeros(numStepsBefore); [ 1, 1, 1, 0, 0, 0, -1, -1, -1] .* B; zeros(numStepsAfter)], # Pyramid\n",
        "    \"C1\" =>   [zeros(numStepsBefore); [ 3, 2, -3, 2, -1, 3, 1, -3, -2, 3, -1, -2, -1, 3, -2, -2] .* B/3; zeros(numStepsAfter)], # Complex 1\n",
        "    \"C2\" =>   [zeros(numStepsBefore); [ 2, 2, -3, 1, 2, 1, -3, 2, 3, -1,  -3,  1, -2, 3, -2, -3] .* B/3; zeros(numStepsAfter)], # Complex 2\n",
        ")\n",
        "\n",
        "p = plot(layout=(4,4), legend=false); \n",
        "pslotnum(n) = n + (n>4 ? 4 : 0) # plot in slots 1 - 4, 9 - 12\n",
        "for (i,(terrainname, terrainbumps)) in enumerate(δs)\n",
        "    # plot the terrain profile in space (not to scale)\n",
        "    plotterrain!(p[pslotnum(i)], cumsum(terrainbumps)./B .* bumpHeightDimless, setfirstbumpstep=true,ylims=(-0.1,0.2),showaxis=false,grid=false)\n",
        "    # minimum-work strategy for terrain\n",
        "    results = optwalk(wstar4s, length(terrainbumps), δs=terrainbumps, boundarywork = false) # optimizing push-offs (boundarywork=false means start from nominal walking)\n",
        "    plotvees!(p[pslotnum(i)+4], results, boundaryvels=results.boundaryvels, speedtype=:midstance, setfirstbumpstep=true,title=terrainname, tchange = 0, ylims=(0.3,0.575))\n",
        "    vline!(p[pslotnum(i)+4], [0]) # mark where the first uneven step is\n",
        "end\n",
        "display(p)"
      ],
      "id": "bb96e9b3-856f-4664-87d2-c3b5b1f23cd6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Walk over a simple bump with no compensation\n",
        "\n",
        "Model walks with constant push-offs for steady walking, and encounters\n",
        "the up-step without any compensation. As a result of the unexpected\n",
        "upward step, the model loses speed, and with repeated constant\n",
        "push-offs, will eventually regain nominal speed. The number of regaining\n",
        "steps is described by the persistence distance. This model expends the\n",
        "same energy as level walking, but accumulates a time deficit compared to\n",
        "minimum-work compensation. Walking over a bump generally requires more\n",
        "time or more work. More detail is available from Darici, Temeltas, and\n",
        "Kuo (2020)."
      ],
      "id": "2b084eb8-f8d7-4682-8d60-7b9b651c608d"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No compensation total work cost = 0.4433306466750797\n",
            "Min-work compensation total work cost = 0.5538343313152624"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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9BgCApgTXjwEAAOhHz93RAAAAoOgD6nFUVFS7du0MDQ0ZrxMIBKrLBwAA0By8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\nigpdXV1+YXx8vLS09KFDh8QYGwCgV3CEYvKxEx4wJxcAA4CQXqU1a9Y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5c+YQK6h+CjIy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\nJO//Ac+/7LPnsuwsAAAAAElFTkSuQmCC\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final time deficit = -1.2734506601085016"
          ]
        }
      ],
      "source": [
        "upstep = δs[2][2] # up-step terrain, get the terrain array\n",
        "nsteps = length(upstep)\n",
        "nocompresult = multistep(wstar4s, Ps=fill(wstar4s.P,nsteps),δangles=upstep,boundaryvels=(wstar4s.vm,wstar4s.vm))\n",
        "println(\"No compensation total work cost = \", nocompresult.totalcost)\n",
        "println(\"Min-work compensation total work cost = \", upstepresult.totalcost)\n",
        "p = multistepplot(nocompresult, legend=false, boundarywork=false)\n",
        "display(p)\n",
        "plot(cumsum(upstepresult.steps.tf),label=\"min work\")\n",
        "plot!(cumsum(nocompresult.steps.tf), xlabel=\"step\",ylabel=\"accumulated time\", label=\"no compensation\")\n",
        "println(\"Final time deficit = \", -sum(upstepresult.steps.tf)+sum(nocompresult.steps.tf))"
      ],
      "id": "b44a36f1-6e92-446b-8712-c494252a4596"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Walk over a single bump with a reactive compensation\n",
        "\n",
        "Here the model does not anticipate the up-step and loses speed and time\n",
        "upon first contact with it. Thereafter, the model compensates and\n",
        "catches up to the level ground model by looking ahead and adjusting the\n",
        "trajectory of push-offs. This strategy therefore actually anticipates\n",
        "and optimally compensates for all steps other the first uneven one. It\n",
        "is almost impossible to regain time without some knowledge and goal for\n",
        "the terrain ahead. More detail is available from Darici, Temeltas, and\n",
        "Kuo (2020)."
      ],
      "id": "fd1099b3-dfa7-435b-b8f6-bf5156c919c7"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Reactive contrl total work cost = 0.5756333115295249\n",
            "Up-step min-work control total work cost = 0.5538343313152624"
          ]
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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qOkXvd0pMTGzdurV8++jRo2PGjPnzzz8zMzMtLS3T0tLkV4IRQpolk0rvrZsi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gU1dX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\nAADE+3+q255u5CL7iQAAAABJRU5ErkJggg==\n"
          }
        },
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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SlLF0ovxBgvtXq+yDBhI+VfqnLCG/JzM9j9PTA/h7gyhnoaHKhPLS75WLzZs3d+vWrVq1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\n"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final time deficit = 2.1316282072803006e-14"
          ]
        }
      ],
      "source": [
        "nbump = Int(floor((nsteps+1)/2))\n",
        "reactresults1 = multistep(wstar4s, Ps=fill(wstar4s.P,nbump),δangles=upstep[1:nbump],boundaryvels=(wstar4s.vm,wstar4s.vm))\n",
        "reactresults2 = optwalk(wstar4s, length(upstepresult.steps)-nbump, totaltime = upstepresult.totaltime - reactresults1.totaltime,boundaryvels=(reactresults1.steps[end].vm,wstar4s.vm), boundarywork=(false,false))\n",
        "reactresult = cat(reactresults1, reactresults2)\n",
        "println(\"Reactive contrl total work cost = \", reactresult.totalcost)\n",
        "println(\"Up-step min-work control total work cost = \", upstepresult.totalcost)\n",
        "p = multistepplot(reactresult,boundarywork=false) # plot concatenation of two simulations\n",
        "display(p)\n",
        "p = plot(cumsum(upstepresult.steps.tf),label=\"up-step min-work\")\n",
        "plot!(p, cumsum(reactresult.steps.tf), xlabel=\"step\",ylabel=\"accumulated time\", label=\"reactive\")\n",
        "display(p)\n",
        "println(\"Final time deficit = \", -sum(upstepresult.steps.tf)+sum(reactresult.steps.tf))"
      ],
      "id": "cc8abb90-0f4b-4629-88c9-1327f1076c11"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Julia code\n",
        "\n",
        "This page is viewable as [Jupyter notebook](uneventerrain.ipynb), [plain\n",
        "Julia](uneventerrain.jl) text, or [HTML](uneventerrain.html).\n",
        "\n",
        "# Matlab code\n",
        "\n",
        "There is also extensive Matlab code for an earlier implementation of the\n",
        "same model. See [Matlab directory](../matlab). There is very limited\n",
        "documentation of this code.\n",
        "\n",
        "## Experimental data\n",
        "\n",
        "The data from accompanying human subjects experiment are available in a\n",
        "[separate data and code\n",
        "repository](https://github.com/kuo-lab/uneventerrainexperiment/). The\n",
        "code is in Matlab, and the data files are in .mat format, which is\n",
        "compatible with HDF5.\n",
        "\n",
        "## References\n",
        "\n",
        "Darici, Osman, and Arthur D. Kuo. 2022. “Humans Optimally Anticipate and\n",
        "Compensate for an Uneven Step During Walking.” Edited by Lena H Ting.\n",
        "*eLife* 11 (January): e65402. <https://doi.org/10.7554/eLife.65402>.\n",
        "\n",
        "Darici, Osman, Hakan Temeltas, and Arthur D. Kuo. 2020. “Anticipatory\n",
        "Control of Momentum for Bipedal Walking on Uneven Terrain.” *Scientific\n",
        "Reports* 10 (1): 540. <https://doi.org/10.1038/s41598-019-57156-6>."
      ],
      "id": "442886c5-bcdb-4c97-9446-158fbe0d9552"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "name": "julia-1.8",
      "display_name": "Julia 1.8.5",
      "language": "julia"
    }
  }
}
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