A computer accesses a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory. The computer computes a first Jacobian of the input matrix with respect to an input tangent space. The computer computes a second Jacobian of the output matrix with respect to the input matrix. The computer computes a third Jacobian of an output tangent space with respect to the input matrix. The computer applies symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third 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, the second symbolic expression representing a computed tangent-space Jacobian.

A computer accesses a first symbolic expression for an output matrix as a function of an input matrix at a computing device comprising processing circuitry and memory. The computer computes a first Jacobian of the input matrix with respect to an input tangent space. The computer computes a second Jacobian of the output matrix with respect to the input matrix. The computer computes a third Jacobian of an output tangent space with respect to the input matrix. The computer applies symbolic matrix multiplication to the first Jacobian, the second Jacobian, and the third 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, the second symbolic expression representing a computed tangent-space Jacobian.

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.

A method (900) for estimating boundaries of an OOI. The method includes obtaining (s902) a first point cloud comprising a set of N points. The method also includes obtaining (s904) a set of K images. The method also includes, for each point included in the set of N points, identifying (s906), for each one of the K images, the point's location within a 2D space corresponding to the image, thereby obtaining, for each point included in the set of N points, K location identifiers. The method also includes, for each point included in the set of N points, determining (s908) a motion metric for the point using the K location identifiers for the point. The method also includes using (s910) the N motion metrics to form a subset of the N points. The method also includes, for each point included in the subset of points, obtaining (s912) a location identifier for the point. The method also includes using (s914) the location identifiers to estimate a center of the OOI and then using (s916) the estimated center of the OOI to identify boundaries for the OOI.

A method (900) for estimating boundaries of an OOI. The method includes obtaining (s902) a first point cloud comprising a set of N points. The method also includes obtaining (s904) a set of K images. The method also includes, for each point included in the set of N points, identifying (s906), for each one of the K images, the point's location within a 2D space corresponding to the image, thereby obtaining, for each point included in the set of N points, K location identifiers. The method also includes, for each point included in the set of N points, determining (s908) a motion metric for the point using the K location identifiers for the point. The method also includes using (s910) the N motion metrics to form a subset of the N points. The method also includes, for each point included in the subset of points, obtaining (s912) a location identifier for the point. The method also includes using (s914) the location identifiers to estimate a center of the OOI and then using (s916) the estimated center of the OOI to identify boundaries for the OOI.

A method of incident management performed by a first UAV UE in a UAV swarm, the method includes: transmitting one or more incident reports; and if a recovery command for the first UAV UE is received, performing a recovery operation according to the recovery command.

A flight management system for unmanned aerial vehicles (UAVs), in which the UAV is equipped for cellular fourth generation (4G) flight control. The UAV carries on-board a 4G modem, an antenna connected to the modem for providing for downlink wireless RF. A computer is connected to the modem. A 4G infrastructure to support sending via uplink and receiving via downlink from and to the UAV. The infrastructure further includes 4G base stations capable of communicating with the UAV along its flight path. An antenna in the base station is capable of supporting a downlink to the UAV. A control centre accepts navigation related data from the uplink. In addition, the control centre further includes a connection to the 4G infrastructure for obtaining downlinked data. A computer for calculating location of the UAV using navigation data from the downlink.

An aerial vehicle having more basic structure and safety measures. The aerial vehicle according to the present invention includes a thrust unit having a plurality of rotary vanes for generating thrust, a tail, a fuselage that connects the thrust unit and the tail, a main wing provided in a substantially center of the fuselage, and a control unit for controlling at least the main wing. When the aerial vehicle makes a landing, the control unit controls the main wing so that a part of the main wing becomes a lower end.

Unmanned aerial vehicles (UAVs) may facilitate the generation of a virtual reconstruction model of a vehicle collision. UAVs may collect data (including images) related to the vehicle collision, such as with the insured's permission, which may be received by an external computing device associated with the insurer and utilized to perform a photogrammetric analysis of the images to determine vehicle impact points, the road layout at the scene of the collision, the state of the traffic light at the scene of the collision, the speeds and directions of vehicles, etc. This data may be used to generate a virtual reconstruction model of the vehicle collision. An insurer may use the virtual reconstruction model to perform various insurance-related tasks, such as allocating fault to drivers or autonomous vehicles involved in the vehicle collision, and adjustment of insurance pricing based upon the fault allocation.

Unmanned aerial vehicles (UAVs) may facilitate insurance-related tasks. UAVs may actively be dispatched to an area surrounding a property, and collect data related to property. A location for an inspection of a property to be conducted by a UAV may be received, and one or more images depicting a view of the location may be displayed via a user interface. Additionally, a geofence boundary may be determined based on an area corresponding to a property boundary, where the geofence boundary represents a geospatial boundary in which to limit flight of the UAV. Furthermore, a navigation route may be determined which corresponds to the geofence boundary for inspection of the property by the UAV, the navigation route having waypoints, each waypoint indicating a location for the UAV to obtain drone data. The UAV may be directed around the property using the determined navigation route.