Drone Formation

 

Teaching a drone to fly is different from teaching a swarm of drones to fly. A central controller can issue a group command and when each of the drones execute the command, the formation flies. If the formation is unchanged, the group command is merely relayed across to the group members. The drone is one group for the purpose of relaying the same command.  When the fleet changes formation, the command changes to individual members. Each unit moves from one position to another without colliding with one another.

The movement has as much degree of freedom as a particle. A drone is often represented as a volumetric pixel or voxel for short. An altimeter and a GPS co-ordinate are sufficient to let the unit maintain its position. When the group command is issued, the movement of the group is specified. Consensus algorithms help with the group behavior without worrying about the exact position of each unit in the group. The flight of any one unit can be written in the form of unicycle model with u1 as the velocity and the u2 as the change in the heading or the angle relative Cartesian co-ordinates. The term unicycle refers to the cosine and sine as the x and y axis displacements. Unicycle consensus algorithms can help the group achieve the intended formation.

One of the most used drone fleet navigations is the Simultaneous Location and Mapping algorithm which provides a framework within which the drones can plan their paths. A drone only needs to know its location, build or acquire a map of its surroundings, plan a path in terms of a series of positions if not the next linear displacement. Consensus helps to determine paths do not have conflicts.  Without imminent collision, units can take their time to arrive at their final formation.

Conditions are not always ideal even for the most direct displacements. Wind and obstruction are some of the challenges encountered. A unit might not have the flexibility to move in any direction and must co-ordinate movement to its moving parts to achieve the intended effect. When the current position is hard to maintain and movement to the final position is off by external influence, the path can be included to modify positions to reduce the sum of squares of errors to arrive at the designated position. As a combination of external influence and internal drive to reduce the errors, the points along the alternate path can be determined. An obstruction to a linear displacement for a drone unit would then form a path with positions along a rough semi-circle around the obstruction.

This notion of depth estimation is another navigation technique where the unit’s sensors are enhanced to give a better reference for the surroundings to the unit and then the flight path is optimized. The term comes from the traditional techniques in image processing where it is used to refer to the task of measuring distance of each pixel relative to the camera. Depth is extracted from either monocular or stereo images. Mutli-view geometry helps find the relationships between images.

A cost function helps to minimize the error between the current and the final location which is not a predesignated one but an iterative transition state that is determined by a steepest gradient descent.