From 8d538e04f9c13d9ebbdb169876fbdd5956e35ae6 Mon Sep 17 00:00:00 2001 From: Alfredo Canziani Date: Wed, 1 May 2019 15:35:43 -0400 Subject: [PATCH] Add model predictive controller learning --- 14-truck_backer-upper.ipynb | 437 ++++++++++++++++++++++++++++ car-trailer-k.png | Bin 0 -> 10592 bytes car-trailer-w.png | Bin 0 -> 10797 bytes slides/09 - Controller learning.pdf | Bin 0 -> 1221498 bytes 4 files changed, 437 insertions(+) create mode 100644 14-truck_backer-upper.ipynb create mode 100644 car-trailer-k.png create mode 100644 car-trailer-w.png create mode 100644 slides/09 - Controller learning.pdf diff --git a/14-truck_backer-upper.ipynb b/14-truck_backer-upper.ipynb new file mode 100644 index 000000000..499d1744e --- /dev/null +++ b/14-truck_backer-upper.ipynb @@ -0,0 +1,437 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from matplotlib.pylab import *\n", + "from matplotlib.patches import Rectangle\n", + "from matplotlib.collections import PatchCollection\n", + "from matplotlib.lines import Line2D\n", + "π = pi" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "style.use(['dark_background', 'bmh'])\n", + "%matplotlib notebook" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Car-trailer diagram (inverted image `car-trainer-k.png` available as well):\n", + "![car-trailer](car-trailer-w.png)\n", + "\n", + "Car-trailer equation:\n", + "\\begin{align}\n", + "\\dot x &= s \\cos \\theta_0 \\\\\n", + "\\dot y &= s \\sin \\theta_0 \\\\\n", + "\\dot \\theta_0 &= \\frac{s}{L} \\tan \\phi \\\\\n", + "\\dot \\theta_1 &= \\frac{s}{d_1} \\sin(\\theta_1 - \\theta_0)\n", + "\\end{align}\n", + "where $s$: signed speed, $\\phi$: negative steering angle," + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "class Truck:\n", + " def __init__(self, display=False):\n", + "\n", + " self.W = 1 # car and trailer width, for drawing only\n", + " self.L = 1 * self.W # car length\n", + " self.d = 4 * self.L # d_1\n", + " self.s = -0.1 # speed\n", + " self.display = display\n", + " \n", + " self.box = [0, 40, -10, 10]\n", + " if self.display:\n", + " self.f = figure(figsize=(10, 5), num='The truck backer-upper', facecolor='none')\n", + " self.ax = self.f.add_axes([0.01, 0.01, 0.98, 0.98], facecolor='black')\n", + " self.patches = list()\n", + " \n", + " self.ax.axis('equal')\n", + " b = self.box\n", + " self.ax.axis([b[0] - 1, b[1], b[2], b[3]])\n", + " self.ax.set_xticks([], []); self.ax.set_yticks([], [])\n", + " self.ax.axhline(); self.ax.axvline()\n", + "\n", + " self.reset()\n", + " \n", + " def reset(self, ϕ=0):\n", + " self.ϕ = ϕ # car initial steering angle\n", + " \n", + " # self.θ0 = deg2rad(30) # car initial direction\n", + " # self.θ1 = deg2rad(-30) # trailer initial direction\n", + " # self.x, self.y = 20, -5 # initial car coordinates\n", + " \n", + " self.θ0 = random() * 2 * π # 0 <= ϑ₀ < 2π\n", + " self.θ1 = (random() - 0.5) * π / 2 + self.θ0 # -π/4 <= ϑ₁ - ϑ₀ < π/4\n", + " self.x = (random() * .75 + 0.25) * self.box[1]\n", + " self.y = (random() - 0.5) * (self.box[3] - self.box[2])\n", + " \n", + " # If poorly initialise, then re-initialise\n", + " if not self.valid():\n", + " self.reset(ϕ)\n", + " \n", + " # Draw, if display is True\n", + " if self.display: self.draw()\n", + " \n", + " def step(self, ϕ=0, dt=1):\n", + " \n", + " # Check for illegal conditions\n", + " if self.is_jackknifed():\n", + " print('The truck is jackknifed!')\n", + " return\n", + " \n", + " if self.is_offscreen():\n", + " print('The car or trailer is off screen')\n", + " return\n", + " \n", + " self.ϕ = ϕ\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " \n", + " # Perform state update\n", + " self.x += s * cos(θ0) * dt\n", + " self.y += s * sin(θ0) * dt\n", + " self.θ0 += s / L * tan(ϕ) * dt\n", + " self.θ1 += s / d * sin(θ0 - θ1) * dt\n", + " \n", + " return (self.x, self.y, self.θ0, *self._traler_xy(), self.θ1)\n", + " \n", + " def _get_atributes(self):\n", + " return (\n", + " self.x, self.y, self.W, self.L, self.d, self.s,\n", + " self.θ0, self.θ1, self.ϕ\n", + " )\n", + " \n", + " def _traler_xy(self):\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " return x - d * cos(θ1), y - d * sin(θ1)\n", + " \n", + " def is_jackknifed(self):\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " return abs(θ0 - θ1) * 180 / π > 90\n", + " \n", + " def is_offscreen(self):\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " \n", + " x1, y1 = x + 1.5 * L * cos(θ0), y + 1.5 * L * sin(θ0)\n", + " x2, y2 = self._traler_xy()\n", + " \n", + " b = self.box\n", + " return not (\n", + " b[0] <= x1 <= b[1] and b[2] <= y1 <= b[3] and\n", + " b[0] <= x2 <= b[1] and b[2] <= y2 <= b[3]\n", + " )\n", + " \n", + " def valid(self):\n", + " return not self.is_jackknifed() and not self.is_offscreen()\n", + " \n", + " def draw(self):\n", + " if not self.display: return\n", + " if self.patches: self.clear()\n", + " self._draw_car()\n", + " self._draw_trailer()\n", + " self.f.canvas.draw()\n", + " \n", + " def clear(self):\n", + " for p in self.patches:\n", + " p.remove()\n", + " self.patches = list()\n", + " \n", + " def _draw_car(self):\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " ax = self.ax\n", + " \n", + " x1, y1 = x + L / 2 * cos(θ0), y + L / 2 * sin(θ0)\n", + " bar = Line2D((x, x1), (y, y1), lw=5, color='C2', alpha=0.8)\n", + " ax.add_line(bar)\n", + "\n", + " car = Rectangle(\n", + " (x1, y1 - W / 2), L, W, 0, color='C2', alpha=0.8, transform=\n", + " matplotlib.transforms.Affine2D().rotate_deg_around(x1, y1, θ0 * 180 / π) +\n", + " ax.transData\n", + " )\n", + " ax.add_patch(car)\n", + "\n", + " x2, y2 = x1 + L / 2 ** 0.5 * cos(θ0 + π / 4), y1 + L / 2 ** 0.5 * sin(θ0 + π / 4)\n", + " left_wheel = Line2D(\n", + " (x2 - L / 4 * cos(θ0 + ϕ), x2 + L / 4 * cos(θ0 + ϕ)),\n", + " (y2 - L / 4 * sin(θ0 + ϕ), y2 + L / 4 * sin(θ0 + ϕ)),\n", + " lw=3, color='C5', alpha=1)\n", + " ax.add_line(left_wheel)\n", + "\n", + " x3, y3 = x1 + L / 2 ** 0.5 * cos(π / 4 - θ0), y1 - L / 2 ** 0.5 * sin(π / 4 - θ0)\n", + " right_wheel = Line2D(\n", + " (x3 - L / 4 * cos(θ0 + ϕ), x3 + L / 4 * cos(θ0 + ϕ)),\n", + " (y3 - L / 4 * sin(θ0 + ϕ), y3 + L / 4 * sin(θ0 + ϕ)),\n", + " lw=3, color='C5', alpha=1)\n", + " ax.add_line(right_wheel)\n", + " \n", + " self.patches += [car, bar, left_wheel, right_wheel]\n", + " \n", + " def _draw_trailer(self):\n", + " x, y, W, L, d, s, θ0, θ1, ϕ = self._get_atributes()\n", + " ax = self.ax\n", + " \n", + " x, y = x - d * cos(θ1), y - d * sin(θ1) - W / 2\n", + " trailer = Rectangle(\n", + " (x, y), d, W, 0, color='C0', alpha=0.8, transform=\n", + " matplotlib.transforms.Affine2D().rotate_deg_around(x, y + W/2, θ1 * 180 / π) +\n", + " ax.transData\n", + " )\n", + " ax.add_patch(trailer)\n", + " \n", + " self.patches += [trailer]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "truck = Truck(display=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "ϕ = deg2rad(-35) # positive left, negative right\n", + "truck.step(ϕ)\n", + "truck.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "truck.reset()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "import torch.nn as nn\n", + "from torch.optim import SGD\n", + "from tqdm import tqdm" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Build expert data set\n", + "\n", + "episodes = 10\n", + "data_set = list()\n", + "truck = Truck(); episodes = 10_000\n", + "\n", + "for episode in tqdm(range(episodes)):\n", + " \n", + " truck.reset()\n", + " states = list()\n", + " \n", + " while truck.valid():\n", + " ϕ = (random() - 0.5) * π / 2\n", + " states.append((ϕ, *truck.step(ϕ)))\n", + " truck.draw()\n", + " \n", + " data_set.append(states)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "len(data_set)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "state_size = 6\n", + "steering_size = 1\n", + "hidden_units_e = 45\n", + "\n", + "emulator = nn.Sequential(\n", + " nn.Linear(steering_size + state_size, hidden_units_e),\n", + " nn.ReLU(),\n", + " nn.Linear(hidden_units_e, state_size)\n", + ")\n", + "\n", + "optimiser_e = SGD(emulator.parameters(), lr=0.05)\n", + "criterion = nn.MSELoss()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "train_set = data_set[:8000]\n", + "test_set = data_set[8000:]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "tensor_train_set = torch.cat([torch.Tensor(episode) for episode in train_set])\n", + "tensor_test_set = torch.cat([torch.Tensor(episode) for episode in test_set])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mean = tensor_train_set.mean(0)\n", + "std = tensor_train_set.std(0)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "train_data = (tensor_train_set - mean) / std\n", + "test_data = (tensor_test_set - mean) / std" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "len(train_set)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Train... BUG! Can you spot it?\n", + "# What is one of the main assumptions for training a net?\n", + "i = 0\n", + "for episode in range(len(train_set)):\n", + " episode_loss = 0\n", + " for _ in range(len(train_set[episode]) - 1):\n", + " ϕ_state = train_data[i]\n", + " next_state_prediction = emulator(ϕ_state)\n", + " \n", + " next_state = train_data[i + 1, 1:]\n", + " loss = criterion(next_state_prediction, next_state)\n", + " episode_loss += loss.item()\n", + " \n", + " optimiser_e.zero_grad()\n", + " loss.backward()\n", + " optimiser_e.step()\n", + " i += 1\n", + " \n", + " # Skip end, because there is no next_frame\n", + " i += 1\n", + " \n", + " if (episode + 1) % 1000 == 0 or episode == 0:\n", + " print(f'{episode + 1:4d} / {len(train_set)}, {episode_loss:.10f}')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Test\n", + "i = 0\n", + "total_loss = 0\n", + "with torch.no_grad():\n", + " for episode in range(len(test_set)):\n", + " for _ in range(len(test_set[episode]) - 1):\n", + " ϕ_state = test_data[i]\n", + " next_state_prediction = emulator(ϕ_state)\n", + "\n", + " next_state = train_data[i + 1, 1:]\n", + " total_loss += criterion(next_state_prediction, next_state).item()\n", + "\n", + " i += 1\n", + "\n", + " # Skip end, because there is no next_frame\n", + " i += 1\n", + " \n", + "print(f'Test loss: {loss.item():.10f}')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Here you need to insert the code for training the controller\n", + "# by using the emulator for backpropagation\n", + "\n", + "# If you succeed, feel free to send a PR" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": 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