Abstract: A computer accesses a first symbolic expression for an output value as a function of an input value. The computer computes a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition. The computer computes a second symbolic Jacobian of the output value with respect to the input value. The computer computes a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition. The computer applies symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space. The computer provides a representation of the second symbolic expression.

Abstract: A computer of an unmanned aerial vehicle (UAV) accesses, from a memory unit, a problem definition comprising cost functions associated with travel of the UAV. The computer causes movement of the UAV based on the cost functions. The computer adjusts one or more of the cost functions during a flight of the UAV. The computer causes further movement of the UAV based on the adjusted one or more of the cost functions.

Abstract: In some examples, a computing device receives, from an unmanned aerial vehicle (UAV), a first image from a first camera on the UAV and a plurality of second images from a plurality of second cameras on the UAV. The plurality of second cameras may be positioned on the UAV for providing a plurality of different fields of view in a plurality of different directions around the UAV. Further, the first camera has a longer focal length than the second cameras. The computing device presents, on a display, a composite image including at least a portion of the first image within a merged image generated from the plurality of second images. The presented composite image enables a user to at least one of: zoom out from the at least one first image to the merged image, or zoom in from the merged image to the at least one first image.

Abstract: In some examples, an unmanned aerial vehicle (UAV) may determine, based on a three-dimensional (3D) model including a plurality of points corresponding to a scan target, a scan plan for scanning at least a portion of the scan target. For instance, the scan plan may include a plurality of poses for the UAV to assume to capture images of the scan target. The UAV may capture with one or more image sensors, one or more images of the scan target from one or more poses of the plurality of poses. Further, the UAV may determine an update to the 3D model based at least in part on the one or more images. Additionally, the UAV may update the scan plan based at least in part on the update to the 3D model.

Abstract: In some examples, an unmanned aerial vehicle (UAV) may determine a first acceleration of the UAV based at least on information from an onboard accelerometer received at least one of prior to or during takeoff. The UAV may determine a second acceleration of the UAV based at least on location information received via a satellite positioning system receiver at least one of prior to or during takeoff. The UAV may further determine a relative heading of the UAV based at least in part on the first acceleration and the second acceleration, and may be directed to navigate an environment based at least on the determined relative heading.

Abstract: Methods and systems are disclosed for an unmanned aerial vehicle (UAV) configured to autonomously navigate a physical environment while capturing images of the physical environment. In some embodiments, the motion of the UAV and a subject in the physical environment may be estimated based in part on images of the physical environment captured by the UAV. In response to estimating the motions, image capture by the UAV may be dynamically adjusted to satisfy a specified criterion related to a quality of the image capture.

Abstract: In some examples, an unmanned aerial vehicle (UAV) may determine a plurality of contour paths spaced apart from each other along at least one axis associated with a scan target. For instance, each contour path may be spaced away from a surface of the scan target based on a selected distance. The UAV may determine a plurality of image capture locations for each contour path. The image capture locations may indicate locations at which an image of a surface of the scan target is to be captured. The UAV may navigate along the plurality of contour paths based on a determined speed while capturing images of the surface of the scan target based on the image capture locations.

Abstract: In some examples, an unmanned aerial vehicle (UAV) may control a position of a first camera to cause the first camera to capture a first image of a target. The UAV may receive a plurality of second images from a plurality of second cameras, the plurality of second cameras positioned on the UAV for providing a plurality of different fields of view in a plurality of different directions around the UAV, the first camera having a longer focal length than the second cameras. The UAV may combine at least some of the plurality of second images to generate a composite image corresponding to the first image and having a wider-angle field of view than the first image. The UAV may send the first image and the composite image to a computing device.

Abstract: An autonomous vehicle that is equipped with image capture devices can use information gathered from the image capture devices to plan a future three-dimensional (3D) trajectory through a physical environment. To this end, a technique is described for image-space based motion planning. In an embodiment, a planned 3D trajectory is projected into an image-space of an image captured by the autonomous vehicle. The planned 3D trajectory is then optimized according to a cost function derived from information (e.g., depth estimates) in the captured image. The cost function associates higher cost values with identified regions of the captured image that are associated with areas of the physical environment into which travel is risky or otherwise undesirable. The autonomous vehicle is thereby encouraged to avoid these areas while satisfying other motion planning objectives.

Abstract: An autonomous vehicle that is equipped with image capture devices can use information gathered from the image capture devices to plan a future three-dimensional (3D) trajectory through a physical environment. To this end, a technique is described for image-space based motion planning. In an embodiment, a planned 3D trajectory is projected into an image-space of an image captured by the autonomous vehicle. The planned 3D trajectory is then optimized according to a cost function derived from information (e.g., depth estimates) in the captured image. The cost function associates higher cost values with identified regions of the captured image that are associated with areas of the physical environment into which travel is risky or otherwise undesirable. The autonomous vehicle is thereby encouraged to avoid these areas while satisfying other motion planning objectives.

Abstract: In some examples, an unmanned aerial vehicle (UAV) may receive location information via the global navigation satellite system (GNSS) receiver and may receive acceleration information via an onboard accelerometer. The UAV may determine a first measurement of acceleration of the UAV in a navigation frame of reference based on information from the accelerometer prior to or during takeoff. In addition, the UAV may determine a second measurement of acceleration of the UAV in a world frame of reference based on the location information received via the GNSS receiver prior to or during takeoff. The UAV may determine a relative heading of the UAV based on the first and second acceleration measurements. The determined relative heading may be used for navigation of the UAV at least one of during or after takeoff of the UAV.

Abstract: In some examples, an unmanned aerial vehicle (UAV) employs one or more image sensors to capture images of a scan target and may use distance information from the images for determining respective locations in three-dimensional (3D) space of a plurality of points of a 3D model representative of a surface of the scan target. The UAV may compare a first image with a second image to determine a difference between a current frame of reference position for the UAV and an estimate of an actual frame of reference position for the UAV. Further, based at least on the difference, the UAV may determine, while the UAV is in flight, an update to the 3D model including at least one of an updated location of at least one point in the 3D model, or a location of a new point in the 3D model.

Abstract: Described herein are systems and methods for structure scan using an unmanned aerial vehicle. For example, some methods include accessing a three-dimensional map of a structure; generating facets based on the three-dimensional map, wherein the facets are respectively a polygon on a plane in three-dimensional space that is fit to a subset of the points in the three-dimensional map; generating a scan plan based on the facets, wherein the scan plan includes a sequence of poses for an unmanned aerial vehicle to assume to enable capture, using image sensors of the unmanned aerial vehicle, of images of the structure; causing the unmanned aerial vehicle to fly to assume a pose corresponding to one of the sequence of poses of the scan plan; and capturing one or more images of the structure from the pose.

Abstract: Described herein are systems and methods for structure scan using an unmanned aerial vehicle. For example, some methods include accessing a three-dimensional map of a structure; generating facets based on the three-dimensional map, wherein the facets are respectively a polygon on a plane in three-dimensional space that is fit to a subset of the points in the three-dimensional map; generating a scan plan based on the facets, wherein the scan plan includes a sequence of poses for an unmanned aerial vehicle to assume to enable capture, using image sensors of the unmanned aerial vehicle, of images of the structure; causing the unmanned aerial vehicle to fly to assume a pose corresponding to one of the sequence of poses of the scan plan; and capturing one or more images of the structure from the pose.

Abstract: Described herein are systems for roof scan using an unmanned aerial vehicle.

Abstract: In some examples, a computing apparatus may include one or more non-transitory computer-readable storage media and program instructions stored on the one or more computer-readable storage media that, when executed by one or more processors, direct the computing apparatus to perform various steps. For example, the program instructions may continually present a graphical user interface (GUI) at the computing apparatus including a display of a current view of the physical environment from a perspective of an aerial vehicle. The program instructions may detect user interactions with the GUI while the aerial vehicle is in flight. The user interactions may include instructions directing the aerial vehicle to maneuver within the physical environment and configure parameters for scanning a three-dimensional (3D) scan volume. The program instruction may then transmit, to the aerial vehicle, data encoding the instructions for performing a 3D scan of the 3D scan volume.

Abstract: Sports and fitness applications for an autonomous unmanned aerial vehicle (UAV) are described. In an example embodiment, a UAV can be configured to track a human subject using perception inputs from one or more onboard sensors. The perception inputs can be utilized to generate values for various performance metrics associated with the activity of the human subject. In some embodiments, the perception inputs can be utilized to autonomously maneuver the UAV to lead the human subject to satisfy a performance goal. The UAV can also be configured to autonomously capture images of a sporting event and/or make rule determinations while officiating a sporting event.

Abstract: Sports and fitness applications for an autonomous unmanned aerial vehicle (UAV) are described. In an example embodiment, a UAV can be configured to track a human subject using perception inputs from one or more onboard sensors. The perception inputs can be utilized to generate values for various performance metrics associated with the activity of the human subject. In some embodiments, the perception inputs can be utilized to autonomously maneuver the UAV to lead the human subject to satisfy a performance goal. The UAV can also be configured to autonomously capture images of a sporting event and/or make rule determinations while officiating a sporting event.

Abstract: Autonomous aerial navigation in low-light and no-light conditions includes using night mode obstacle avoidance intelligence and mechanisms for vision-based unmanned aerial vehicle (UAV) navigation to enable autonomous flight operations of a UAV in low-light and no-light environments using infrared data.

Abstract: Methods and systems are disclosed for an unmanned aerial vehicle (UAV) configured to autonomously navigate a physical environment while capturing images of the physical environment. In some embodiments, the motion of the UAV and a subject in the physical environment may be estimated based in part on images of the physical environment captured by the UAV. In response to estimating the motions, image capture by the UAV may be dynamically adjusted to satisfy a specified criterion related to a quality of the image capture.