ADMM_variant_demo.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "-l34xq6wi2xr"
      },
      "outputs": [],
      "source": [
        "from cvxpy import *\n",
        "import numpy as np\n",
        "from multiprocessing import Process, Pipe\n",
        "from scipy import sparse\n",
        "import cvxpy as cp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "nyYnVWgAjaBL"
      },
      "outputs": [],
      "source": [
        "# Number of robots.\n",
        "N = 3\n",
        "\n",
        "#Discrete time horizon\n",
        "T = 10\n",
        "\n",
        "# Dimension of the state space (2D pose for each robot :( x, y, theta) ).\n",
        "nx = 6 * N\n",
        "\n",
        "# Dimension of the input space ((v_x, v_y) for each robot)\n",
        "nu = 3 * N\n",
        "\n",
        "# Discrete time model of a double integrator (in R^3)\n",
        "# x:(px,py,pz,vx,vy,vz)\n",
        "# u:(ax,ay,az)\n",
        "h = 0.1 #Discretization interval\n",
        "Ad = sparse.csc_matrix([[1 ,0 ,0, h, 0, 0],\n",
        "                        [0, 1 ,0, 0, h, 0],\n",
        "                        [0, 0, 1, 0, 0, h],\n",
        "                        [0, 0, 0, 1, 0, 0],\n",
        "                        [0, 0, 0, 0, 1, 0],\n",
        "                        [0, 0, 0, 0, 0, 1]])\n",
        "\n",
        "Bd = sparse.csc_matrix([[h**2/2, 0, 0],\n",
        "                        [0,h**2/2, 0],\n",
        "                        [0 , 0, h**2/2],\n",
        "                        [h, 0, 0],\n",
        "                        [0, h, 0],\n",
        "                        [0, 0, h]])\n",
        "\n",
        "# List of all the f_i functions for each robot.\n",
        "f_list = []\n",
        "\n",
        "\n",
        "# Initialize robot positions and goal positions randomly.\n",
        "np.random.seed(0)\n",
        "# robot_positions = np.random.rand(N, 3)  # Random initial positions.\n",
        "goal_state = np.random.rand(N, 6)*2   # Random goal positions.\n",
        "for i in range(goal_state.shape[0]):\n",
        "  goal_state[i][3:] = np.zeros(3)\n",
        "\n",
        "# Formulate the model predictive control problem.\n",
        "objective = 0\n",
        "Q = np.eye(6)\n",
        "R = np.eye(3)*0.1\n",
        "Qf = Q*10\n",
        "f_list = []\n",
        "x0 = np.array([1.5,2.5,1,0,0,0,\n",
        "                   -1.5,1.1,1,0, 0, 0,\n",
        "                   -2.5, 1.5, 1, 0, 0, 0 ])\n",
        "\n",
        "xr = np.array([-1.5,0.5,1,0,0,0,\n",
        "                1.5,-1.1,1,0, 0, 0,\n",
        "              2.5, -1.5, 1, 0, 0, 0 ])\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "MEdI8V87VLZ4"
      },
      "outputs": [],
      "source": [
        "def distance_to_goal(x,xf,n_agents,n_states):\n",
        "    n_d = 3\n",
        "    return np.linalg.norm((x - xf).reshape(n_agents, n_states)[:, :n_d], axis=1)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "wHAYlZbDizeP"
      },
      "outputs": [],
      "source": [
        "# Parameters for the ADMM algorithm.\n",
        "rho = 0.5\n",
        "MAX_ITER = 30\n",
        "r_min = 0.3*2\n",
        "# Parameters for ADMM.\n",
        "# MAX_ITER_ADMM = 15\n",
        "neighbors = [[1,2],[0,2],[0,1]]  # List of neighbor indices for each agent including itself\n",
        "\n",
        "def run_worker(agent_idx, pipe, x_curr):\n",
        "    pk = Parameter((T+1)*nx + T*nu, value=np.zeros(((T+1)*nx + T*nu)))\n",
        "    x_init = Parameter(6 , value = np.zeros(6))\n",
        "    xi = Variable((T+1)*nx + T*nu)\n",
        "    constr = []\n",
        "    constr += [xi[agent_idx*6:(agent_idx+1)*6] ==x_init]\n",
        "    x_init.value = x_curr[agent_idx*6:(agent_idx+1)*6]\n",
        "    objective_i = 0\n",
        "    for t in range(T):\n",
        "      objective_i += quad_form(xi[:(T+1)*nx][t*nx:(t+1)*nx][i*6:(i+1)*6]-xr[agent_idx*6:(agent_idx+1)*6], Q) \\\n",
        "                      + quad_form(xi[(T+1)*nx:][t*nu:(t+1)*nu][i*3:(i+1)*3], R)\n",
        "\n",
        "    objective_i += quad_form(xi[T*nx:(T+1)*nx][i*6:(i+1)*6]-xr[agent_idx*6:(agent_idx+1)*6], Qf)\n",
        "    for k in range(T):\n",
        "      x_next = Ad@xi[:(T+1)*nx][(k)*nx:(k+1)*nx][agent_idx*6:(agent_idx+1)*6] + Bd@xi[(T+1)*nx:][k*nu:(k+1)*nu][agent_idx*3:(agent_idx+1)*3]\n",
        "      constr += [xi[:(T+1)*nx][(k+1)*nx:(k+2)*nx][agent_idx*6:(agent_idx+1)*6] == x_next]\n",
        "      constr += [abs(xi[(T+1)*nx:][(k)*nu:(k+1)*nu][agent_idx*3:(agent_idx+1)*3]) <= np.array([2, 2, 2])]\n",
        "      #Collision avoidance via Buffered Voronoi Cells:\n",
        "      p_i_prev = x_curr[agent_idx*6:(agent_idx+1)*6][:3]\n",
        "      p_i_next = x_next[:3]\n",
        "      for j in range(N):\n",
        "        if j != agent_idx:\n",
        "          # continue\n",
        "          p_j_prev = x_curr[j*6:(j+1)*6][:3]\n",
        "\n",
        "          a_ij  =  (p_i_prev -p_j_prev)/cp.norm(p_i_prev -p_j_prev)\n",
        "          b_ij = a_ij @ (p_i_prev + p_j_prev)/2 + r_min/2\n",
        "          constr += [ (a_ij @ p_i_next) >= b_ij ]\n",
        "\n",
        "    dual_update = 0\n",
        "    while True:\n",
        "        # Primal update\n",
        "        primal_objective = objective_i + pk.T @ xi\n",
        "        x_neighbor = pipe.recv()\n",
        "        for neighbor_i in neighbors[agent_idx]:\n",
        "          for neighbor_j in neighbors[agent_idx]:\n",
        "              if neighbor_j != neighbor_i and neighbor_i < neighbor_j:\n",
        "                # print(neighbor_i, neighbor_j)\n",
        "                primal_objective += rho/2 * sum_squares(xi - (x_neighbor[neighbor_j] + x_neighbor[neighbor_i])/2)\n",
        "\n",
        "        primal_problem = Problem(Minimize(primal_objective),constr)\n",
        "        primal_problem.solve()\n",
        "\n",
        "        pipe.send((xi.value))\n",
        "        # Dual update\n",
        "        for neighbor_idx in neighbors[agent_idx]:\n",
        "            dual_update += (xi.value - x_neighbor[neighbor_idx])\n",
        "        pk.value += rho * dual_update\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "92wcIgIoUAfn",
        "outputId": "60b08fc7-0327-438a-bdca-52ac491d2bab"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Current MPC iteration is 1\n",
            "Current MPC iteration is 2\n",
            "Current MPC iteration is 3\n",
            "Current MPC iteration is 4\n",
            "Current MPC iteration is 5\n",
            "Current MPC iteration is 6\n",
            "Current MPC iteration is 7\n",
            "Current MPC iteration is 8\n",
            "Current MPC iteration is 9\n",
            "Current MPC iteration is 10\n",
            "Current MPC iteration is 11\n",
            "Current MPC iteration is 12\n",
            "Current MPC iteration is 13\n",
            "Current MPC iteration is 14\n",
            "Current MPC iteration is 15\n",
            "Current MPC iteration is 16\n",
            "Current MPC iteration is 17\n",
            "Current MPC iteration is 18\n",
            "Current MPC iteration is 19\n",
            "Current MPC iteration is 20\n",
            "Current MPC iteration is 21\n",
            "Current MPC iteration is 22\n",
            "Current MPC iteration is 23\n",
            "Current MPC iteration is 24\n",
            "Current MPC iteration is 25\n",
            "Current MPC iteration is 26\n",
            "Current MPC iteration is 27\n",
            "Current MPC iteration is 28\n",
            "Current MPC iteration is 29\n",
            "Current MPC iteration is 30\n",
            "Current MPC iteration is 31\n",
            "Current MPC iteration is 32\n",
            "Current MPC iteration is 33\n",
            "Current MPC iteration is 34\n",
            "Current MPC iteration is 35\n",
            "Current MPC iteration is 36\n",
            "Max MPC iters reached!\n"
          ]
        }
      ],
      "source": [
        "## Run in receding-horizon fashion:\n",
        "# Setup the workers.\n",
        "mpc_iter =0\n",
        "x_curr = x0\n",
        "x_dims = [6]*N\n",
        "n_dims = [3]*N\n",
        "primal_err_record = []\n",
        "X_full = np.zeros((0, nx))\n",
        "X_full = np.r_[X_full, x_curr.reshape(1,-1)]\n",
        "while not np.all(distance_to_goal(x_curr,xr,N,6)) <= 0.1:\n",
        "  \n",
        "  pipes = []\n",
        "  procs = []\n",
        "  for i in range(N):\n",
        "      local, remote = Pipe()\n",
        "      pipes += [local]\n",
        "      procs += [Process(target=run_worker, args=(i, remote, x_curr))]\n",
        "      procs[-1].start()\n",
        "\n",
        "  # ADMM loop.\n",
        "  # sol_dict = {}\n",
        "  ## Set up empty lsits for recording the primal feasibility and dual feasibility\n",
        "  # primal_err = []\n",
        "  # dual_err = []\n",
        "  x_neighbor = [np.zeros((T+1)*nx + T*nu) for _ in range(N)]\n",
        "\n",
        "  primal_err = [np.inf]\n",
        "  admm_iter = 0\n",
        "  for _ in range(MAX_ITER):\n",
        "      x_i_local = []\n",
        "      for i, pipe in enumerate(pipes):\n",
        "          pipe.send(x_neighbor)\n",
        "          xi_values = pipe.recv()\n",
        "          x_i_local.append(xi_values)\n",
        "          # sol_dict[\"agent{0}\".format(i)] = xi_values\n",
        "      x_neighbor = x_i_local\n",
        "      err = 0\n",
        "      for i in range(len(x_i_local)):\n",
        "        for j in range(1,len(x_i_local)-1): #Check these indices\n",
        "          err += np.linalg.norm(x_i_local[i]-x_i_local[j])\n",
        "\n",
        "      primal_err.append(err)\n",
        "      admm_iter += 1\n",
        "      if np.abs(primal_err[admm_iter]-primal_err[admm_iter-1]) <= 0.05:\n",
        "        break\n",
        "\n",
        "  [p.terminate() for p in procs]\n",
        "  primal_err_record.append(primal_err)\n",
        "  x_curr = x_i_local[-1][:(T+1)*nx].reshape((T+1,nx))[1,:]\n",
        "  u_curr = x_i_local[-1][(T+1)*nx:].reshape((T,nu))[0,:]\n",
        "  X_full = np.r_[X_full, x_curr.reshape(1,-1)]\n",
        "  mpc_iter += 1\n",
        "  print(f'Current MPC iteration is {mpc_iter}')\n",
        "  if mpc_iter > 35:\n",
        "    print('Max MPC iters reached!')\n",
        "    break\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "tOJEAxkZuOaw",
        "outputId": "9356b1fe-3fd5-4823-8be3-da6b00344658"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'ADMM Iterations ')"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.figure()\n",
        "plt.plot(primal_err_record[10])\n",
        "plt.ylabel('Aggregated MSE Error Over All ADMM Iterations')\n",
        "plt.xlabel('ADMM Iterations ')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.4"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}