sliding_mode_control.ipynb

{
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   "source": [
    "%%capture\n",
    "# Load the quadrotor simulator from a previous notebook\n",
    "%run quadsim.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "<style>.impl-inner{background-color:#e4ffe6} .impl-outer{background-color:#e4ebff} .text_cell_render p { text-align: justify; text-justify: inter-word;}</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "from IPython.core.display import HTML\n",
    "HTML('<style>.impl-inner{background-color:#e4ffe6} .impl-outer{background-color:#e4ebff} .text_cell_render p { text-align: justify; text-justify: inter-word;}</style>')"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sliding Mode Control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This discussion on sliding mode control for a multirotor closely follows the work of L'Afflitto et al. [1], in the notation of Khalil [2]. A diagram of the control scheme (taken from [1]) is shown below. In sliding mode control, trajectories of the system are steered to a subspace of the state space (i.e., the sliding manifold) in finite time. Once on this sliding surface, the system can asymptotically converge to the origin without regard to matched uncertainties. In [1], the control architecture shown below is used with sliding mode control to design an autopilot that steers a quadrotor to a given location with a given yaw angle.\n",
    "\n",
    "A more introductory implementation of SMC is found in the [notebook](smc_cranfield.ipynb) based on Shaik's work."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Control Scheme Diagram](assets/smc_control_scheme.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theory - System Modeling\n",
    "\n",
    "Consider a nonlinear system of the form [2, eq 14.1]\n",
    "\\begin{equation}\\label{eq:general_nonlinear_sys}\n",
    "\\dot{x} = f(x) + B(x)[G(x)E(x)u + \\delta(t,x,u)],\\quad x \\in \\mathbb{R}^n, \\ u \\in \\mathbb{R}^p\n",
    "\\end{equation}\n",
    "where $f$, $B$, and $E$ are known, while $G$ and $\\delta$ could be uncertain. We assume that $E(x)$ is a nonsingular matrix and that $G(x)$ is a diagonal matrix whose elements are positive and bounded away from zero.\n",
    "\n",
    "Suppose that $f(0) = 0$ so that, in the absence of $\\delta$, the origin is an open-loop equilibrium point. **Our goal is to design a state feedback control law to stabilize the origin for all uncertainties in $G$ and $\\delta$.**\n",
    "\n",
    "Given a diffeomorphism $T$, \\eqref{eq:general_nonlinear_sys} can be written in *regular form* [2, eq 14.4] as:\n",
    "\\begin{align}\n",
    "\\dot\\eta &= f_a(\\eta, \\xi) \\label{eq:normal-eta} \\\\\n",
    "\\dot\\xi  &= f_b(\\eta, \\xi) + G(x)E(x)u + \\delta(t, x, u). \\label{eq:normal-xi}\n",
    "\\end{align}\n",
    "\n",
    "Note that a large class of mechanical systems may be written in regular form, with the kinematics captured by \\eqref{eq:normal-eta} and the dynamics captured by \\eqref{eq:normal-xi}. This is great because kinematics are typically assumed to be perfectly known, while the dynamics of a system are subject to modeling errors and uncertainties in the system's inertial properties [1]."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practice - System Modeling\n",
    "In keeping with the architecture in the above figure from [1], we will consider the <span class=\"impl-inner\">inner loop</span> and the <span class=\"impl-outer\">outer loop</span> as separate nonlinear systems, writing each in the form of \\eqref{eq:general_nonlinear_sys} and creating two sliding mode controllers that work together to stabilize the system around trajectories."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"impl-inner\">\n",
    "\n",
    "For the purposes of control, we consider the inner loop kinematics of a quadrotor to be\n",
    "\\begin{align}\n",
    "\\dot{r_z} &= v_z \\\\\n",
    "\\dot{\\phi} &\\approx p \\\\\n",
    "\\dot{\\theta} &\\approx q \\\\\n",
    "\\dot{\\psi} &\\approx r \\\\\n",
    "\\end{align}\n",
    "where we have assumed small angles s.t. $\\Gamma \\approx I_{3 \\times 3}$. The inner loop dynamics are\n",
    "\\begin{align}\n",
    "\\ddot{r_z} &= g - \\frac{F}{m}\\cos\\phi\\cos\\theta \\\\\n",
    "\\dot\\omega &= -I^{-1} (\\omega \\times I\\omega + M).\n",
    "\\end{align}\n",
    "<br>\n",
    "In our specific case, we can express the quadrotor system in the form of \\eqref{eq:general_nonlinear_sys} with the following definitions:\n",
    "\\begin{align}\n",
    "x &\\triangleq\n",
    "\\begin{bmatrix} x_1 & x_2 & x_3 & x_4 & x_5 & x_6 & x_7 & x_8 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} r_z & \\phi & \\theta & \\psi & \\dot{r}_z & p & q & r \\end{bmatrix}^\\top \\\\\n",
    "u &\\triangleq\n",
    "\\begin{bmatrix} u_1 & u_2 & u_3 & u_4 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} F & \\tau_\\phi & \\tau_\\theta & \\tau_\\psi \\end{bmatrix}^\\top.\n",
    "\\end{align}\n",
    "<br>\n",
    "Which evolves as\n",
    "\\begin{align}\\label{eq:inner-loop-dynamics-ss}\n",
    "\\dot{x} =\n",
    "\\begin{bmatrix} \\dot{x}_1 \\\\ \\dot{x}_2 \\\\ \\dot{x}_3 \\\\ \\dot{x}_4 \\\\ \\dot{x}_5 \\\\ \\dot{x}_6 \\\\ \\dot{x}_7 \\\\ \\dot{x}_8 \\end{bmatrix} =\n",
    "\\begin{bmatrix} \\dot{r}_z \\\\ \\dot\\phi \\\\ \\dot\\theta \\\\ \\dot\\psi \\\\ \\ddot{r}_z \\\\ \\dot{p} \\\\ \\dot{q} \\\\ \\dot{r} \\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "    x_5 \\\\ x_6 \\\\ x_7 \\\\ x_8 \\\\\n",
    "    g - \\frac{u_1}{m}\\cos x_2 \\cos x_3 \\\\\n",
    "    \\frac{J_y - J_z}{J_x} x_7 x_8 + \\frac{1}{J_x} u_2 \\\\\n",
    "    \\frac{J_z - J_x}{J_y} x_6 x_8 + \\frac{1}{J_y} u_3 \\\\\n",
    "    \\frac{J_x - J_y}{J_z} x_6 x_7 + \\frac{1}{J_z} u_4\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "<br>\n",
    "In order to transform these inner-loop dynamics into the regular form, we must identify the certain and uncertain components. We can break up \\eqref{eq:inner-loop-dynamics-ss} into\n",
    "\\begin{align}\n",
    "\\dot{x} =\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    x_5 \\\\ x_6 \\\\ x_7 \\\\ x_8 \\\\\n",
    "    g \\\\\n",
    "    \\frac{J_y - J_z}{J_x} x_7 x_8 \\\\\n",
    "    \\frac{J_z - J_x}{J_y} x_6 x_8 \\\\\n",
    "    \\frac{J_x - J_y}{J_z} x_6 x_7\n",
    "\\end{bmatrix}}_{f(x)} +\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    0_{4\\times 4} \\\\ \\hdashline\n",
    "    I_{4\\times 4}\n",
    "\\end{bmatrix}}_{B(x)}\n",
    "\\left(\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\frac{\\cos x_2\\cos x_3}{m} &0&0&0 \\\\\n",
    "0& \\frac{1}{J_x} &0&0 \\\\\n",
    "0&0& \\frac{1}{J_y} &0 \\\\\n",
    "0&0&0& \\frac{1}{J_z}\n",
    "\\end{bmatrix}}_{G(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "-1&0&0&0 \\\\\n",
    "0&1&0&0 \\\\\n",
    "0&0&1&0 \\\\\n",
    "0&0&0&1\n",
    "\\end{bmatrix}}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "u_1 \\\\ u_2 \\\\ u_3 \\\\ u_4\n",
    "\\end{bmatrix}}_{u} +\n",
    "\\underbrace{0_{4\\times 1}}_{\\delta(t, x, u)}\n",
    "\\right).\n",
    "\\end{align}\n",
    "<br>\n",
    "Note how $G(x)$ contains the mass and the inertia terms, which are likely to be uncertain.\n",
    "<br>\n",
    "<br>\n",
    "We then use the identity diffeomorphism $T:D\\to\\mathbb{R}^{n=8}, x\\mapsto x$ to transform this system into the regular form:\n",
    "\\begin{align} \\label{eq:inner-regular-transform}\n",
    "\\eta &=\n",
    "\\begin{bmatrix} x_1 & x_2 & x_3 & x_4 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} r_z & \\phi & \\theta & \\psi \\end{bmatrix}^\\top \\in \\mathbb{R}^{n-p=4} \\\\\n",
    "\\xi &=\n",
    "\\begin{bmatrix} x_5 & x_6 & x_7 & x_8 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} \\dot{r_z} & p & q & r \\end{bmatrix}^\\top \\in \\mathbb{R}^{p=4},\n",
    "\\end{align}\n",
    "<br>\n",
    "which evolves as\n",
    "<br>\n",
    "\\begin{align}\n",
    "\\dot\\eta &=\n",
    "\\begin{bmatrix} \\dot{x_1} \\\\ \\dot{x_2} \\\\ \\dot{x_3} \\\\ \\dot{x_4} \\end{bmatrix} =\n",
    "\\begin{bmatrix} x_5 \\\\ x_6 \\\\ x_7 \\\\ x_8 \\end{bmatrix} = f_a(\\eta, \\xi) = \\xi \\\\\n",
    "\\dot\\xi &=\n",
    "\\begin{bmatrix} \\dot{x_5} \\\\ \\dot{x_6} \\\\ \\dot{x_7} \\\\ \\dot{x_8} \\end{bmatrix} =\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    g \\\\\n",
    "    \\frac{J_y - J_z}{J_x} x_7 x_8 \\\\\n",
    "    \\frac{J_z - J_x}{J_y} x_6 x_8 \\\\\n",
    "    \\frac{J_x - J_y}{J_z} x_6 x_7\n",
    "\\end{bmatrix}}_{f_b(\\eta,\\xi)} +\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\frac{\\cos x_2\\cos x_3}{m} & 0_{1\\times 3} \\\\\n",
    "0_{3\\times 1} & I^{-1}\n",
    "\\end{bmatrix}}_{G(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "-1 & 0_{1\\times 3} \\\\\n",
    "0_{3\\times 1} & I_{3\\times 3}\n",
    "\\end{bmatrix}}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "u_1 \\\\ u_2 \\\\ u_3 \\\\ u_4\n",
    "\\end{bmatrix}}_{u} +\n",
    "\\underbrace{0_{4\\times 1}}_{\\delta(t, x, u)}\n",
    "\\end{align}\n",
    "</div>"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "<div class=\"impl-outer\">\n",
    "\n",
    "The outer loop kinematics are\n",
    "$$\n",
    "\\begin{align}\n",
    "\\dot{r}_x &= v_x \\\\\n",
    "\\dot{r}_y &= v_y\n",
    "\\end{align}\n",
    "$$\n",
    "with dynamics\n",
    "$$\n",
    "\\begin{align}\n",
    "\\ddot{r}_x &= -\\frac{u_1}{m}\\left( \\cos\\phi\\sin\\theta\\cos\\psi + \\sin\\phi\\sin\\psi \\right) \\\\\n",
    "\\ddot{r}_y &= -\\frac{u_1}{m}\\left( \\cos\\phi\\sin\\theta\\sin\\psi - \\sin\\phi\\cos\\psi \\right).\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "Expressing the outer loop in state-space form yields\n",
    "$$\n",
    "\\begin{align}\n",
    "x &\\triangleq\n",
    "\\begin{bmatrix} x_1 & x_2 & x_3 & x_4 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} r_x & r_y & \\dot{r}_x & \\dot{r}_y \\end{bmatrix}^\\top \\\\\n",
    "u &\\triangleq\n",
    "\\begin{bmatrix} d_1 & d_2 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} \\theta^d & \\phi^d \\end{bmatrix}^\\top.\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "Using the small-angle approximation ($\\cos\\theta\\approx 1$; $\\sin\\theta\\approx\\theta$), we can write the evolution of the state vector as\n",
    "$$\n",
    "\\begin{align}\\label{eq:outer-loop-dynamics-ss}\n",
    "\\dot{x} =\n",
    "\\begin{bmatrix} \\dot{x}_1 \\\\ \\dot{x}_2 \\\\ \\dot{x}_3 \\\\ \\dot{x}_4 \\end{bmatrix} =\n",
    "\\begin{bmatrix} \\dot{r}_x \\\\ \\dot{r}_y \\\\ \\ddot{r}_x \\\\ \\ddot{r}_y \\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "    x_3 \\\\ x_4 \\\\\n",
    "    -\\frac{u_1}{m}\\left( \\cos\\phi\\sin\\theta\\cos\\psi + \\sin\\phi\\sin\\psi \\right) \\\\\n",
    "    -\\frac{u_1}{m}\\left( \\cos\\phi\\sin\\theta\\sin\\psi - \\sin\\phi\\cos\\psi \\right)\n",
    "\\end{bmatrix} \\approx\n",
    "\\begin{bmatrix}\n",
    "    x_3 \\\\ x_4 \\\\\n",
    "    -\\frac{u_1}{m}\\left( \\theta\\cos\\psi + \\phi\\sin\\psi \\right) \\\\\n",
    "    -\\frac{u_1}{m}\\left( \\theta\\sin\\psi - \\phi\\cos\\psi \\right)\n",
    "\\end{bmatrix}.\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "Similar as with the inner loop, we break \\eqref{eq:outer-loop-dynamics-ss} into certain and uncertain components so that it is of the form of \\eqref{eq:general_nonlinear_sys}.\n",
    "$$\n",
    "\\begin{align}\n",
    "\\dot{x} =\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    x_3 \\\\ x_4 \\\\ 0 \\\\ 0\n",
    "\\end{bmatrix}}_{f(x)} +\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    0_{2\\times 2} \\\\ \\hdashline\n",
    "    I_{2\\times 2}\n",
    "\\end{bmatrix}}_{B(x)}\n",
    "\\left(\n",
    "\\underbrace{\\left( \\frac{1}{m} I_{2\\times 2} \\right)}_{G(x)}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}-u_1&0\\\\0&u_1\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\cos\\psi&\\sin\\psi \\\\\n",
    "-\\sin\\psi&\\cos\\psi\n",
    "\\end{bmatrix}\n",
    "}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\theta^d \\\\ \\phi^d\n",
    "\\end{bmatrix}}_{u} +\n",
    "\\underbrace{0_{4\\times 1}}_{\\delta(t, x, u)}\n",
    "\\right).\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "Again using the identity diffeomorphism $T:D\\to\\mathbb{R}^{n=4}, x\\mapsto x$, we transform the system into regular form:\n",
    "$$\n",
    "\\begin{align}\n",
    "\\eta &=\n",
    "\\begin{bmatrix} x_1 & x_2 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} r_x & r_y \\end{bmatrix}^\\top \\in \\mathbb{R}^{n-p=2} \\\\\n",
    "\\xi &=\n",
    "\\begin{bmatrix} x_3 & x_4 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} \\dot{r}_x & \\dot{r}_y \\end{bmatrix}^\\top \\in \\mathbb{R}^{p=2},\n",
    "\\end{align}\n",
    "$$\n",
    "which evolves as\n",
    "$$\n",
    "\\begin{align}\n",
    "\\dot\\eta &=\n",
    "\\begin{bmatrix} \\dot{x}_1 \\\\ \\dot{x}_2 \\end{bmatrix} =\n",
    "\\begin{bmatrix} x_3 \\\\ x_4 \\end{bmatrix} = f_a(\\eta, \\xi) = \\xi \\\\\n",
    "\\dot\\xi &=\n",
    "\\begin{bmatrix} \\dot{x}_3 \\\\ \\dot{x}_4 \\end{bmatrix} =\n",
    "\\underbrace{\\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}}_{f_b(\\eta,\\xi)} +\n",
    "\\underbrace{\\left( \\frac{1}{m} I_{2\\times 2} \\right)}_{G(x)}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}-u_1&0\\\\0&u_1\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "\\cos\\psi&\\sin\\psi \\\\\n",
    "-\\sin\\psi&\\cos\\psi\n",
    "\\end{bmatrix}\n",
    "}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\theta^d \\\\ \\phi^d\n",
    "\\end{bmatrix}}_{u} +\n",
    "\\underbrace{0_{4\\times 1}}_{\\delta(t, x, u)}\n",
    "\\end{align}\n",
    "$$\n",
    "</div>"
   ]
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   "source": [
    "## Theory - Stabilization\n",
    "\n",
    "Given a system modelled in regular form, a stabilizing sliding mode controller can be designed. \n",
    "\n",
    "> We start by selecting the sliding manifold to be $s = \\xi - \\phi(\\eta) = 0$ so that when motion is restricted to the manifold, the reduced-order model $\\dot\\eta = f_a(\\eta, \\phi(\\eta))$ has an asymptotically stable origin. The design of $\\phi(\\eta)$ amounts to solving a stabilization problem for the system $\\dot\\eta = f_a(\\eta,\\xi)$ with $\\xi$ viewed as the control input. This stabilization problem may be solved using any other technique, such as backstepping, feedback linearzation, etc. Upon designing a stabilizing controller $\\phi(\\eta)$, we must design an input $u$ that steers trajectories of $\\dot\\xi$ to the manifold $s=0$ (i.e., steers $\\xi$ to $\\phi(\\eta)$) in finite time and maintains it there for all future time.\n",
    "\n",
    "<p style=\"text-align: right\">Khalil, p. 564 [2]</p>\n",
    "\n",
    "We can achieve this by inspecting the time-evolution of the manifold $s$, which is\n",
    "$$\n",
    "\\begin{equation}\\label{eq:general-sdot}\n",
    "\\dot{s} = f_b(\\eta,\\xi) - \\frac{\\partial\\phi}{\\partial\\eta} f_a(\\eta,\\xi) + G(x)E(x)u + \\delta(t,x,u)\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "The control is given by\n",
    "$$\n",
    "\\begin{equation}\\label{eq:general-smc-control}\n",
    "u = E^{-1}(x)\\left\\{ -L(x)\\left[ f_b(\\eta,\\xi) - \\frac{\\partial\\phi}{\\partial\\eta} f_a(\\eta,\\xi) \\right] + v \\right\\}\n",
    "\\end{equation}\n",
    "$$\n",
    "where\n",
    "\\begin{equation}\n",
    "v = -\\beta(x) \\text{sgn}(s).\n",
    "\\end{equation}\n",
    "\n",
    "If $\\hat{G}(x)$ is an approximation of the uncertain matrix $G(x)$ and we have access to it, then we let $L(x) = \\hat{G}^{-1}$. Otherwise, let $L(x)=0$ and there will be no continuous component to the control---it will rely soley on the switching characteristic of $v$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practice - Inner Loop Stabilization\n",
    "For the sake of notation and understanding, we will first design and implement a sliding mode controller to stabilize the <span class=\"impl-inner\">inner loop</span> to the origin. With this implementation, we will be able to see how deviations from $\\begin{bmatrix} r_x & \\phi & \\theta & \\psi \\end{bmatrix}^\\top = \\mathbf{0}$ are regulated back to $\\mathbf{0}$."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"impl-inner\">\n",
    "The inner loop control strategy for stabilization about the origin is defined as follows:\n",
    "$$\n",
    "\\begin{equation}\n",
    "s = \\xi - \\phi(\\eta) = \\xi + K_1\\eta,\n",
    "\\end{equation}\n",
    "$$\n",
    "where $K_1$ is a positive-definite diagonal matrix. Therefore, $\\frac{\\partial\\phi}{\\partial\\eta} = -K_1$. Rearranging the control in equation \\eqref{eq:general-smc-control}, we have the expression [1, eq 23]\n",
    "$$\n",
    "\\begin{equation}\\label{eq:smc-control}\n",
    "u =  u_{eq} + E^{-1}(x)v,\n",
    "\\end{equation}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "u_{eq} = -E^{-1}L(x)\\left[ f_b(\\eta,\\xi) - \\frac{\\partial\\phi}{\\partial\\eta}f_a(\\eta,\\xi) \\right]\n",
    "$$\n",
    "and\n",
    "$$\n",
    "v = -\\beta(x)\\text{sgn}(s).\n",
    "$$\n",
    "<br>\n",
    "Given that we have estimates of the inertial properties of the quadrotor, we let $L(x)=\\hat{G}^{-1}$. Using the definitions from our inner loop modeling above and plugging them in to \\eqref{eq:smc-control}, we have\n",
    "$$\n",
    "\\begin{equation}\\label{eq:inner-stabilizing-control}\n",
    "u = -\n",
    "\\underbrace{\\begin{bmatrix} -1 & 0_{1\\times 3} \\\\ 0_{3\\times 1} & I_{3\\times 3} \\end{bmatrix}}_{E^{-1}(x)}\n",
    "\\underbrace{\\begin{bmatrix} \\frac{m}{\\cos x_2\\cos x_3} & 0_{1\\times 3} \\\\ 0_{3\\times 1} & J \\end{bmatrix}}_{G^{-1}(x)}\n",
    "\\left\\{\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "g \\\\\n",
    "\\frac{J_y - J_z}{J_x} x_7 x_8 \\\\\n",
    "\\frac{J_z - J_x}{J_y} x_6 x_8 \\\\\n",
    "\\frac{J_x - J_y}{J_z} x_6 x_7\n",
    "\\end{bmatrix}}_{f_b(\\eta,\\xi)}\n",
    "+ K_1\\xi\n",
    "\\right\\}\n",
    "+\n",
    "\\underbrace{\\begin{bmatrix} -1 & 0_{1\\times 3} \\\\ 0_{3\\times 1} & I_{3\\times 3} \\end{bmatrix}}_{E^{-1}(x)} v.\n",
    "\\end{equation}\n",
    "$$\n",
    "<br>\n",
    "Simplifying and breaking up into the 4 individual control channels gives\n",
    "$$\n",
    "\\begin{align}\n",
    "u_1 &= \\frac{m}{\\cos\\phi\\cos\\theta}\\left[ g +k_{r_z}\\dot{r}_z\\right] + \\beta_{r_z}\\text{sgn}(s_{r_z}) \\label{eq:shaik-u1} \\\\\n",
    "u_2 &= -J_x\\left[ \\frac{J_y - J_z}{J_x} qr + k_\\phi \\dot{\\phi}\\right] - \\beta_\\phi \\text{sgn}(s_\\phi) \\\\\n",
    "u_3 &= -J_y\\left[ \\frac{J_z - J_x}{J_y} pr + k_\\theta \\dot{\\theta}\\right] - \\beta_\\theta \\text{sgn}(s_\\theta) \\\\\n",
    "u_4 &= -J_z\\left[ \\frac{J_x - J_y}{J_z} pq + k_\\psi \\dot{\\psi}\\right] - \\beta_\\psi \\text{sgn}(s_\\psi). \\label{eq:shaik-u4}\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "By plugging these control equations into \\eqref{eq:general-sdot}, it can be verified that the known components are canceled and the switching component is left behind, which causes $\\dot{V} = -c(x)\\left|s\\right| < 0$.\n",
    "<br><br>\n",
    "    Note one difference from <a href=\"smc_cranfield.ipynb\">Shaik's SMC implementation</a> is that the switching component is <i>inside</i> the bracket. This would seem to minimize the analytical upper bound necessary to prove that the control is stable in the sense of Lyapunov, but doesn't seem to make a difference in practice.\n",
    "<br><br>\n",
    "Another difference between this and Shaik's implementation is that there are sign differences. This comes from how Shaik defined the tracking error. Instead of the more common $e \\triangleq x - x^d$, he defined the error as $e \\triangleq x^d - x$. This causes the sign of the surface to be flipped, which causes $\\text{sgn}(-s) = -\\text{sgn}(s)$.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class StabilizingSMC(Controller):\n",
    "    \"\"\"Sliding Mode Controller\n",
    "    \n",
    "    This implementation of SMC only performs stabilization\n",
    "    of the inner loop. That means that there is no way\n",
    "    for the inner loop to track a reference other than zero.\n",
    "    \n",
    "    This controller can be seen in action if the initial\n",
    "    attitude and/or altitude state of the quadrotor is non-zero.\n",
    "    \n",
    "    Also note that this controller uses sgn(x) instead of sat(x).\n",
    "    As a result of this, chattering in the control effort and in\n",
    "    the state can be seen. This is addressed later in the notebook.\n",
    "    \n",
    "    Inertial quantities are deviated from the true simulation\n",
    "    values so as to represent SMC's robustness to uncertainty.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        self.name = \"SMC: Stabilized Inner Loop\"\n",
    "        \n",
    "        # estimates of the physical properties of the quadrotor\n",
    "        self.g = 9.8\n",
    "        self.mass = 4\n",
    "        self.I = np.diag(np.array([0.1, 0.1, 0.1]))\n",
    "        \n",
    "        # proportional control law \\phi(\\eta) that stabilizes the inner \\dot\\eta = f_a system\n",
    "        self.K1 = np.diag(np.array([3,3,4,1]))\n",
    "                   \n",
    "    def inner(self, state):\n",
    "        \n",
    "        def fa(eta, xi):\n",
    "            return xi\n",
    "\n",
    "        def fb(eta, xi):\n",
    "            # extract omega from xi\n",
    "            omega = xi[1:4]\n",
    "\n",
    "            r = np.zeros((4,1))\n",
    "            r[0,0] = self.g\n",
    "            r[1:4] = -np.linalg.inv(self.I).dot(np.cross(omega, self.I.dot(omega), axis=0))\n",
    "            return r\n",
    "        \n",
    "        # Transform the system into the form of HK (14.4) and (14.5)\n",
    "        eta = np.array([state.flatten()[[2, 6, 7, 8]]]).T # r_z, ph, th, ps\n",
    "        xi = np.array([state.flatten()[[5, 9, 10, 11]]]).T # \\dot{r_z}, p, q, r\n",
    "        \n",
    "        ph = eta.flatten()[1]\n",
    "        th = eta.flatten()[2]\n",
    "        ps = eta.flatten()[3]\n",
    "        \n",
    "        # Build the inv(E(x)) matrix\n",
    "        Einv = np.diag(np.array([-1,1,1,1]))\n",
    "        \n",
    "        # Build the L(x) = inv(G(x)) matrix\n",
    "        L = np.eye(4)\n",
    "        L[0, 0] = self.mass/(np.cos(ph)*np.cos(th))\n",
    "        L[1:4, 1:4] = self.I\n",
    "        \n",
    "        # continuous control to cancel known terms: equation (18) of [1].\n",
    "        ueq = -Einv.dot(L.dot(fb(eta, xi) + self.K1.dot(fa(eta, xi))))\n",
    "        \n",
    "        # Build the matrix of sliding surfaces\n",
    "        SS = xi + self.K1.dot(eta)\n",
    "        \n",
    "        # Gains\n",
    "        Beta = np.diag(np.array([6,1,7,2]))\n",
    "        \n",
    "        # switching components of the control: equation (20) of [1]\n",
    "        # (but with a boundary on the sliding surface to mitigate chattering)\n",
    "        gamma = -Beta.dot(np.sign(SS))\n",
    "        \n",
    "        # equation (23) of [1]\n",
    "        u = ueq + Einv.dot(gamma)\n",
    "        \n",
    "        return u\n",
    "    \n",
    "    def update(self, commanded, state, pkt, Ts):\n",
    "        \n",
    "        #\n",
    "        # Inner Loop\n",
    "        #\n",
    "        \n",
    "        u = self.inner(state)\n",
    "        \n",
    "        # actuator commands\n",
    "        return u, commanded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7fd8c0ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7fe35e748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quad = Quadrotor(r=np.array([[0],[0],[5]]),\n",
    "                 v=np.array([[0],[0],[0]]),\n",
    "               Phi=np.array([[0.1],[-0.8],[3.15]]))\n",
    "sim = Simulator(quad=quad, ctrl=StabilizingSMC())\n",
    "sim.run(15, Ts=0.01)\n",
    "sim.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aside - Chattering\n",
    "The discontinuous switching component $\\text{sgn}(s)$ is used to maintain trajectories on the surface $s=0$. However, because there is uncertainty in every system, $s$ is typically always varying about $0$, causing the control to rapidly switch signs so that $s=0$ can be maintained. This creates an undesired effect known as chattering, which can be seen in the control effort from the inner loop stabilization controller above. To alleviate this, a margin is created around the surface $s=0$ so that the sensitivity is reduced and as long as trajectories are in the *neighborhood* of $s=0$ the control is successful. This can be implemented by replacing the signum function $\\text{sgn}(s)$ with a saturation function, as shown below. The transition region can be controlled by scaling the surface by a variable $\\epsilon$, such as $\\text{sat}(\\frac{s}{\\epsilon})$, where $0.1 \\le \\epsilon \\le 1$ is a typical range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table>\n",
    "    <tr>\n",
    "        <td><img src=\"assets/fig_sgn.svg\" width=\"75%\" /></td>\n",
    "        <td><img src=\"assets/fig_sat.svg\" width=\"75%\" /></td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A vectorized saturation function is implemented using `numpy` below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sat(v):\n",
    "    v = np.copy(v)\n",
    "    v[np.abs(v) > 1] = np.sign(v[np.abs(v) > 1])\n",
    "    return v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theory - Tracking\n",
    "\n",
    "In general, tracking a trajectory amounts to stabilizing the error between the current and the desired to zero. To this end, we rewrite the state-space representation as an error-state representation. Define the error as $\\tilde{x_i} \\triangleq x_i - x_i^d$, where $x_i^d$ is the desired reference value of $x_i$. The sliding surface must also be rewritten in terms of error. The vector of all reference signals is defined as $y$.\n",
    "\n",
    "In this error representation, it is assumed that $y \\in C^2$ and that $y$, $\\dot y$, and $\\ddot y$ are all available online. Given an arbitrary twice-differentiable signal, its derivative may numerically be computed using a [*dirty derivative*](utils.ipynb#Derivative-Filter)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practice - Tracking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will redefine the state-space systems of the <span class=\"impl-inner\">inner</span> and <span class=\"impl-outer\">outer</span> loops to use the error-state representation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"impl-inner\">\n",
    "\n",
    "We start with the regular form of the inner loop, as written in equation \\eqref{eq:inner-regular-transform}. Expressing as an error state, we have\n",
    "$$\n",
    "\\begin{align}\n",
    "\\tilde\\eta &= \\eta - y =\n",
    "\\begin{bmatrix} \\tilde{x}_1 & \\tilde{x}_2 & \\tilde{x}_3 & \\tilde{x}_4 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} r_z-r_z^d & \\phi-\\phi^d & \\theta-\\theta^d & \\psi-\\psi^d \\end{bmatrix}^\\top \\\\\n",
    "\\tilde\\xi &= \\xi - \\dot y =\n",
    "\\begin{bmatrix} \\tilde{x}_5 & \\tilde{x}_6 & \\tilde{x}_7 & \\tilde{x}_8 \\end{bmatrix}^\\top =\n",
    "\\begin{bmatrix} \\dot{r}_z-\\dot{r}_z^d & p-\\dot\\phi^d & q-\\dot\\theta^d & r-\\dot\\psi^d \\end{bmatrix}^\\top \\\\\n",
    "y &= \\begin{bmatrix} r_z^d & \\phi^d & \\theta^d & \\psi^d \\end{bmatrix}^\\top\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "which evolves as\n",
    "<br>\n",
    "$$\n",
    "\\begin{align}\n",
    "\\dot{\\tilde\\eta} &=\n",
    "\\begin{bmatrix} \\dot{\\tilde x}_1 \\\\ \\dot{\\tilde x}_2 \\\\ \\dot{\\tilde x}_3 \\\\ \\dot{\\tilde x}_4 \\end{bmatrix} =\n",
    "\\begin{bmatrix} \\tilde x_5 \\\\ \\tilde x_6 \\\\ \\tilde x_7 \\\\ \\tilde x_8 \\end{bmatrix} = f_a(\\tilde\\eta, \\tilde\\xi) = \\tilde\\xi \\\\\n",
    "\\dot{\\tilde\\xi} &=\n",
    "\\begin{bmatrix} \\dot{\\tilde x}_5 \\\\ \\dot{\\tilde x}_6 \\\\ \\dot{\\tilde x}_7 \\\\ \\dot{\\tilde x}_8 \\end{bmatrix} =\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    g \\\\\n",
    "    \\frac{J_y - J_z}{J_x} qr \\\\\n",
    "    \\frac{J_z - J_x}{J_y} pr \\\\\n",
    "    \\frac{J_x - J_y}{J_z} pq\n",
    "\\end{bmatrix}}_{f_b(\\eta,\\xi)} -\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    \\ddot{r}_z^d \\\\\n",
    "    \\ddot{\\phi}^d \\\\\n",
    "    \\ddot{\\theta}^d \\\\\n",
    "    \\ddot{\\psi}^d\n",
    "\\end{bmatrix}}_{\\ddot y} +\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\frac{\\cos \\phi\\cos \\theta}{m} & 0_{1\\times 3} \\\\\n",
    "0_{3\\times 1} & J^{-1}\n",
    "\\end{bmatrix}}_{G(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "-1 & 0_{1\\times 3} \\\\\n",
    "0_{3\\times 1} & I_{3\\times 3}\n",
    "\\end{bmatrix}}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "u_1 \\\\ u_2 \\\\ u_3 \\\\ u_4\n",
    "\\end{bmatrix}}_{u}.\n",
    "\\end{align}\n",
    "$$\n",
    "<br>\n",
    "Therefore, the new tracking control is very similar to the stabilizing control \\eqref{eq:inner-stabilizing-control}, but with the subtraction of the reference signals $y$ and their first and second derivatives:\n",
    "$$\n",
    "\\begin{equation}\n",
    "u = -\n",
    "\\underbrace{\\begin{bmatrix} -1 & 0_{1\\times 3} \\\\ 0_{3\\times 1} & I_{3\\times 3} \\end{bmatrix}}_{E^{-1}(x)}\n",
    "\\underbrace{\\begin{bmatrix} \\frac{m}{\\cos \\phi\\cos \\theta} & 0_{1\\times 3} \\\\ 0_{3\\times 1} & J \\end{bmatrix}}_{G^{-1}(x)}\n",
    "\\left\\{\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "g \\\\\n",
    "\\frac{J_y - J_z}{J_x} qr \\\\\n",
    "\\frac{J_z - J_x}{J_y} pr \\\\\n",
    "\\frac{J_x - J_y}{J_z} pq\n",
    "\\end{bmatrix}}_{f_b(\\eta,\\xi)} -\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "    \\ddot{r}_z^d \\\\\n",
    "    \\ddot{\\phi}^d \\\\\n",
    "    \\ddot{\\theta}^d \\\\\n",
    "    \\ddot{\\psi}^d\n",
    "\\end{bmatrix}}_{\\ddot y}\n",
    "+ K_1(\\xi-\\dot y)\n",
    "\\right\\}\n",
    "+\n",
    "\\underbrace{\\begin{bmatrix} -1 & 0_{1\\times 3} \\\\ 0_{3\\times 1} & I_{3\\times 3} \\end{bmatrix}}_{E^{-1}(x)} v,\n",
    "\\end{equation}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\begin{equation}\n",
    "v = -\\beta(x)\\text{sgn}(\\tilde s)\n",
    "\\end{equation}\n",
    "$$\n",
    "and the sliding surface is redefined to be\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tilde s = \\tilde\\xi + K_1\\tilde\\eta = (\\xi-\\dot y) + K_1(\\eta-y).\n",
    "\\end{equation}\n",
    "$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"impl-outer\">\n",
    "\n",
    "Following the same pattern as was done for the inner loop, the outer loop is rewritten in an error-state representation, with the reference signal defined as\n",
    "$$\n",
    "\\begin{equation}\n",
    "y = \\begin{bmatrix} r_x^d & r_y^d \\end{bmatrix}^\\top.\n",
    "\\end{equation}\n",
    "$$\n",
    "<br>\n",
    "The regular form of the error state,\n",
    "$$\n",
    "\\begin{align}\n",
    "\\dot{\\tilde\\eta} &=\n",
    "\\begin{bmatrix} \\dot{\\tilde x}_1 \\\\ \\dot{\\tilde x}_2 \\end{bmatrix} =\n",
    "\\begin{bmatrix} \\tilde x_3 \\\\ \\tilde x_4 \\end{bmatrix} = f_a(\\tilde\\eta, \\tilde\\xi) = \\tilde\\xi \\\\\n",
    "\\dot{\\tilde\\xi} &=\n",
    "\\begin{bmatrix} \\dot{\\tilde x}_3 \\\\ \\dot{\\tilde x}_4 \\end{bmatrix} =\n",
    "\\underbrace{\\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}}_{f_b(\\eta,\\xi)} -\n",
    "\\underbrace{\\begin{bmatrix} \\ddot{r}_x^d \\\\ \\ddot{r}_y^d \\end{bmatrix}}_{\\ddot y} +\n",
    "\\underbrace{\\left( \\frac{1}{m} I_{2\\times 2} \\right)}_{G(x)}\n",
    "\\underbrace{\n",
    "\\begin{bmatrix}-u_1&0\\\\0&u_1\\end{bmatrix}\n",
    "\\begin{bmatrix} \\cos\\psi&\\sin\\psi \\\\ -\\sin\\psi&\\cos\\psi \\end{bmatrix}\n",
    "}_{E(x)}\n",
    "\\underbrace{\\begin{bmatrix}\n",
    "\\theta^d \\\\ \\phi^d\n",
    "\\end{bmatrix}}_{u},\n",
    "\\end{align}\n",
    "$$\n",
    "leads to the tracking control\n",
    "$$\n",
    "\\begin{equation}\n",
    "u = -\n",
    "\\underbrace{\n",
    "\\begin{bmatrix} \\cos\\psi&-\\sin\\psi \\\\ \\sin\\psi&\\cos\\psi \\end{bmatrix}\n",
    "\\begin{bmatrix}-\\frac{1}{u_1}&0\\\\0&\\frac{1}{u_1}\\end{bmatrix}\n",
    "}_{E^{-1}(x)}\n",
    "\\underbrace{\\begin{bmatrix} m&0\\\\0&m \\end{bmatrix}}_{G^{-1}(x)}\n",
    "\\left\\{\n",
    "\\underbrace{\\begin{bmatrix} 0\\\\0 \\end{bmatrix}}_{f_b(\\eta,\\xi)} -\n",
    "\\underbrace{\\begin{bmatrix} \\ddot{r}_x^d \\\\ \\ddot{r}_y^d \\end{bmatrix}}_{\\ddot y}\n",
    "+ K_2(\\xi-\\dot y)\n",
    "\\right\\}\n",
    "+ E^{-1}(x) v,\n",
    "\\end{equation}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\begin{equation}\n",
    "v = -\\beta(x)\\text{sgn}(\\tilde s)\n",
    "\\end{equation}\n",
    "$$\n",
    "and the sliding surface is redefined to be\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\tilde s = \\tilde\\xi + K_2\\tilde\\eta = (\\xi-\\dot y) + K_2(\\eta-y).\n",
    "\\end{equation}\n",
    "$$\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SMC(Controller):\n",
    "    \"\"\"Sliding Mode Controller\n",
    "    \n",
    "    This implementation of SMC includes the ability\n",
    "    to track reference signals, as opposed to the\n",
    "    StabilizingSMC class above. In addition, this\n",
    "    class utilizes a saturation function instead\n",
    "    of the naive signum function for the switching\n",
    "    component of the controller.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        self.name = \"SMC\"\n",
    "        \n",
    "        # dirty-derivative filters\n",
    "        self.dyidt = DirtyDerivative(order=1, tau=0.0125)\n",
    "        self.dyidt2 = DirtyDerivative(order=2, tau=0.025)\n",
    "        self.dyodt = DirtyDerivative(order=1, tau=0.025)\n",
    "        self.dyodt2 = DirtyDerivative(order=2, tau=0.05)\n",
    "        \n",
    "        # Value of total thrust from last iteration\n",
    "        self.u1_d1 = 0\n",
    "        \n",
    "        # estimates of the physical properties of the quadrotor\n",
    "        self.g = 9.81\n",
    "        self.mass = 3.81\n",
    "        self.I = np.diag(np.array([0.1, 0.1, 0.1]))\n",
    "        \n",
    "        # proportional control law \\phi(\\eta) that stabilizes the inner \\dot\\eta = f_a system\n",
    "        self.K1 = np.diag(np.array([2,5,5,1]))\n",
    "        \n",
    "        # proportional control law \\phi(\\eta) that stabilizes the outer \\dot\\eta = f_a system\n",
    "        self.K2 = np.diag(np.array([1,1]))\n",
    "               \n",
    "    def inner(self, desired, state, Ts):\n",
    "        \n",
    "        def fa(eta, xi):\n",
    "            return xi\n",
    "\n",
    "        def fb(eta, xi):\n",
    "            # extract omega from xi\n",
    "            omega = xi[1:4]\n",
    "\n",
    "            r = np.zeros((4,1))\n",
    "            r[0,0] = self.g\n",
    "            r[1:4] = -np.linalg.inv(self.I).dot(np.cross(omega, self.I.dot(omega), axis=0))\n",
    "            return r\n",
    "        \n",
    "        # Create the reference signal vector\n",
    "        y = np.atleast_2d(desired).T # make a col vector\n",
    "        ydot = self.dyidt.update(y, Ts)\n",
    "        yddot = self.dyidt2.update(ydot, Ts)\n",
    "        \n",
    "        # Transform the system into the form of HK (14.4) and (14.5)\n",
    "        eta = np.array([state.flatten()[[2, 6, 7, 8]]]).T # r_z, ph, th, ps\n",
    "        xi = np.array([state.flatten()[[5, 9, 10, 11]]]).T # \\dot{r_z}, p, q, r\n",
    "\n",
    "        # for convenience\n",
    "        ph = eta.flatten()[1]\n",
    "        th = eta.flatten()[2]\n",
    "        ps = eta.flatten()[3]\n",
    "        \n",
    "        # Build the inv(E(x)) matrix\n",
    "        Einv = np.diag(np.array([-1,1,1,1]))\n",
    "        \n",
    "        # Build the L(x) = inv(G(x)) matrix\n",
    "        L = np.eye(4)\n",
    "        L[0, 0] = self.mass/(np.cos(ph)*np.cos(th))\n",
    "        L[1:4, 1:4] = self.I\n",
    "        \n",
    "        # continuous control to cancel known terms: equation (18) of [1].\n",
    "        ueq = -Einv.dot(L.dot( (fb(eta, xi) - yddot) + self.K1.dot( fa(eta-y, xi-ydot) )))\n",
    "        \n",
    "        # Build the matrix of sliding surfaces\n",
    "        SS = (xi-ydot) + self.K1.dot(eta-y)\n",
    "        \n",
    "        # Gains\n",
    "        Beta = np.diag(np.array([11,5,5,2]))\n",
    "        \n",
    "        # switching components of the control: equation (20) of [1]\n",
    "        # (but with a boundary on the sliding surface to mitigate chattering)\n",
    "        gamma = -Beta.dot(sat( SS/1 ))\n",
    "        \n",
    "        # equation (23) of [1]\n",
    "        u = ueq + Einv.dot(gamma)\n",
    "        \n",
    "        return u\n",
    "    \n",
    "    def outer(self, desired, u1, state, Ts):\n",
    "        \n",
    "        # Make sure the thrust is non-zero\n",
    "        if u1 == 0:\n",
    "            return np.array([0,0])\n",
    "        \n",
    "        def fa(eta, xi):\n",
    "            return xi\n",
    "\n",
    "        def fb(eta, xi):\n",
    "            return np.zeros((2,1))\n",
    "        \n",
    "        # Create the reference signal vector\n",
    "        y = np.atleast_2d(desired).T # make a col vector\n",
    "        ydot = self.dyodt.update(y, Ts)\n",
    "        yddot = self.dyodt2.update(ydot, Ts)\n",
    "                \n",
    "        # Transform the system into the form of HK (14.4) and (14.5)\n",
    "        eta = np.array([state.flatten()[[0, 1]]]).T # r_x, r_y\n",
    "        xi = np.array([state.flatten()[[3, 4]]]).T # \\dot{r}_x, \\dot{r}_y\n",
    "        \n",
    "        ps = state.flatten()[8]\n",
    "        \n",
    "        # Build the inv(E(x)) matrix\n",
    "        R = np.array([\n",
    "            [ np.cos(ps), np.sin(ps)],\n",
    "            [-np.sin(ps), np.cos(ps)],\n",
    "        ])\n",
    "        Einv = R.T.dot(np.diag(np.array([-1.0/u1,1.0/u1])))\n",
    "        \n",
    "        # Build the L(x) = inv(G(x)) matrix\n",
    "        L = self.mass*np.eye(2)\n",
    "        \n",
    "        # continuous control to cancel known terms: equation (18) of [1].\n",
    "        ueq = -Einv.dot(L.dot( (fb(eta, xi) - yddot) + self.K2.dot( fa(eta-y, xi-ydot) )))\n",
    "        \n",
    "        # Build the matrix of sliding surfaces\n",
    "        SS = (xi-ydot) + self.K2.dot(eta-y)\n",
    "        \n",
    "        # Gains\n",
    "        Beta = np.diag(np.array([15,15]))\n",
    "        \n",
    "        # switching components of the control: equation (20) of [1]\n",
    "        # (but with a boundary on the sliding surface to mitigate chattering)\n",
    "        gamma = -Beta.dot(sat(SS/1))\n",
    "        \n",
    "        # equation (23) of [1]\n",
    "        u = ueq + Einv.dot(gamma)\n",
    "        \n",
    "        return u\n",
    "    \n",
    "    def update(self, commanded, state, pkt, Ts):\n",
    "        \n",
    "        #\n",
    "        # Outer Loop\n",
    "        #\n",
    "        \n",
    "        ref = self.outer(commanded.flatten()[[0, 1]], self.u1_d1, state, Ts)\n",
    "        \n",
    "        #\n",
    "        # Inner Loop\n",
    "        #\n",
    "        \n",
    "        # build reference signal for inner loop\n",
    "        rz_ref = commanded.flatten()[2]\n",
    "        ph_ref = ref.flatten()[1]\n",
    "        th_ref = ref.flatten()[0]\n",
    "        ps_ref = commanded.flatten()[8]\n",
    "        desired = np.array([rz_ref, ph_ref, th_ref, ps_ref])\n",
    "        \n",
    "        u = self.inner(desired, state, Ts)\n",
    "\n",
    "        # Save total thrust for the outer loop\n",
    "        self.u1_d1 = u.flatten()[0]\n",
    "        \n",
    "        # update the commanded states\n",
    "        commanded[6] = ph_ref\n",
    "        commanded[7] = th_ref\n",
    "        \n",
    "        # actuator commands\n",
    "        return u, commanded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7fd936908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb83c0f0ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quadrotor state after 2000 iters:\n",
      "\tr:     [[ 1.004  2.000 -1.000]].T\n",
      "\tPhi:   [[ 0.246  0.000  1.571]].T\n",
      "\tv:     [[ 0.065  0.000 -0.000]].T\n",
      "\tomega: [[ 0.063 -0.000  0.000]].T\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Instantiate a quadrotor model with the given initial conditions\n",
    "quad = Quadrotor(r=np.array([[0],[0],[-10]]),\n",
    "                 v=np.array([[0],[0],[0]]),\n",
    "               Phi=np.array([[-0.1],[0],[0]]))\n",
    "\n",
    "# Instantiate a tracking sliding mode controller\n",
    "ctrl = SMC()\n",
    "\n",
    "# Setup a setpoint commander\n",
    "cmdr = Commander(default=True)\n",
    "cmdr.attitude(np.array([0,0,np.pi/2]))\n",
    "\n",
    "def set_position(i, Ts):\n",
    "    f = 0.25\n",
    "    x = np.cos(2*np.pi*f*i*Ts)\n",
    "    return np.array([x, 2, -1])\n",
    "\n",
    "cmdr.position(set_position)\n",
    "\n",
    "# Run the simulation\n",
    "sim = Simulator(quad, ctrl, cmdr=cmdr)\n",
    "sim.run(20, Ts=0.01)\n",
    "sim.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "Sliding mode control is a fairly straightforward controller to implement with low computational demands (i.e., no optimization---it is all just linear algebra). Although there are various ways to approach the design of a sliding mode controller, the principle is the same:\n",
    "<br><br>\n",
    "1. Identify a sliding surface such as $s = \\xi - \\phi(\\eta) = 0$ that you can drive system trajectories to. Once the system is on this manifold, it *slides* to the origin using the control law $\\phi(\\eta)$, which is typically designed to be linear (i.e., $\\phi(\\eta) = -K\\eta$) but could be anything.\n",
    "<br><br>\n",
    "1. Choose $u$ to drive all system trajectories to the manifold $s=0$. While Khalil gives a general control form in equation \\eqref{eq:general-smc-control}, the fundamental principle is Lyapunov stabiliy analysis. The control $u$ must be designed such that $\\dot{V} = s\\dot{s} < 0$. The control $u$ is often chosen with a continuous part that cancels any known terms from the model, and a discontinuous switching component $\\beta(x)\\text{sgn}(s)$ that guarantees a that the Lyapunov function is negative-definite in the direction of the system's trajectories.\n",
    "<br><br>\n",
    "1. Because $\\text{sgn}(s)$ causes chattering, use $\\text{sat}(\\frac{s}{\\epsilon})$ instead, where $\\epsilon$ is typically small and can be tuned to change the transition region around the manifold $s=0$.\n",
    "\n",
    "<br>\n",
    "\n",
    "Other thoughts:\n",
    "- Ensure that your derivatives are being computed corectly! For an $n$th-order derivative, make sure to wait until you have seen $n$ measurements."
   ]
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   "source": [
    "## References\n",
    "\n",
    "[1] A. L’Afflitto, R. Anderson, and K. Mohammadi, “An Introduction to Nonlinear Robust Control for Unmanned Quadrotor Aircraft,” IEEE Control Syst. Mag., vol. 38, no. June, pp. 102–121, 2018.\n",
    "\n",
    "[2] H. K. Khalil, Nonlinear Systems. Princeton, NJ: Prentice Hall, 2002.\n",
    "\n",
    "[3] M. K. Shaik and J. F. Whidborne, “Robust Sliding Mode Control of a Quadrotor,” 11th Int. Conf. Control, pp. 1–5, 2016."
   ]
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