{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github", "tags": [ "no-tex" ] }, "source": [ "\"Open" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "JoW4C_OkOMhe", "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Note: you may need to restart the kernel to use updated packages.\n" ] } ], "source": [ "%pip install -q -U gtbook" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "10-snNDwOSuC", "tags": [ "remove-cell" ] }, "outputs": [], "source": [ "import torch\n", "import numpy as np\n", "import plotly.subplots as pls\n", "import plotly.graph_objects as go\n", "import plotly.express as px\n", "\n", "import gtsam\n", "from gtsam import Point2\n", "import gtbook.drone as gtbook_drone\n", "from gtbook.drone import Drone\n", "\n", "try:\n", " import google.colab\n", "except:\n", " import plotly.io as pio\n", " pio.renderers.default = \"png\"\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=FutureWarning)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "id": "nAvx4-UCNzt2" }, "source": [ "```{index} planning; trajectory optimization\n", "```\n", "\n", "# Trajectory Optimization\n", "\n", "> We can optimize over future trajectories, as well.\n", "\n", "\"Splash\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "```{index} trajectory optimization", "```", "In the previous section we saw how use factor graphs for visual SLAM and structure from motion. These perception algorithms are typically run after the robot has gathered some visual information, and provide information about what happened in the past. But how can we plan for the future? \n", "\n", "We already saw that RRTs are a useful tool for planning in a continuous, potentially high dimensional state space. However, RRTs are not concerned with optimality. They aim for feasible paths, where sometimes feasibility means \"collision-free\" and sometimes it includes honoring the system dynamics. But if we want to achieve optimal trajectories in terms of time to goal, best use of energy, or minimum distance, we need to turn to other methods.\n", "\n", "In this section we will discuss optimization methods for control. In particular, we will use **trajectory optimization**, to minimize the cost associated with the trajectory to be executed in the future. These costs can be associated with staying away from obstacles, or other desirable properties like minimizing power consumption to preserve battery life. RRTs and trajectory optimization can be combined, where an RRT provides a good \"broad strokes\" trajectory, and a trajectory optimization smooths out and fine-tunes the final trajectory." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "We explain trajectory optimization using a very simple problem: how to get from point A to point B. This seems like an easy problem, as we all know the answer should be a straight line, right? But, it is not as easy for drones, as we have to account for the drone's attitude, and we might have to accelerate and decelerate at the start and end points. Come to think of it, maybe we are already flying at a certain velocity at point A, and want to have a certain velocity at point B! Clearly, this is not as easy as it appears.\n", "\n", "Below we go about finding an optimal trajectory in steps:\n", "- We explain how finding an optimal *path* is all we need to do as a first step.\n", "- We discuss how to represent environments that contain obstacles using maps.\n", "- We introduce factor graphs to find an optimal path in those maps.\n", "- We show how a path solution can be converted into a *trajectory* using interpolation in time.\n", "\n", "Once we have developed methods for computing an optimal trajectory,\n", "we then show the broad outlines of building a simple cascaded controller that is able to execute these trajectories. \n", "Using the drone kinematics and dynamics models from Section 7.2, we show how to implement such controllers and evaluate them in simulation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} path, trajectory", "```", "## Optimizing for Position\n", "\n", "> Position is all we need for the first step.\n", "\n", "In many applications, the drone configuration can effectively be decomposed into its position and orientation\n", "components: the position variables define a path through Euclidean space, and the orientation\n", "variables can be used to achieve the desired accelerations and velocities of the drone to follow \n", "that path (recall\n", "that a drone exerts thrust parallel to its body $z$-axis, so the orientation of the drone\n", "determines the direction of motion). \n", "We know from Section 7.2 that the drone's attitude will *affect* position: \n", "pitch or roll will affect the velocity, which that will integrate into position. \n", "When given a continuous set of positions (i.e., a curve in $\\mathbb{R}^3$) to get us from A to B, we can obtain the pitch, roll, and thrust trajectories to realize it.\n", "This very mechanism for controlling motion is also a source of complexity: a drone is **under-actuated**.\n", "We cannot directly control all six DOF, since we have only four rotors. \n", "\n", "Recall from Section 5.5 that a free **path** is defined as a continuous mapping of\n", "the unit interval to the free configuration space: $\\gamma : [0,1] \\rightarrow {\\cal Q}_\\mathrm{free}$,\n", "such that $q(0) = q_\\mathrm{init}$ and $q(1) = q_\\mathrm{goal}$.\n", "This unit-length parameterization of the path hides the dynamics of the drone;\n", "there is no notion of time in this representation.\n", "When we choose a time parameterization of the path, the resulting $\\gamma(t)$ defines\n", "a **trajectory**, which fully defines the dynamics of the desired motion.\n", "For example, we can differntiate the trajectory with respect to time to obtain the instantaneous velocity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we decouple position and orientation, the problem of finding a path for the position variables\n", "is to compute a continuous $\\gamma: [0,1] \\rightarrow \\mathbb{R}^3$, i.e., we ignore the orientation of the drone.\n", "In this chapter, we will do so using an optimization-based approach.\n", "There are many ways one can do this, some better than others, but here strive for simplicity:\n", "we discretize the time interval in which we expect to fly, and solve for a corresponding sequence of positions\n", "$(X_1, \\dots X_K)$ that satisfy our objectives. These objectives include\n", "\n", "- a desired starting position,\n", "- a desired goal position,\n", "- an objective function to facilitate obstacle avoidance, and\n", "- a smoothness objective that bounds velocity and/or acceleration.\n", "\n", "If these objectives are in conflict, we can assign them weights such that we trade off some against others. *Constrained optimization* techniques allow to set hard constraints and/or bounds, but we do not use those here. Instead, we opt for a simple nonlinear least-squares scheme that finds the path $X^*$ that minimizes the following objective:\n", "\n", "$$\n", "X^* = \\arg \\min \\sum_{k=1}^K \\phi_k(X_k)^2 + \\sum_{k=1}^{K-1} \\psi_k(X_k, X_{k+1})^2\n", "$$\n", "\n", "where $X_k$ is the position at time, and $\\phi_k(X_k)$ and $\\psi_k(X_k, X_{k+1})$ are unary and binary objectives, respectively, that we want to minimize. \n", "Desired start and goal position, as well as obstacle avoidance are examples of unary objectives, while smoothness is a binary objective, which can be expressed in terms of the distance between successive points along the path.\n", "\n", "It will not come as any surprise that we can also use factor graph optimization to solve this optimization problem.\n", "The objective above is exactly the expression of a nonlinear factor graph, except that the factors now derive from objectives we want to minimize, rather than measurement errors. In the next section we work out in detail how to do so.\n", "\n", "Note that when we use this discrete optimization approach, the result is merely a set of points,\n", "not a continuous path. Below, we will show how to convert the discretized path into a smooth trajectory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} occupancy map, cost map", "```", "## Occupancy and Cost Maps\n", "\n", "> We can use maps to encode costs to minimize.\n", "\n", "A popular approach to represent environments with obstacles is to use an **occupancy map**. An occupancy map is essentially a 2D array of cells, and we have already used this concept in Section 4.3. \n", "After we choose a certain resolution (for example, 10 cm by 10 cm), each cell in the map contains a probability for the presence of an obstacle. This concept can be extended to distinguish between various types of obstacles, \n", "for example if some obstacles pose more significant threat than others.\n", "\n", "This extended version of an occupancy can be further extended to a **cost map**, \n", "where areas with less hazardous obstacles (like tall grass) are considered less costly compared to more dangerous ones (like flying into a tree). Cost maps do not encode *occupancy* but rather encode the cost of being in a particular location. For our purposes, we will start directly with cost maps instead of creating true occupancy maps.\n", "\n", "To illustrate, let us consider creating a simple example cost map. \n", "We will begin by considering the 2D case, which corresponds to the case of a drone flying at constant altitude. \n", "In the `gtbook/drone` library, we have a function named `create_random_map`. \n", "This function requires as parameters the width $W$, height $H$, and the number of obstacles,\n", "and it creates a map that contains a random arrangement of obstacles. Width and height are given in meters, and the resolution is hardcoded at 10 cm. An optional parameter is a random seed, which allows for the reproduction of the exact experiment setup. Obstacles are generated with costs chosen randomly between 0.5 and 1.0.\n", "\n", "The following code snippet demonstrates how to generate a random map with 50 obstacles. Most of the environment has a cost of zero, and the obstacles are rendered in different shades of red based on their cost. Occasionally two obstacles overlap in which case the costs are added." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Create a random cost map\n", "W, H = 30, 10 # 30m x 10m\n", "cost_map = gtbook_drone.create_random_map(W, H, num_obstacles=50, seed=7)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Cost map with randomly generated obstacles, at 10cm resolution.\n", "#| label: fig:obstacles\n", "fig = px.imshow(cost_map, color_continuous_scale='Reds')\n", "fig.update_layout(coloraxis_showscale=False, margin=dict(l=0, r=0, t=0, b=0), width=1000)\n", "fig.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A disadvantage to the map shown above is that large areas of the map contain cells with zero cost,\n", "and therefore provide no information about locality of obstacles.\n", "The transition from obstacle-free space to obstacle-occupied space is abrupt.\n", "To improve the situation, we can smooth the \n", "cost map with a differentiable kernel, like a Gaussian. \n", "We can use convolution to do this, just as we did for computer vision problems Section 5.4.\n", "A Gaussian kernel is a very popular choice for smoothing an image and removing noise, but here we wil use it to make the cost map \"better behaved\" for our purposes.\n", "\n", "To do this in code, we have to be a bit careful.\n", "We implemented maps in this section with PyTorch, following the image processing code in Section 5.4, and the cost map above is a torch tensor. \n", "In particular, the cost map is represented as a grayscale image 100 pixels tall and 300 pixels wide.\n", "Convolving an image with a kernel is relatively easy in PyTorch, although we need to juggle some tensor dimensions because by convention, `conv2d` operates on $\\text{batch} \\times \\text{channel} \\times \\text{height} \\times \\text{width}$ tensors. There is no need to deeply understand what is going on here, though." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "sigma = 0.5 # 0.5m standard deviation for the Gaussian kernel\n", "K = 21 # 21x21 kernel is big enough to accommodate that standard deviation\n", "kernel = gtbook_drone.gaussian_kernel(sigma*10, K) # multiply by 10 as map is 10cm resolution\n", "batch = cost_map[None, None, ...] # Add batch and channel dimensions\n", "blurred = torch.conv2d(batch, kernel, padding='same')[0, 0, ...]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Cost map blurred with 0.5 meter Gaussian kernel.\n", "#| label: fig:blurred\n", "fig = px.imshow(blurred, color_continuous_scale='Reds')\n", "fig.update_layout(coloraxis_showscale=False, margin=dict(l=0, r=0, t=0, b=0), width=1000)\n", "fig.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Making Costs (Truly) Differentiable\n", "\n", "> Continuous smoothing, not convolution.\n", "\n", "The discrete cost maps above are not differentiable; as we cross cell boundaries, the value of cost\n", "makes a discontinuous jump.\n", "Because of this, the factors $\\phi_k(X_k)$ are not differentiable, which is a requirement of our optimization-based\n", "approach.\n", "\n", "To obtain truly differentiable factors, however, we can construct a custom Gaussian kernel at the *exact location*\n", "at which we want to evaluate the cost. Remember we are trying to minimize a *path*, by selecting a set of positions $X_k$ at discrete time stamps $t_k$. It is important to realize that each $X_k$ can take on arbitrary real values\n", "(not just integer coordinates of cells in the grid), and that the grid is an\n", "approximate, discretized representation of the world and the cost of moving through the world. \n", "\n", "In nonlinear optimization, the story is always the same: evaluate the cost *and* its derivatives at a current guess for all $X_k$, and then use the spatial derivatives of the cost at each discretized pose $X_k$ to update the path\n", "to a lower cost solution. We will use a factor graph to evaluate the cost and its derivative, so it is important that this cost is smooth and differentiable.\n", "\n", "If we merely smooth a discretized cost map, as above, the result is still discretized, however smooth it looks to us. To get the *exact* value of the cost, and its derivatives, we can create a Gaussian kernel centered *exactly* at our current *continuous* position.\n", "The function `gaussian_filter` defined in `gtbook` does just that: it evaluates a single Gaussian kernel operator given a standard deviation, a continuous map location, and the cost map. The code below shows that this gives the exact same result as a lookup in the blurred image when given an integer coordinate, but it *also* works for non-integer coordinates." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Local cost at [7.5 5.3] is 0.135\n" ] } ], "source": [ "xy = Point2(7.5, 5.3) # point in map, in meters\n", "uv = 10*xy # continuous position in image\n", "local_result = gtbook_drone.gaussian_filter(sigma*10, uv, cost_map, K)\n", "print(f\"Local cost at {xy} is {local_result:.3f}\")\n", "\n", "# When uv are at integer values, blurred image gives the same result:\n", "assert np.allclose(local_result, blurred[int(uv[1]), int(uv[0])])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get the derivatives we blur the vertical and horizontal gradient images, respectively. \n", "Because convolution is a linear operation, \n", "we can compute the directional derivatives of the Gaussian kernel, *or* we can apply the convolution on a gradient image. We choose the latter, by first using the Sobel operator we encountered in Section 5.4 to create gradient images: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Compute gradients:\n", "sobel_u, sobel_v = gtbook_drone.sobel_kernels()\n", "grad_u = torch.conv2d(batch, sobel_u, padding='same')[0,0,...]\n", "grad_v = torch.conv2d(batch, sobel_v, padding='same')[0,0,...]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Obstacle cost map, blurred cost map, and both vertical and horizontal sobel gradients.\n", "#| label: fig:obstacles-2x2\n", "fig = pls.make_subplots(rows=2, cols=2)\n", "fig.add_trace(go.Heatmap(z=cost_map, colorscale='reds', showscale=False), row=1, col=1)\n", "fig.add_trace(go.Heatmap(z=blurred, colorscale='reds', showscale=False), row=1, col=2)\n", "fig.add_trace(go.Heatmap(z=grad_u, colorscale='rdbu', showscale=False), row=2, col=1)\n", "fig.add_trace(go.Heatmap(z=grad_v, colorscale='rdbu', showscale=False), row=2, col=2)\n", "for i in [1,2]:\n", " for j in [1,2]:\n", " fig.update_xaxes(title_text=\"\", showticklabels=False, row=i, col=j)\n", " fig.update_yaxes(title_text=\"\", showticklabels=False, row=i, col=j)\n", "fig.update_layout(margin=dict(l=0, r=0, t=10, b=0), width=1000)\n", "fig.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Figure 3 shows both cost map and its blurred version, as well as the (un-blurred) gradient images `grad_u` and `grad_v`. We can then combined these into one rank-3 tensor and evaluate the cost *and* derivatives in one operation:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.135 0.004 -0.004]\n" ] } ], "source": [ "combined = torch.stack([cost_map, grad_u, grad_v], dim=0)\n", "print(np.round(gtbook_drone.gaussian_filter(sigma*10, uv, combined, K),3))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gives us exactly what we need: because we blur the cost map, the vertical component of the gradient, and the horizontal component of the gradient, we obtain three numbers: the cost at the location $u,v$, the derivative of the cost with respect to a change in $u$, and the derivative of the cost with respect to a change in $v$. Next, we show how to use this super-power in the context of factor graph optimization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Factor Graphs for Trajectory Optimization\n", "\n", "Now that we can evaluate cost and its derivatives at any location, we can create factors. Since occupancy maps or cost maps are not built into GTSAM, we use its facility to create a custom factor from arbitrary python code. A `gtsam.CustomFactor` just has a constructor that can take an arbitrary python callback function, along with a `Key` (and a noise model). At evaluation, the callback function gets a handle to the factor and a `gtsam.Values` object, and it does three things:\n", "\n", "- check which variable is involved, by asking the factor;\n", "- with that key, extract the current estimate from the passed in `Values`;\n", "- calculate the cost, and if asked, its derivatives.\n", "\n", "The fact that we can do this for arbitrary python code is very convenient, and is used below to create cost factors that interrogate the cost map, using our localized Gaussian filter, and if asked, its derivatives:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def cost_func(factor: gtsam.CustomFactor, v: gtsam.Values, H: list[np.ndarray]):\n", " \"\"\"Cost function for the custom factor.\"\"\"\n", " # Extract the Point2 variable using the key in the factor\n", " point = v.atPoint2(factor.keys()[0])\n", "\n", " uv = 10 * point # Convert to map coordinates\n", "\n", " if H is None:\n", " cost = gtbook_drone.gaussian_filter(sigma * 10, uv, cost_map, K)\n", " else:\n", " # If derivatives are needed, calculate them here:\n", " cost, cost_x, cost_y = gtbook_drone.gaussian_filter(sigma * 10, uv, combined, K)\n", " H[0] = np.array([[cost_x, cost_y]])\n", "\n", " return np.array([cost]).astype(float)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us discretize the path using $M=100$ discrete time steps, using the keys $k\\in 1...M$. We can define a start and goal point, and initialize the path as straight line. In other words, we initialize according to this formula:\n", "\n", "$$\n", "X_k = (1-\\alpha)\\ X_{\\text{start}} + \\alpha\\ X_{\\text{goal}} \\text{~~~with~} \\alpha = \\frac{k-1}{M-1},\n", "$$\n", "\n", "Who knows, we might be lucky and hit no obstacles along the way:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "M = 100 # Number of points\n", "start, goal = Point2(2, 5), Point2(28, 5)\n", "initial = gtsam.Values()\n", "for k in range(1,M+1):\n", " alpha = (k-1)/(M-1)\n", " initial.insert(k, (1-alpha)*start + alpha*goal)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Initial path estimate plotted on the cost map.\n", "#| label: fig:initial\n", "initial_path = 10*gtsam.utilities.extractPoint2(initial)\n", "fig = px.imshow(cost_map, color_continuous_scale='Reds')\n", "fig.add_trace(go.Scatter(x=initial_path[:,0], y=initial_path[:,1], mode='lines+markers', line=dict(color='gray')))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, margin=dict(l=0, r=0, t=0, b=0), width=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting this path on the cost map shows that, in this instance, we are not lucky, however: the path definitely passes through some obstacles. We can immediately create all obstacle cost factors now, and evaluate the cost to confirm that this is not a zero-cost path. Since these factors are nonlinear, we store them in a `gtsam.NonlinearFactorGraph`:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Graph has 100 factors\n" ] } ], "source": [ "obstacle_factors = gtsam.NonlinearFactorGraph()\n", "for k in range(1,M+1):\n", " custom_factor = gtsam.CustomFactor(None, [k], cost_func)\n", " obstacle_factors.add(custom_factor)\n", "print(f\"Graph has {obstacle_factors.size()} factors\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cost profile along the path clearly shows the obstacles along the path. We can evaluate both the individual costs and the sum-of-squares cost $\\sum\\psi_k(X_k)^2$ of a factor graph. The former gives us a cost profile along the way, and the latter represents an aggregate loss that we would like to minimize. We show the former as a bar graph below:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Costs for the initial trajectory estimate.\n", "#| label: fig:initial-costs\n", "costs = [obstacle_factors.at(i).unwhitenedError(initial) for i in range(M)]\n", "fig = px.bar(costs, range_y=[0, 0.2])\n", "fig.update_layout(yaxis_title='Cost', coloraxis_showscale=False, showlegend=False, height=300, width=1000, margin=dict(l=10, r=10, t=10, b=10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A complete path/trajectory optimization problem needs more than just obstacle factors, however. We also need to add start and goal factors, as well as smoothness factors. Smoothness factors are implemented using a `gtsam.BetweenFactor`, \n", "and these help to ensure that the distance between successive points on the path is not too great.\n", "\n", "Start and goal factors impose penalties when the starting point, $X_1$, is not near to the current position,\n", "or the final point, $X_K$, is not near the goal position.\n", "Both of these can be implemented as simple \"priors\" on the variables with keys $k=1$ and $k=100$. Note that a \"prior factor\" in GTSAM is just a quadratic cost, and in an estimation context that indeed corresponds to a Gaussian prior on a continuous point. In our current *planning* context we abuse that factor to simply have a quadratic cost at the path boundaries.\n", "\n", "Both types of factors are added in the code below:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# We start by copying the obstacle factors:\n", "graph = gtsam.NonlinearFactorGraph()\n", "graph.push_back(obstacle_factors)\n", "\n", "constrained2 = gtsam.noiseModel.Constrained.All(2) # We *insist* on the start and goal points!\n", "graph.addPriorPoint2(1, start, constrained2)\n", "graph.addPriorPoint2(M, goal, constrained2)\n", "\n", "# The strength of the smoothness factors is controlled by a `precision` value: higher is stronger.\n", "# Feel free to change the precision value below and see how the optimizer behaves:\n", "smoothness_model = gtsam.noiseModel.Isotropic.Precision(2, 0.01)\n", "for k in range(1, M):\n", " graph.add(gtsam.BetweenFactorPoint2(k, k+1, gtsam.Point2(0.0, 0.0), smoothness_model))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To optimize, we use a Levenberg Marquardt nonlinear optimizer. This optimizer, which we have encountered before in Section 6.4, linearizes the factors at every iteration and takes a cautious second-order minimization step. The \"cautiousness\" is governed by a parameter $\\lambda$ that essentially selects between gradient descent ($\\lambda$ high) and a second-order Gauss-Newton step ($\\lambda$ low). In our potentially very non-linear cost landscape it is good practice to start of the optimizer with a relatively high value for $\\lambda$:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial cost: 0.236\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Final cost: 0.064\n" ] } ], "source": [ "print(f\"Initial cost: {graph.error(initial):.3f}\")\n", "params = gtsam.LevenbergMarquardtParams()\n", "params.setlambdaInitial(100)\n", "# params.setVerbosityLM(\"SUMMARY\") # uncomment this line to see the LM progress\n", "optimizer = gtsam.LevenbergMarquardtOptimizer(graph, initial, params)\n", "result = optimizer.optimize()\n", "print(f\"Final cost: {graph.error(result):.3f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The optimizer is very fast, on the order of milliseconds for this example, so it can be used in an online planner that continuously re-plans as the cost map is updated with new information. When used for flying a drone, we can execute on the initial part of the trajectory and then immediately re-plan. This scheme is version of \"model-predictive\" control (MPC), which is frequently used in actual autonomous vehicles and drones.\n", "\n", "In our case, the optimizer finds a very nice path that navigates some tricky obstacle configurations, especially in the right half of the environment:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Initial and final path plotted on the blurred cost map.\n", "#| label: fig:final\n", "result_path = 10*gtsam.utilities.extractPoint2(result)\n", "fig = px.imshow(blurred, color_continuous_scale='Reds')\n", "fig.add_trace(go.Scatter(x=initial_path[:,0], y=initial_path[:,1], mode='lines+markers', line=dict(color='gray')))\n", "fig.add_trace(go.Scatter(x=result_path[:,0], y=result_path[:,1], mode='lines+markers', line=dict(color='green')))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, width=1000, margin=dict(l=0, r=0, t=0, b=0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cost profile along this final path is not entirely down to zero, as we have to navigate some tight obstacle configurations along the way. However, when plotted on the same scale it looks much better than for the initial path:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Costs for the optimized path.\n", "#| label: fig:final-costs\n", "costs = [obstacle_factors.at(i).unwhitenedError(result) for i in range(M)]\n", "fig = px.bar(costs, range_y=[0, 0.2])\n", "fig.update_layout(yaxis_title='Cost', coloraxis_showscale=False, showlegend=False, width=1000, height=300, margin=dict(l=10, r=10, t=10, b=10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise\n", "\n", "Uncomment the line that calls `setVerbosityLM` in the optimization code to get a sense of how the optimization proceeds. Plot the result." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing\n", "\n", "> From path to trajectory.\n", "\n", "We now convert our discretized optimal path to a discretized optimal *trajectory*. \n", "Here we will do so very simply by assigning a total execution time $T$ to the path. \n", "If we impose uniform $\\Delta t$ between successive points in the path,\n", "we can associate a time $t_k = (k-1) \\Delta t$ to each point $X_k$ in the path.\n", "\n", "We have to choose $T$ judiciously. \n", "We may want to go fast, but we need to make sure trajectory respects the drone's dynamic constraints:\n", "a drone can't stop on a dime or go faster than certain limits. \n", "If we choose $T$ to be small, we are asking the drone to fly fast, and we might hit thrust limits. If we choose $T$ to be high, the drone will fly more slowly. For this example, we choose $T=20$ as a reasonable compromise,\n", "as this should lead to an average velocity be a bit above 1 m/s.\n", "\n", "Once we have a discretized translational trajectory that is well behaved, we can \"upgrade\" it to include\n", "full position and attitude in two different ways: in advance, by solving a large optimization problem, or physically, in real-time, by using a tracking controller. The latter is what we will do below.\n", "\n", "Even after assigning $T$, we still have only a discretized trajectory -- a discrete set of points\n", "with corresponding time stamps. A discretized trajectory is not great.\n", "For example, it is not so easy to obtain accurate velocities and accelerations from a *discretized* trajectory. Below we use a class `SmoothTrajectory` which takes a discretized path and a given $T$, and fits a polynomial to\n", "the discretized path. \n", "The smoothness of the resulting trajectory is determined by a parameter, $N$,\n", "which defines the degree of the polynomial approximation.\n", "Details of this process, however, are beyond the scope of this book.\n", "\n", "The code to create this trajectory is shown below.\n", "Note that above we computed a trajectory for a fixed altitude.\n", "Here, we set the altitude to be a 1.5m. We choose $N=20$, which is a good trade off between computational cost and smoothness, but feel free to experiment with other values. Also, we set the flag `boundaries` to True, which enforces zero acceleration at the endpoints." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "# Add height of 1.5 meters\n", "xy = gtsam.utilities.extractPoint2(result)\n", "path = np.hstack([xy, np.full((len(xy),1), 1.5)])\n", "\n", "T = 20.0\n", "smooth = gtbook_drone.SmoothTrajectory(path, N=20, a=0, b=T, boundaries=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then evaluate and visualize the smoothed trajectory at *any* time t between 0 and T:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Discretized and smoothed trajectory.\n", "#| label: fig:smoothed\n", "timestamps = np.linspace(0.0 , T, 250)\n", "desired_rn = smooth.evaluate(timestamps) # desired trajectory in navigation frame\n", "\n", "fig = px.imshow(blurred, color_continuous_scale='Reds')\n", "fig.add_trace(go.Scatter(x=result_path[:,0], y=result_path[:,1], mode='lines', line=dict(color='green')))\n", "fig.add_trace(go.Scatter(x=10*desired_rn[:,0], y=10*desired_rn[:,1], mode='lines', line=dict(color='blue')))\n", "fig.add_trace(go.Scatter(x=10*smooth.points[:,0], y=10*smooth.points[:,1], mode='markers', line=dict(color='blue')))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, margin=dict(l=0, r=0, t=0, b=0), width=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, it is instructive to inspect the velocity profiles as well:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: smoothed trajectory as time series.\n", "#| label: fig:smoothed-series\n", "desired_vn = smooth.velocities(timestamps) # desired velocity in navigation frame\n", "desired_an = smooth.accelerations(timestamps) # desired acceleration in navigation frame\n", "fig = pls.make_subplots(rows=2, cols=1, shared_xaxes=True)\n", "fig.add_trace(go.Scatter(x=timestamps, y=desired_vn[:,0], mode='lines', line=dict(color='blue'), name='vx'), row=1, col=1)\n", "fig.add_trace(go.Scatter(x=timestamps, y=desired_vn[:,1], mode='lines', line=dict(color='blue'), name='vy'), row=2, col=1)\n", "fig.update_yaxes(title_text=\"Velocity in x\", row=1, col=1)\n", "fig.update_yaxes(title_text=\"Velocity in y\", row=2, col=1)\n", "fig.update_xaxes(title_text=\"Time (s)\", row=2, col=1)\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, width=1000, height=300, margin=dict(l=80, r=60, t=10, b=10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that, for our chosen T=20, the drone flies at velocities between 1 and 1.6 m/s, which is what we expected for T=20." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} vectored thrust", "```", "## A Virtual Vectored Thrust\n", "\n", "> What we want, in theory...\n", "\n", "We control the position of the drone using a 3DOF vectored thrust input: thrust magnitude, roll, and pitch. The idea outlined here is a simplified version of the geometric controller in a 2019 paper by {cite:t}`Gamagedara19acc_geometric_control`, but while the paper is fairly advanced, the idea is rather simple. Remember the translational equations of motion from Section 7.2:\n", "\n", "$$\n", "\\begin{align}\n", "\\dot r^n &= v^n \\\\\n", "m \\dot v ^n &= R^n_b f + m g^n\n", "\\end{align}\n", "$$\n", "\n", "where $m$ is the mass. Let us concentrate on the dynamics part: we *know* the acceleration $\\dot v^n_d$ we want from our planned trajectory, and gravity is a given. Hence, to make the drone do what we want, we can only change the quantity $R^n_b f$. Let us call that the **vectored thrust** $T^n$, where the superscript $n$ denotes that the thrust is defined in the navigation frame. Then, to obtain the *desired* acceleration $\\dot v^n_d$, the vectored thrust $T^n$ has to satisfy\n", "\n", "$$\n", "T^n = m \\dot v^n_d - m g^n.\n", "$$\n", "\n", "You can think of $T^n$, which is a 3D vector, as a thrust vector that pushes the drone toward where it needs to be. It can move the drone forwards or backwards by pitching appropriately, and left or right by rolling. But of course, at all times we need to make sure it cancels gravity as well, which explains the second term above. Even after gravity compensation, to gain or lose altitude, the thrust magnitude can be adjusted to make either happen. In control parlance, $T^n$ can be thought of as a *virtual control input*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All of this is implemented in the `vectored_thrust` function below. It takes a `Drone` instance like the one we developed in Section 7.2, as well as a desired acceleration $a^n_d$. We redefined the `Drone` class in the `gtbook.drone` module so we can use it here, as well." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "desired_thrust[0] = [ 0.25988069 -0.34011288 9.81 ]\n", "desired_thrust[-1] = [-0.18333472 0.19575027 9.81 ]\n" ] } ], "source": [ "def vectored_thrust(drone:Drone, an_d:np.ndarray):\n", " \"\"\"Calculate the vectored thrust at timestamp k.\"\"\"\n", " return drone.mass * (an_d - drone.gn)\n", "\n", "# now calculate all the desired thrust vectors:\n", "drone = Drone(rn=desired_rn[0], vn=desired_vn[0], nRb=gtsam.Rot3(), wb=gtsam.Point3())\n", "print(f\"desired_thrust[0] = {vectored_thrust(drone, desired_an[0])}\")\n", "print(f\"desired_thrust[-1] = {vectored_thrust(drone, desired_an[-1])}\")" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: Smoothed trajectory with vectored thrust vectors.\n", "#| label: fig:vectored-thrust\n", "X, Y, Z = desired_rn[::5, 0], desired_rn[::5, 1], np.zeros_like(desired_rn[::5, 0])\n", "\n", "fig = px.scatter_3d(x=X, y=Y, z=Z)\n", "fig.update_traces(marker=dict(size=2))\n", "\n", "# Add thrust vectors as 3d arrows\n", "vectors = np.array([vectored_thrust(drone, desired_an[k]) for k in range(0,250,5)])\n", "Tx, Ty, Tz = 0.2*vectors[:, 0], 0.2*vectors[:, 1], 0.2*vectors[:, 2]\n", "for i in range(len(X)):\n", " fig.add_trace(go.Scatter3d(x=[X[i], X[i] + Tx[i]], y=[Y[i], Y[i] + Ty[i]], z=[Z[i], Z[i] + Tz[i]],\n", " mode='lines', line=dict(color='blue', width=2)))\n", "\n", "# Set aspect ratio based on W and Height of the map\n", "fig.update_layout(scene=dict(aspectratio=dict(x=1.2, y=H/W, z=2/W)))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, margin=dict(l=0, r=0, t=0, b=0))\n", "\n", "# Apply the camera settings to the layout\n", "fig.update_layout(scene_camera=dict(eye=dict(x=-1, y=0.2, z=0.5)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows the desired vectored thrust for the optimized trajectory for our example. If you execute this section's notebook on colab you would be able to rotate the figure and ascertain that all thrust vectors, even if they are of different lengths, all have exactly the same vertical projection magnitude. This is of course by design, to cancel out gravity in the absence of any requested vertical height changes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} feedback control", "```", "## Combining Open Loop and Feedback Control\n", "\n", "> What we want, in practice!\n", "\n", "The virtual thrust vector is an example of an **open-loop control** strategy. \n", "Open-loop controllers provide a predefined input to the system at each moment of time,\n", "without taking notice of how the system is actually performing.\n", "Given the planned trajectory, we *calculate* what we think should happen at every moment,\n", "and this is used as the control input. This could work *if* the drone perfectly tracks the planned trajectory;\n", "however, inevitably small errors will occur, maybe through wind, or model inaccuracies, or small variations in motor thrust. In addition, motors might hit their thrust limits and not be able to deliver the desired thrust completely. More importantly the pitch/roll controller (see below) that is supposed to deliver the thrust vector direction will have a small but consequential lag. All of these issues mean that errors *will* occur and the system will have to deal with them. \n", "\n", "To make this work, we need to incorporate **feedback control** terms that correct for tracking errors.\n", "Feedback, or closed-loop control, allows the input at each moment of time to be a function of the drone's\n", "state.\n", "A typical approach is to define the control input as a function of the error\n", "between desired and observed behavior.\n", "In our case, we will use the position and velocity errors.\n", "We define\n", "the *desired* position $X_d$ and *desired* velocity $\\dot X_d$ at any given time,\n", "which leads to the following controller:\n", "\n", "$$\n", "T^n = m \\dot v^n_d - m g^n - K_x (X - X_d) - K_v (\\dot X - \\dot X_d)\n", "$$\n", "\n", "This now requires tuning two additional parameters, $K_x$ and $K_v$, for the *proportional* and *derivative* control terms respectively (such a controller is called, appropriately, PD control). \n", "\n", "It *is* important to note that $X_d$ and $\\dot{X}_d$ are exactly the optimal trajectory that we optimized for above. The subscript $d$ denotes \"desired\" and strictly speaking these are functions of time $t$, as are the current position $X$ and velocity $\\dot X$. However, we chose to not clutter up the notation too much by explicitly omitting the time dependence. \n", "\n", "The proposed controller is relatively easy to implement in code:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tn = [ 0.24371061 -0.25264278 9.81 ]\n" ] } ], "source": [ "def thrust_controller(drone, rn_d, vn_d, an_d, Kx=1.0, Kv=1.0):\n", " \"\"\"Calculate the vectored thrust, adjusted for tracking errors, given desired rn/vn.\"\"\"\n", " Tn = vectored_thrust(drone, an_d)\n", " Tn -= Kx * (drone.rn - rn_d)\n", " Tn -= Kv * (drone.vn - vn_d)\n", " return Tn\n", "\n", "# Usage example:\n", "Tn = thrust_controller(drone, desired_rn[1], desired_vn[1], desired_an[1])\n", "print(f\"Tn = {Tn}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} controller gain", "```", "We can set up a small simulation to see how this controller behaves in practice, and in particular how the controller behaves for different values of $K_x$ and $K_v$. A factor like this is called a **controller gain**, and choosing the gains optimally is a standard problem in control theory.\n", "\n", "Below we use the same simulation strategy as in Section 7.2, and in particular use the `Drone` class that was defined there. In the simulation below we do not worry about the rotation yet:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "K = len(desired_rn)\n", "delta_t = T / K # time between samples\n", "\n", "# Initialize the drone:\n", "drone = Drone(rn=desired_rn[0].copy(), vn=desired_vn[0].copy(), nRb=gtsam.Rot3(), wb=gtsam.Point3(0,0,0))\n", "\n", "# reserve space for the executed trajectory:\n", "executed = np.zeros((K+1, 3))\n", "\n", "# integrate forward\n", "executed[0] = drone.rn\n", "for k in range(K):\n", " desired_Tn = thrust_controller(drone, desired_rn[k], desired_vn[k], desired_an[k])\n", " drone.integrate_thrust_vector(desired_Tn, delta_t)\n", " drone.integrate_kinematics(delta_t)\n", " executed[k+1] = drone.rn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the executed trajectory below shows we are almost tracking perfectly now:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: The executed trajectory, in red, as compared with the desired trajectory, in blue.\n", "#| label: fig:executed_vs_desired\n", "fig = px.imshow(blurred, color_continuous_scale='Reds')\n", "fig.add_trace(go.Scatter(x=10*desired_rn[:,0], y=10*desired_rn[:,1], mode='lines', line=dict(color='blue')))\n", "fig.add_trace(go.Scatter(x=10*executed[:,0], y=10*executed[:,1], mode='lines', line=dict(color='red')))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, width=1000, margin=dict(l=0, r=0, t=0, b=0))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: 3D trajectory using virtual thrust control.\n", "#| label: fig:outer-controller-3d\n", "nRb = np.tile(np.eye(3),(K,1,1)) # level attitude\n", "fig = gtbook_drone.show_executed(desired_rn, executed, nRb, K, 1)\n", "fig.update_layout(scene_camera=dict(eye=dict(x=-4, y=-3.5, z=2.5)), width=1000).show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercises:\n", "- Try setting the proportional and derivative constants $K_x$ and $K_v$ to 0, in isolation or both. Describe to yourself what happens.\n", "- Try setting one or the other to a very high value (1000). What is happening then?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Vectoring using Fast Rotational Dynamics\n", "\n", "While we cannot *instantaneously* produce the desired vectored thrust $T^n$ at any given time, the dynamics of a quadrotor are fast enough that we can get rather close. Remember that the inertia matrix, which resists rotational acceleration, is typically small around the roll and pitch axes. Let us recall the the (approximate) rotational equations of motion, in the body frame $B$:\n", "\n", "$$\n", "\\begin{align}\n", "\\dot{R}^n_b\t&= R^n_b\\hat{\\omega}^b \\\\\n", "I \\dot{\\omega}^b &\\approx \\tau^b\n", "\\end{align}\n", "$$\n", "\n", "For typical drone configurations the inertial matrix $I$ can be well approximated as $\\text{diag}(I_{xx},I_{yy},I_zz)$, with the roll-pitch components $I_{xx}, I_{yy} << I_{zz}$, the yaw component. Since $I_{xx}$ and $I_{yy}$ are small, and we have four powerful motors that can provide differential thrust very quickly, those dynamics are quite fast. Hence, if the attitude $R^n_b$ does not yet align the total thrust $f$ with the desired thrust vector $T^n$, we can quickly make it so by rotating.\n", "\n", "To figure out how to make the drone tilt, think of a video game where you are given a two axis controller and the screen displays the *current* orientation of the drone's Z-axis $\\hat k^n_b$ and the *desired* thrust vector $T^n$. Your job is to align the two by rolling (rotate around the body X-axis $\\hat x^n_b$) and pitching (rotating around the body Y-axis $\\hat y^n_n$). Looking at the drone from the outside, in the navigation frame, this will actually be rather hard: typically the controls are fixed to the *body* frame, and at every step you need to perform a mental rotation to find the right action. That is why racing drone pilots much prefer to use a \"first person view\" or FPV display and controller." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} proportional", "```", "The mathematical equivalent of FPV for a control *algorithm* is to rotate everything into the body frame. Taking the desired thrust vector $T^n$ and multiplying it with the transpose of the attitude $R^n_b$ (which is the inverse rotation, recall Sections 6.1 and 7.1) yields the desired thrust vector $T^b$ in the body frame:\n", "\n", "$$\n", "T^b = (R^n_b)^T T^n.\n", "$$\n", "\n", "Let us examine each component of this three-vector $T^b$, in the body frame, in turn. Let us name the 3 components $T_F$, $T_L$, and $T_U$, as we are using the XYZ = Forward-Left-Up convention.\n", "\n", "- When $T_F$ is *positive*, the desired thrust vector is ahead of the drone, and we should *pitch* forward. Looking from the tip of the Left/$y$-axis, this corresponds to a counter-clockwise, i.e., positive angular velocity $\\omega^b_y>0$ around the Left/$y$-axis Likewise, if $T_F$ is *negative*, we should rotate clockwise around the $y$-axis, i.e., $\\omega^b_y>0$. This inspires a control law for the torque around Y as follows:\n", "\n", " $$\n", " \\tau^b_y = K_F T_F;\n", " $$\n", "\n", "- When $T_L$ is positive, the desired thrust vector is to the left, and we should *roll*. Looking from the tip of the Forward/$x$-axis, this corresponds to a clock-wise, i.e., *negative* angular velocity $\\omega^b_x$. This inspires a control law for the torque around X as follows:\n", "\n", " $$\n", " \\tau^b_x = - K_L T_L;\n", " $$\n", "\n", "- The component $T_U$ along the body Up/$z$-axis is a good approximation of the total thrust we need, and in fact is exactly correct if the thrust vector is already aligned correctly. So, we set\n", "\n", " $$\n", " f = T_U\n", " $$\n", "\n", "The three control laws above constitute a simple yet effective controller for the drone, with $K_F$ and $K_L$ constants that govern how aggressive the controller is.\n", "The torque control laws above correspond to simple **proportional** controllers in control theory, with $-T_F$ and $T_L$ acting as errors to be driven to zero. \n", "The higher the values of $K_F$ and $K_L$, the faster the controller will try to remove those errors, but this could also lead to oscillations and even instabilities. While this is out of scope for the current text, we can obtain a more stable aggressive controller by adding a derivative term as well that is a function of the angular velocity." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "vectors[0] = [ 0.26 -0.34 9.81]\n", "control[0] = [0.034 0.026 9.81 ]\n" ] } ], "source": [ "def attitude_controller(nT: np.ndarray, nRb: gtsam.Rot3, K: float = 0.1):\n", " \"\"\"Calculate the vectored thrust for the desired thrust vector, given in nav frame.\"\"\"\n", " # Rotate the desired thrust vector to body frame:\n", " T_F, T_L, T_U = nRb.unrotate(nT) # equivalent to nRb.inverse().rotate(nT)\n", "\n", " # Calculate the desired roll and pitch torques:\n", " tau_x = - K * T_L\n", " tau_y = K * T_F\n", "\n", " # Return alongside total thrust to be commanded:\n", " return tau_x, tau_y, T_U\n", "\n", "nRb = gtsam.Rot3() # Assume the robot is initially level\n", "print(f\"vectors[0] = {np.round(vectors[0],2)}\")\n", "print(f\"control[0] = {np.round(attitude_controller(vectors[0], nRb),4)}\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example, with $K_F = K_L = K = 0.1$, illustrates the behavior: we want to increase the thrust $T_F$ in the $x$ direction to $0.26$, so we will positively *pitch* around the Y-axis: counter-clockwise, pointing the $z$-axis forward. Likewise, we want a thrust towards the right ($T_L = -0.34$), so we need to roll counter-clockwise, as well, around the Forward/$x$-axis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calculating Motor Thrust Vectors\n", "\n", "Creating the requested torque and thrust by the control law is done by adjusting the individual motor thrusts $f_i$. Recalling the force-torque equation in Section 7.2, if we ensure $f_{1} + f_{3} = f_{2} + f_{4}$ we obtain :\n", "\n", "$$\n", "\\tau^b = l \\begin{bmatrix}\n", "f_{1}-f_{2}-f_{3}+f_{4}\\\\\n", "f_{1}+f_{2}-f_{3}-f_{4}\\\\\n", "0\n", "\\end{bmatrix}\n", "$$\n", "\n", "The thrust vector magnitude $F^b_z = f$ can be adjusted quickly as well:\n", "\n", "$$\n", "f = f_1 + f_2 + f_3 + f_4.\n", "$$\n", "and hence we now have four equations in four unknowns. Solving for the forces yields\n", "\n", "$$\n", "\\begin{align}\n", "f_1 &= 0.25 \\left( f + \\tau_x/l + \\tau_y/l \\right) \\\\\n", "f_2 &= 0.25 \\left( f - \\tau_x/l + \\tau_y/l \\right) \\\\\n", "f_3 &= 0.25 \\left( f + \\tau_x/l - \\tau_y/l \\right) \\\\\n", "f_4 &= 0.25 \\left( f - \\tau_x/l - \\tau_y/l \\right)\n", "\\end{align}\n", "$$\n", "where $l$ is the arm length, and $\\tau_x$ and $\\tau_y$ are the roll and pitch moment, respectively.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The piece of code below implements this; however, this simplified code does not make any guarantees on not hitting torque limits. Hence, in practice more sophisticated approaches are used return a solution subject to actual control limits, while still trying to deliver some desired torques and/or thrust." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "motor_speeds[-1] = (2.670523603807631, 2.5035980337877324, 2.401401966212205, 2.234476396192306)\n" ] } ], "source": [ "def control_to_motor_speeds(tau_x: float, tau_y: float, f: float, L: float = np.sqrt(0.002)):\n", " \"\"\"Convert the desired torques and thrust to motor speeds.\"\"\"\n", " # Calculate the motor speeds:\n", " f_1 = 0.25 * (f + tau_x/L + tau_y/L)\n", " f_2 = 0.25 * (f - tau_x/L + tau_y/L)\n", " f_3 = 0.25 * (f + tau_x/L - tau_y/L)\n", " f_4 = 0.25 * (f - tau_x/L - tau_y/L)\n", "\n", " # Return as a tuple\n", " return f_1, f_2, f_3, f_4\n", "\n", "print(f\"motor_speeds[-1] = {control_to_motor_speeds(*attitude_controller(vectors[-1], nRb))}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code Example\n", "\n", "To simulate both controllers working together, we now also need to account for attitude.\n", "The code below does this." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "dt = delta_t/10\n", "\n", "# Reserve space for the executed trajectory, including attitude:\n", "executed = np.zeros((K+1, 3))\n", "nRb = np.zeros((K + 1, 3, 3), float)\n", "\n", "# We again initialize at the desired position and velocity for k=0,\n", "# and (as before) have the drone face east (X-axis in navigation frame) initially:\n", "drone = Drone(rn=desired_rn[0].copy(), vn=desired_vn[0].copy(), nRb=gtsam.Rot3(), wb=gtsam.Point3(0,0,0))\n", "\n", "nRb = np.zeros((K + 1, 3, 3), float) # Now also store attitude\n", "\n", "# integrate forward\n", "executed[0] = drone.rn\n", "nRb[0] = drone.nRb.matrix()\n", "for k in range(K):\n", " desired_Tn = thrust_controller(drone, desired_rn[k], desired_vn[k], desired_an[k])\n", "\n", " # Inner loop: a fast roll/pitch controller:\n", " for j in range(10):\n", " # Calculate roll/pitch/thrust controls:\n", " tau_x, tau_y, T_U = attitude_controller(desired_Tn, drone.nRb, K=0.5)\n", "\n", " # clip thrust to be between 0 and 20 Newtons:\n", " T_U = np.clip(T_U, 0, 20)\n", "\n", " # Integrate both dynamics and kinematics in one step:\n", " drone.integrate(T_U, gtsam.Point3(tau_x, tau_y, 0), dt)\n", "\n", " executed[k+1] = drone.rn\n", " nRb[k] = drone.nRb.matrix()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} cascaded controller", "```", "Note that in the code we now have an outer and an inner loop. The outer loop is for the \"slow\" translational dynamics, whereas the inner loop simulates the \"fast\" attitude dynamics. Such a **cascaded controller** is a typical design choice for drone applications." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: 2D trajectory using cascaded controller, on cost map.\n", "#| label: fig:cascaded-control-2d\n", "fig = px.imshow(blurred, color_continuous_scale='Reds')\n", "fig.add_trace(go.Scatter(x=10*desired_rn[:K,0], y=10*desired_rn[:K,1], mode='lines', line=dict(color='blue')))\n", "fig.add_trace(go.Scatter(x=10*executed[:K,0], y=10*executed[:K,1], mode='lines', line=dict(color='red')))\n", "fig.update_layout(coloraxis_showscale=False, showlegend=False, width=1000, margin=dict(l=0, r=0, t=0, b=0))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#| caption: 3D trajectory with cascaded controller.\n", "#| label: fig:cascaded-control-3d\n", "fig = gtbook_drone.show_executed(desired_rn, executed, nRb, K, 1)\n", "fig.update_layout(scene_camera=dict(eye=dict(x=-4, y=-3.5, z=2.5)), width=1000).show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the 3D plot above we see that the controller tracks the desired trajectory quite well.\n", "\n", "### Exercise\n", "\n", "Try playing with the gain $K$ of the attitude controller. What do you observe. Any theories?" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Planning and Controlling Yaw\n", "\n", "Controlling yaw is a crucial aspect in the design of FPV or camera drones, as it enables a drone to point in a specific direction. Since often the drone is equipped with a forward-looking camera, this is obviously useful. \n", "\n", "A simple yaw controller can be implemented to address this, but we will not discuss it in detail here. We would need to also plan the viewing direction of the drone, which involves setting up another objective etc. For example, we could try to ensures that the drone remains pointed at a particular object, e.g., for tasks like aerial photography or inspection.\n", "\n", "Yaw control presents more challenges compared to roll/pitch control. This is because yaw involves imparting a moment around the Z/Up axis, which cannot be done using differential force control. Rather, a moment around Z is created by the moments of the rotors themselves: two spin clockwise, and two others counter-clockwise. By making one or the other pair spin faster, a net moment is imparted. However, the moments so produced are much smaller.\n" ] } ], "metadata": { "colab": { "collapsed_sections": [], "include_colab_link": true, "name": "S75_drone_decision_theory.ipynb", "provenance": [] }, "kernelspec": { "display_name": "Python 3.8.12 ('gtbook')", "language": "python", "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": "3.10.12" }, "latex_metadata": { "affiliation": "Georgia Institute of Technology", "author": "Frank Dellaert and Seth Hutchinson", "title": "Introduction to Robotics" }, "vscode": { "interpreter": { "hash": "9f7376ced4243bb13dfcffa8a3ba834e0602aa8334cd3a1d8ba8d285f4628083" } } }, "nbformat": 4, "nbformat_minor": 2 }