Q1.ipynb

{
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   "cell_type": "code",
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   },
   "outputs": [],
   "source": [
    "import Pkg\n",
    "Pkg.activate(@__DIR__)\n",
    "Pkg.instantiate()\n",
    "import MathOptInterface as MOI\n",
    "import Ipopt \n",
    "import FiniteDiff\n",
    "import ForwardDiff\n",
    "import Convex as cvx \n",
    "import ECOS\n",
    "using LinearAlgebra\n",
    "using Plots\n",
    "using Random\n",
    "using JLD2\n",
    "using Test\n",
    "import MeshCat as mc "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0acb890d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "include(joinpath(@__DIR__, \"utils\",\"fmincon.jl\"))\n",
    "include(joinpath(@__DIR__, \"utils\",\"cartpole_animation.jl\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99b7964e",
   "metadata": {},
   "source": [
    "**NOTE: This question will have long outputs for each cell, remember you can use `cell -> all output -> toggle scrolling` to better see it all**\n",
    "\n",
    "## Q1: Direct Collocation (DIRCOL) for a Cart Pole (30 pts)\n",
    "\n",
    "We are now going to start working with the NonLinear Program (NLP) Solver IPOPT to solve some trajectory optimization problems. First we will demonstrate how this works for simple optimization problems (not trajectory optimization). The interface that we have setup for IPOPT is the following:\n",
    "\n",
    "$$ \\begin{align} \\min_{x} \\quad & \\ell(x) & \\text{cost function}\\\\ \n",
    " \\text{st} \\quad & c_{eq}(x) = 0 & \\text{equality constraint}\\\\\n",
    " & c_L \\leq c_{ineq}(x) \\leq c_U & \\text{inequality constraint}\\\\\n",
    " & x_L \\leq x \\leq x_U & \\text{primal bound constraint}\n",
    " \\end{align}$$\n",
    " \n",
    " where $\\ell(x)$ is our objective function, $c_{eq}(x) = 0$ is our equality constraint, $c_L \\leq c_{ineq}(x) \\leq c_U$ is our bound inequality constraint, and $x_L \\leq x \\leq x_U $ is a bound constraint on our primal variable $x$. \n",
    "<!-- $$ \\begin{align} \\min_{x_{1:N},u_{1:N-1}} \\quad & \\sum_{i=1}^{N-1} \\bigg[ \\frac{1}{2} x_i^TQx_i + \\frac{1}{2} u_i^TRu_i \\bigg] + \\frac{1}{2}x_N^TQ_fx_N\\\\ \n",
    " \\text{st} \\quad & x_1 = x_{\\text{IC}} \\\\ \n",
    " & x_{i+1} = A x_i + Bu_i \\quad \\text{for } i = 1,2,\\ldots,N-1 \n",
    " \\end{align}$$ -->"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f0f4dcc",
   "metadata": {},
   "source": [
    "## Part A: Solve an LP with IPOPT (5 pts)\n",
    "To demonstrate this, we are going to ask you to solve a simple Linear Program (LP):\n",
    " \n",
    " $$ \\begin{align} \\min_{x} \\quad & q^Tx\\\\ \n",
    " \\text{st} \\quad & Ax = b \\\\\n",
    " & Gx \\leq h\n",
    " \\end{align}$$\n",
    " \n",
    " Your job will be to transform this problem into the form shown above and solve it with IPOPT.  To help you interface with IPOPT, we have created a function `fmincon` for you. Below is the docstring for this function that details all of the inputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "863f084f",
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    "scrolled": true
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   "source": [
    "\"\"\"\n",
    "x = fmincon(cost,equality_constraint,inequality_constraint,x_l,x_u,c_l,c_u,x0,params,diff_type)\n",
    "\n",
    "This function uses IPOPT to minimize an objective function \n",
    "\n",
    "`cost(params, x)` \n",
    "\n",
    "With the following three constraints: \n",
    "\n",
    "`equality_constraint(params, x) = 0`\n",
    "`c_l <= inequality_constraint(params, x) <= c_u` \n",
    "`x_l <= x <= x_u` \n",
    "\n",
    "Note that the constraint functions should return vectors. \n",
    "\n",
    "Problem specific parameters should be loaded into params::NamedTuple (things like \n",
    "cost weights, dynamics parameters, etc.). \n",
    "\n",
    "args:\n",
    "    cost::Function                    - objective function to be minimzed (returns scalar)\n",
    "    equality_constraint::Function     - c_eq(params, x) == 0 \n",
    "    inequality_constraint::Function   - c_l <= c_ineq(params, x) <= c_u \n",
    "    x_l::Vector                       - x_l <= x <= x_u \n",
    "    x_u::Vector                       - x_l <= x <= x_u \n",
    "    c_l::Vector                       - c_l <= c_ineq(params, x) <= x_u \n",
    "    c_u::Vector                       - c_l <= c_ineq(params, x) <= x_u \n",
    "    x0::Vector                        - initial guess \n",
    "    params::NamedTuple                - problem parameters for use in costs/constraints \n",
    "    diff_type::Symbol                 - :auto for ForwardDiff, :finite for FiniteDiff \n",
    "    verbose::Bool                     - true for IPOPT output, false for nothing \n",
    "\n",
    "optional args:\n",
    "    tol                               - optimality tolerance \n",
    "    c_tol                             - constraint violation tolerance \n",
    "    max_iters                         - max iterations \n",
    "    verbose                           - verbosity of IPOPT \n",
    "\n",
    "outputs:\n",
    "    x::Vector                         - solution \n",
    "\n",
    "You should try and use :auto for your `diff_type` first, and only use :finite if you \n",
    "absolutely cannot get ForwardDiff to work. \n",
    "\n",
    "This function will run a few basic checks before sending the problem off to IPOPT to \n",
    "solve. The outputs of these checks will be reported as the following:\n",
    "\n",
    "---------checking dimensions of everything----------\n",
    "---------all dimensions good------------------------\n",
    "---------diff type set to :auto (ForwardDiff.jl)----\n",
    "---------testing objective gradient-----------------\n",
    "---------testing constraint Jacobian----------------\n",
    "---------successfully compiled both derivatives-----\n",
    "---------IPOPT beginning solve----------------------\n",
    "\n",
    "If you're getting stuck during the testing of one of the derivatives, try switching \n",
    "to FiniteDiff.jl by setting diff_type = :finite. \n",
    "\"\"\";"
   ]
  },
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   "execution_count": null,
   "id": "b4df44c3",
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   "source": [
    "@testset \"solve LP with IPOPT\" begin \n",
    "        \n",
    "    LP = jldopen(joinpath(@__DIR__,\"utils\",\"random_LP.jld2\"))\n",
    "    \n",
    "    params = (q = LP[\"q\"], A = LP[\"A\"], b = LP[\"b\"], G = LP[\"G\"], h = LP[\"h\"])\n",
    "    \n",
    "    # return a scalar \n",
    "    function cost(params, x)::Real\n",
    "        # TODO: create cost function with params and x \n",
    "        \n",
    "    end\n",
    "    \n",
    "    # return a vector \n",
    "    function equality_constraint(params, x)::Vector\n",
    "        # TODO: create equality constraint function with params and x \n",
    "        \n",
    "    end\n",
    "    \n",
    "    # return a vector\n",
    "    function inequality_constraint(params, x)::Vector\n",
    "        # TODO: create inequality constraint function with params and x \n",
    "        \n",
    "    end\n",
    "\n",
    "    # TODO: primal bounds \n",
    "    # you may use Inf, like Inf*ones(10) for a vector of positive infinity \n",
    "    x_l = \n",
    "    x_u = \n",
    "    \n",
    "    # TODO: inequality constraint bounds \n",
    "    c_l = \n",
    "    c_u = \n",
    "    \n",
    "    # initial guess \n",
    "    x0= randn(20)\n",
    "    \n",
    "    diff_type = :auto   # use ForwardDiff.jl\n",
    "#     diff_type = :finite # use FiniteDiff.jl\n",
    "    \n",
    "    x = fmincon(cost, equality_constraint, inequality_constraint,\n",
    "                x_l, x_u, c_l, c_u, x0, params, diff_type;\n",
    "                tol = 1e-6, c_tol = 1e-6, max_iters = 10_000, verbose = true);\n",
    "    \n",
    "    \n",
    "    @test isapprox(x, [-0.44289, 0, 0, 0.19214, 0, 0, -0.109095,\n",
    "                       -0.43221, 0, 0, 0.44289, 0, 0, 0.192142,\n",
    "                       0, 0, 0.10909, 0.432219, 0, 0], atol = 1e-3)\n",
    "\n",
    "end"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "85f4749f",
   "metadata": {},
   "source": [
    "## Part B: Cart Pole Swingup (20 pts)\n",
    "\n",
    "We are now going to solve for a cartpole swingup. The state for the cartpole is the following: \n",
    "\n",
    "$$ x = [p,\\theta,\\dot{p},\\dot{\\theta}]^T $$ \n",
    "\n",
    "Where $p$ and $\\theta$ can be seen in the graphic `cartpole.png`.\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:cartpole.png\" width=\"300\"/>\n",
    "</div>\n",
    "\n",
    "where we start with the pole in the down position ($\\theta = 0$), and we want to use the horizontal force on the cart to drive the pole to the up position ($\\theta = \\pi$).\n",
    "\n",
    "$$ \\begin{align} \\min_{x_{1:N},u_{1:N-1}} \\quad & \\sum_{i=1}^{N-1} \\bigg[ \\frac{1}{2} (x_i - x_{goal})^TQ(x_i - x_{goal}) + \\frac{1}{2} u_i^TRu_i \\bigg] + \\frac{1}{2}(x_N - x_{goal})^TQ_f(x_N - x_{goal})\\\\ \n",
    " \\text{st} \\quad & x_1 = x_{\\text{IC}} \\\\ \n",
    " & x_N = x_{goal} \\\\ \n",
    " & f_{hs}(x_i,x_{i+1},u_i,dt) = 0 \\quad \\text{for } i = 1,2,\\ldots,N-1 \\\\\n",
    " & -10 \\leq u_i \\leq 10 \\quad \\text{for } i = 1,2,\\ldots,N-1 \n",
    " \\end{align}$$\n",
    " \n",
    " Where $x_{IC} = [0,0,0,0]$, and $x_{goal} = [0, \\pi, 0, 0]$, and $f_{hs}(x_i,x_{i+1},u_i)$ is the implicit integrator residual for Hermite Simpson (see HW1Q1 to refresh on this). Note that while Zac used a first order hold (FOH) on the controls in class (meaning we linearly interpolate controls between time steps), we are using a zero-order hold (ZOH) in this assignment. This means that each control $u_i$ is held constant for the entirety of the timestep. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2de81e9",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# cartpole \n",
    "function dynamics(params::NamedTuple, x::Vector, u)\n",
    "    # cartpole ODE, parametrized by params. \n",
    "\n",
    "    # cartpole physical parameters \n",
    "    mc, mp, l = params.mc, params.mp, params.l\n",
    "    g = 9.81\n",
    "    \n",
    "    q = x[1:2]\n",
    "    qd = x[3:4]\n",
    "\n",
    "    s = sin(q[2])\n",
    "    c = cos(q[2])\n",
    "\n",
    "    H = [mc+mp mp*l*c; mp*l*c mp*l^2]\n",
    "    C = [0 -mp*qd[2]*l*s; 0 0]\n",
    "    G = [0, mp*g*l*s]\n",
    "    B = [1, 0]\n",
    "\n",
    "    qdd = -H\\(C*qd + G - B*u[1])\n",
    "    xdot = [qd;qdd]\n",
    "    return xdot \n",
    "\n",
    "end\n",
    "function hermite_simpson(params::NamedTuple, x1::Vector, x2::Vector, u, dt::Real)::Vector\n",
    "    # TODO: input hermite simpson implicit integrator residual \n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d96addc9",
   "metadata": {},
   "source": [
    "To solve this problem with IPOPT and `fmincon`, we are going to concatenate all of our $x$'s and $u$'s into one vector:\n",
    "\n",
    "$$ Z = \\begin{bmatrix}x_1 \\\\ u_1 \\\\ x_2 \\\\ u_2 \\\\ \\vdots \\\\ x_{N-1} \\\\ u_{N-1} \\\\ x_N \\end{bmatrix} \\in \\mathbb{R}^{N \\cdot nx + (N-1)\\cdot nu} $$ \n",
    "\n",
    "where $x \\in \\mathbb{R}^{nx}$ and $u \\in \\mathbb{R}^{nu}$. Below we will provide useful indexing guide in `create_idx` to help you deal with $Z$.\n",
    "\n",
    "It is also worth noting that while there are inequality constraints present ($-10 \\leq u_i \\leq 10$), we do not need a specific `inequality_constraints` function as an input to `fmincon` since these are just bounds on the primal ($Z$) variable. You should use primal bounds in `fmincon` to capture these constraints.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96249223",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "function create_idx(nx,nu,N)\n",
    "    # This function creates some useful indexing tools for Z \n",
    "    # x_i = Z[idx.x[i]]\n",
    "    # u_i = Z[idx.u[i]]\n",
    "    \n",
    "    # Feel free to use/not use anything here.\n",
    "    \n",
    "    \n",
    "    # our Z vector is [x0, u0, x1, u1, …, xN]\n",
    "    nz = (N-1) * nu + N * nx # length of Z \n",
    "    x = [(i - 1) * (nx + nu) .+ (1 : nx) for i = 1:N]\n",
    "    u = [(i - 1) * (nx + nu) .+ ((nx + 1):(nx + nu)) for i = 1:(N - 1)]\n",
    "    \n",
    "    # constraint indexing for the (N-1) dynamics constraints when stacked up\n",
    "    c = [(i - 1) * (nx) .+ (1 : nx) for i = 1:(N - 1)]\n",
    "    nc = (N - 1) * nx # (N-1)*nx \n",
    "    \n",
    "    return (nx=nx,nu=nu,N=N,nz=nz,nc=nc,x= x,u = u,c = c)\n",
    "end\n",
    "\n",
    "function cartpole_cost(params::NamedTuple, Z::Vector)::Real\n",
    "    idx, N, xg = params.idx, params.N, params.xg\n",
    "    Q, R, Qf = params.Q, params.R, params.Qf\n",
    "    \n",
    "    # TODO: input cartpole LQR cost \n",
    "    \n",
    "    J = 0 \n",
    "    for i = 1:(N-1)\n",
    "        xi = Z[idx.x[i]]\n",
    "        ui = Z[idx.u[i]]\n",
    "       \n",
    "        J += 0 \n",
    "\n",
    "    end\n",
    "    \n",
    "    # dont forget terminal cost \n",
    "    \n",
    "    return J \n",
    "end\n",
    "\n",
    "function cartpole_dynamics_constraints(params::NamedTuple, Z::Vector)::Vector\n",
    "    idx, N, dt = params.idx, params.N, params.dt\n",
    "    \n",
    "    # TODO: create dynamics constraints using hermite simpson \n",
    "    \n",
    "    # create c in a ForwardDiff friendly way (check HW0)\n",
    "    c = zeros(eltype(Z), idx.nc)\n",
    "    \n",
    "    for i = 1:(N-1)\n",
    "        xi = Z[idx.x[i]]\n",
    "        ui = Z[idx.u[i]] \n",
    "        xip1 = Z[idx.x[i+1]]\n",
    "        \n",
    "        # TODO: hermite simpson \n",
    "        c[idx.c[i]] = zeros(4)\n",
    "    end\n",
    "    return c \n",
    "end\n",
    "\n",
    "function cartpole_equality_constraint(params::NamedTuple, Z::Vector)::Vector\n",
    "    N, idx, xic, xg = params.N, params.idx, params.xic, params.xg \n",
    "    \n",
    "    # TODO: return all of the equality constraints \n",
    "    \n",
    "    \n",
    "    return zeros(10) # 10 is an arbitrary number \n",
    "end\n",
    "\n",
    "function solve_cartpole_swingup(;verbose=true)\n",
    "    \n",
    "    # problem size \n",
    "    nx = 4 \n",
    "    nu = 1 \n",
    "    dt = 0.05\n",
    "    tf = 2.0 \n",
    "    t_vec = 0:dt:tf \n",
    "    N = length(t_vec)\n",
    "    \n",
    "    # LQR cost \n",
    "    Q = diagm(ones(nx))\n",
    "    R = 0.1*diagm(ones(nu))\n",
    "    Qf = 10*diagm(ones(nx))\n",
    "    \n",
    "    # indexing \n",
    "    idx = create_idx(nx,nu,N)\n",
    "    \n",
    "    # initial and goal states \n",
    "    xic = [0, 0, 0, 0]\n",
    "    xg = [0, pi, 0, 0]\n",
    "    \n",
    "    # load all useful things into params \n",
    "    params = (Q = Q, R = R, Qf = Qf, xic = xic, xg = xg, dt = dt, N = N, idx = idx,mc = 1.0, mp = 0.2, l = 0.5)\n",
    "    \n",
    "    # TODO: primal bounds \n",
    "    x_l = \n",
    "    x_u =  \n",
    "    \n",
    "\n",
    "    \n",
    "    # inequality constraint bounds (this is what we do when we have no inequality constraints)\n",
    "    c_l = zeros(0)\n",
    "    c_u = zeros(0)\n",
    "    function inequality_constraint(params, Z)\n",
    "        return zeros(eltype(Z), 0)\n",
    "    end\n",
    "    \n",
    "    # initial guess \n",
    "    z0 = 0.001*randn(idx.nz)\n",
    "    \n",
    "    # choose diff type (try :auto, then use :finite if :auto doesn't work)\n",
    "    diff_type = :auto \n",
    "#     diff_type = :finite\n",
    "    \n",
    "    \n",
    "    Z = fmincon(cartpole_cost,cartpole_equality_constraint,inequality_constraint,\n",
    "                x_l,x_u,c_l,c_u,z0,params, diff_type;\n",
    "                tol = 1e-6, c_tol = 1e-6, max_iters = 10_000, verbose = verbose)\n",
    "    \n",
    "    # pull the X and U solutions out of Z \n",
    "    X = [Z[idx.x[i]] for i = 1:N]\n",
    "    U = [Z[idx.u[i]] for i = 1:(N-1)]\n",
    "    \n",
    "    return X, U, t_vec, params \n",
    "end\n",
    "\n",
    "@testset \"cartpole swingup\" begin \n",
    "    \n",
    "    X, U, t_vec = solve_cartpole_swingup(verbose=true)\n",
    "    \n",
    "    \n",
    "    # --------------testing------------------\n",
    "    @test isapprox(X[1],zeros(4), atol = 1e-4)\n",
    "    @test isapprox(X[end], [0,pi,0,0], atol = 1e-4)\n",
    "    Xm = hcat(X...)\n",
    "    Um = hcat(U...)\n",
    "    \n",
    "    # --------------plotting-----------------\n",
    "    display(plot(t_vec, Xm', label = [\"p\" \"θ\" \"ṗ\" \"θ̇\"], xlabel = \"time (s)\", title = \"State Trajectory\"))\n",
    "    display(plot(t_vec[1:end-1],Um',label=\"\",xlabel = \"time (s)\", ylabel = \"u\",title = \"Controls\"))\n",
    "    \n",
    "    # meshcat animation\n",
    "    display(animate_cartpole(X, 0.05))\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2776c49",
   "metadata": {},
   "source": [
    "## Part C: Track DIRCOL Solution (5 pts)\n",
    "\n",
    "Now, similar to HW2 Q2 Part C, we are taking a solution $X$ and $U$ from DIRCOL, and we are going to track the trajectory with TVLQR to account for model mismatch. While we used hermite-simpson integration for the dynamics constraints in DIRCOL, we are going to use RK4 for this simulation. Remember to clamp your control to be within the control bounds. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6967670f",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "function rk4(params::NamedTuple, x::Vector,u,dt::Float64)\n",
    "    # vanilla RK4\n",
    "    k1 = dt*dynamics(params, x, u)\n",
    "    k2 = dt*dynamics(params, x + k1/2, u)\n",
    "    k3 = dt*dynamics(params, x + k2/2, u)\n",
    "    k4 = dt*dynamics(params, x + k3, u)\n",
    "    x + (1/6)*(k1 + 2*k2 + 2*k3 + k4)\n",
    "end\n",
    "\n",
    "@testset \"track cartpole swingup with TVLQR\" begin \n",
    "    \n",
    "    X_dircol, U_dircol, t_vec, params_dircol = solve_cartpole_swingup(verbose = false)\n",
    "    \n",
    "    N = length(X_dircol)\n",
    "    dt = params_dircol.dt \n",
    "    x0 = X_dircol[1]\n",
    "    \n",
    "    # TODO: use TVLQR to generate K's \n",
    "\n",
    "    # use this for TVLQR tracking cost \n",
    "    Q = diagm([1,1,.05,.1])\n",
    "    Qf = 100*Q\n",
    "    R = 0.01*diagm(ones(1))\n",
    "\n",
    "    \n",
    "    # simulation\n",
    "    Xsim = [zeros(4) for i = 1:N]\n",
    "    Usim = [zeros(1) for i = 1:(N-1)]\n",
    "    Xsim[1] = 1*x0 \n",
    "    \n",
    "    # here are the real parameters (different than the one we used for DIRCOL)\n",
    "    # this model mismatch is what's going to require the TVLQR controller to track\n",
    "    # the trajectory successfully. \n",
    "    params_real = (mc = 1.05, mp = 0.21, l = 0.48)\n",
    "    \n",
    "    # TODO: simulate closed loop system with both feedforward and feedback control\n",
    "    # feedforward - the U_dircol controls that we solved for using dircol \n",
    "    # feedback - the TVLQR controls \n",
    "    for i = 1:(N-1)\n",
    "\n",
    "        # add controller and simulation step \n",
    "        \n",
    "    end\n",
    "    \n",
    "    \n",
    "    # -----------------testing-----------------------\n",
    "    xn = Xsim[N]\n",
    "    @test norm(xn)>0\n",
    "    @test 1e-6<norm(xn - X_dircol[end])<.8\n",
    "    @test abs(abs(rad2deg(xn[2])) - 180) < 5 # within 5 degrees \n",
    "    @test maximum(norm.(Usim,Inf)) <= (10 + 1e-3)\n",
    "    \n",
    "    # -----------------plotting----------------------\n",
    "    Xm = hcat(Xsim...)\n",
    "    Xbarm = hcat(X_dircol...)\n",
    "    plot(t_vec,Xbarm',ls=:dash, label = \"\",lc = [:red :green :blue :black])\n",
    "    display(plot!(t_vec,Xm',title = \"Cartpole TVLQR (-- is reference)\",\n",
    "                 xlabel = \"time (s)\", ylabel = \"x\",\n",
    "                 label = [\"p\" \"θ\" \"ṗ\" \"θ̇\"],lc = [:red :green :blue :black]))\n",
    "    \n",
    "    Um = hcat(Usim...)\n",
    "    Ubarm = hcat(U_dircol...)\n",
    "    plot(t_vec[1:end-1],Ubarm',ls=:dash,lc = :blue, label = \"\")\n",
    "    display(plot!(t_vec[1:end-1],Um',title = \"Cartpole TVLQR (-- is reference)\",\n",
    "                 xlabel = \"time (s)\", ylabel = \"u\",lc = :blue, label = \"\"))\n",
    "    \n",
    "    # ----------------animate------------------------\n",
    "    display(animate_cartpole(Xsim, 0.05))\n",
    "    \n",
    "end"
   ]
  }
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