lessons/notebooks/ai_agent/robot_car_2d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A 2D version of the Robot Parking problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a 2D version of the Robot parking problem. Credits for this implemention to  [Thijs van de Laar](https://biaslab.github.io/member/thijs) and [Burak Ergul](https://biaslab.github.io/member/burak). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m environment at `~/biaslab/repos/BMLIP/lessons/notebooks/probprog/workspace/Project.toml`\n"
     ]
    }
   ],
   "source": [
    "using Pkg;Pkg.activate(\"../probprog/workspace/\");Pkg.instantiate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Random\n",
    "Random.seed!(87613) # Set random seed\n",
    "\n",
    "using LinearAlgebra\n",
    "using PyPlot\n",
    "using ForneyLab\n",
    "\n",
    "include(\"environment_2d.jl\") # Include environmental dynamics\n",
    "include(\"helpers_2d.jl\") # Include helper functions for plotting\n",
    "include(\"agent_2d.jl\") # Load agent's internal beliefs over external dynamics\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build model\n",
    "\n",
    "We define the state of the robot (at time $k$) as the current orientation and Cartesian coordinates:\n",
    "\\begin{align}\n",
    "    s_k = (ϕ_k, x_k, y_k)^{T}\\,.\n",
    "\\end{align}\n",
    "\n",
    "The control consists of a change in orientation and subsequent travel distance:\n",
    "\\begin{align}\n",
    "    u_k = (\\Delta\\phi_k, r_k)^{T}\\,.\n",
    "\\end{align}\n",
    "\n",
    "The model factorization did not change:\n",
    "\\begin{align}\n",
    "    p_t(o, s, u) &\\propto p(s_{t-1}) \\prod_{k=t}^{t+T} p(o_k | s_k)\\, p(s_k | s_{k-1}, u_k)\\, p(u_k)\\, \\tilde{p}(o_k)\\,.\n",
    "\\end{align}\n",
    "\n",
    "The specific model assumptions however now include a non-linear transition function $g$:\n",
    "\\begin{align}\n",
    "    p(s_{t-1}) &= \\mathcal{N}(s_{t-1} | m_{s, t-t}, V_{s, t-1})\\\\\n",
    "    p(s_k | s_{k-1}, u_k) &= \\mathcal{N}(s_k | g(s_{k-1}, u_k), \\Gamma^{-1})\\\\\n",
    "    p(o_k | s_k) &= \\mathcal{N}(o_k | s_k, \\Phi^{-1})\\\\\n",
    "    p(u_k) &= \\mathcal{N}(u_k | 0, \\Upsilon) \\text{, for } k>t\\\\\n",
    "    \\tilde{p}(o_k) &= \\mathcal{N}(o_k | 0, \\Sigma) \\text{, for } k>t\\\\\n",
    "    p(u_t) &= \\delta(u_t - \\hat{u}_t)\\\\\n",
    "    \\tilde{p}(o_t) &= \\delta(o_t - \\hat{o}_t)\\,.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Internal model perameters\n",
    "Gamma   = 100.0*diageye(3) # Transition precision\n",
    "Phi     = 10.0*diageye(3) # Observation precision\n",
    "Upsilon = Diagonal([0.25*pi, 1.0].^2) # Control prior variance\n",
    "Sigma   = Diagonal([1.0, 30.0, 30.0]) # Goal prior variance\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 10 # Lookahead\n",
    "\n",
    "# Build internal model\n",
    "fg = FactorGraph()\n",
    "\n",
    "o   = Vector{Variable}(undef, T) # Observed states\n",
    "s_g = Vector{Variable}(undef, T) # Noiseless internal states\n",
    "s   = Vector{Variable}(undef, T) # Noisy internal states\n",
    "u   = Vector{Variable}(undef, T) # Control states\n",
    "\n",
    "@RV s_t_min ~ GaussianMeanVariance(placeholder(:m_s_t_min, dims=(3,)),\n",
    "                                   placeholder(:V_s_t_min, dims=(3,3))) # Prior internal state\n",
    "u_t = placeholder(:u_t, dims=(2,))\n",
    "@RV u[1]   ~ GaussianMeanVariance(u_t, tiny*diageye(2))\n",
    "@RV s_g[1] ~ Nonlinear{Unscented}(s_t_min, u[1], g=g,g_inv=[g_inv_in1,g_inv_in2])\n",
    "@RV s[1]   ~ GaussianMeanPrecision(s_g[1], Gamma)\n",
    "@RV o[1]   ~ GaussianMeanPrecision(s[1], Phi)\n",
    "placeholder(o[1], :o_t, dims=(3,))\n",
    "\n",
    "s_k_min = s[1]\n",
    "for k=2:T\n",
    "    @RV u[k]   ~ GaussianMeanVariance(zeros(2), Upsilon)\n",
    "    @RV s_g[k] ~ Nonlinear{Unscented}(s_k_min, u[k], g=g, g_inv=[g_inv_in1,g_inv_in2]) # Noiseless transition model\n",
    "    @RV s[k]   ~ GaussianMeanPrecision(s_g[k], Gamma) # State transition model including noise\n",
    "    @RV o[k]   ~ GaussianMeanPrecision(s[k], Phi) # Observation model\n",
    "    GaussianMeanVariance(o[k], \n",
    "                         placeholder(:m_o, var_id=:m_o_*k, index=k-1, dims=(3,)),\n",
    "                         placeholder(:V_o, var_id=:V_o_*k, index=k-1, dims=(3,3))) # Goal prior\n",
    "    s_k_min = s[k]\n",
    "end\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Infer algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "function step!(data::Dict, marginals::Dict=Dict(), messages::Vector{Message}=Array{Message}(undef, 59))\n",
      "\n",
      "messages[1] = ruleSPGaussianMeanVarianceOutNPP(nothing, Message(Multivariate, PointMass, m=[0.0, 0.0]), Message(MatrixVariate, PointMass, m=Diagonal([0.6168502750680849, 1.0])))\n",
      "messages[2] = ruleSPGaussianMeanVarianceOutNPP(nothing, Message(Multivariate, PointMass, m=data[:m_s_t_min]), Message(MatrixVariate, PointMass, m=data[:V_s_t_min]))\n",
      "messages[3] = ruleSPGaussianMeanVarianceOutNPP(nothing, Message(Multivariate, PointMass, m=data[:u_t]), Message(MatrixVariate, PointMass, m=Diagonal([1.0e-12, 1.0e-12])))\n",
      "\n",
      "...\n",
      "\n",
      "marginals[:u_2] = messages[1].dist * messages[59].dist\n",
      "\n",
      "return marginals\n",
      "\n",
      "end\n"
     ]
    }
   ],
   "source": [
    "# Schedule message passing algorithm\n",
    "q = PosteriorFactorization(fg)\n",
    "algo = messagePassingAlgorithm(u[2]) # Infer internal states\n",
    "source = algorithmSourceCode(algo)\n",
    "eval(Meta.parse(source)) # Loads the step!() function for inference\n",
    "inspectSnippet(source) # Inspect a snippet of the algorithm code\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Execute algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initial state\n",
    "ϕ_0 = pi # Initial orientation\n",
    "x_0 = 2.0 # Initial coordinates\n",
    "y_0 = 3.0\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 20 # Total simulation time\n",
    "\n",
    "(execute, observe)  = initializeWorld() # Let there be a world\n",
    "(infer, act, slide) = initializeAgent() # Let there be an agent\n",
    "\n",
    "# Step through action-perception loop\n",
    "u_hat = Vector{Vector{Float64}}(undef, N) # Actions\n",
    "o_hat = Vector{Vector{Float64}}(undef, N) # Observations\n",
    "for t=1:N\n",
    "    u_hat[t] = act() # Evoke an action from the agent\n",
    "               execute(u_hat[t]) # The action influences hidden external states\n",
    "    o_hat[t] = observe() # Observe the current environmental outcome (update p)\n",
    "               infer(u_hat[t], o_hat[t]) # Infer beliefs from current model state (update q)\n",
    "               slide() # Prepare for next iteration\n",
    "end\n",
    ";"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### and plot the position track"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot active inference results\n",
    "plotTrajectory(u_hat, o_hat)\n",
    ";"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.5.2",
   "language": "julia",
   "name": "julia-1.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}