Formation Flight Control Based on the Collective Motion of Organisms
Birds and fish sometimes migrate in a huge school or a flock. For instance, sardins tend to make schools consisting tens of thousands or millions of individuals. Starlings sometimes fly over nesting place making flocks consist of tens of thousands of individuals. When we focus on these behaviors, we are surprised to find they are almost same size, they have no leaders, and their motions are amazingly sinchronized. How can these large scale grouping motion be generated and maintained? What kind of artificial stuffs can be realized referring to these hehaviors? To answer thse questions, this research is started.
Three rules
The motion of each individual in a school or a flock depends on the relative position of its neighbors. The individual tends to approach the neighbor when the distance to the neighbor is large, move away from the neighbor to avoid collisition with it when the distance is small, and move in parallel when the distance is intermediate. The figure below is a scematic diagram to show the interaction model. There is an interaction field around the individual and this field is devided into three sub-fields, i.e. attraction, parallel orientation, and repulsion fields. The individual at the center of the field approaches the neighbor when it is in the attraction field, moves in parallel with it when it is in the parallel orientation field, and moves away from it when it is in the repulsion field. This simple rule can generate grouping motions as shown below.
Interaction field
Approach Parallel orientation Repulsion
Calculated scholling motion
Formation flight control of air vehicles
The above model is a 2D model, so it cannot be applied to the control of air vehicles which fly in a 3D space. Here, the 3D interaction model is proposed as shown in a figure below. The interaction field is devided into two sub-fields, i.e. attraction and repulsion fields. The attraction and repulsion vecror Aij is determined as follows:
Aij orients to the neighbor when a distance to the neighbor is smaller than rn, where rn is a neutral distance. Aij orients to the opposite direction of the neighbor when the distance is smaller than rn.
The parallel orientation vector Pij is determined as follows:
where vj is the velocity vector of the neighbor. The moving direction of the central individual αij is then determined by the summation of Aij and Pij as follows:
indicating that the central individual moves in the direction which is determined by the combination of approach, repulsion, and parallel orientation. The parameters A and P are used for the weighting. So A is called "attraction- repulsion gain" and P is called "parallel orientation gain". When multiple neighbors exist, the vectors αij determined by each of the neighbors are summarized and the central individual moves to the direction of the summed vector. The calculated motion is shown below showing that 50 vehicles fly in a formation.
Interaction model
Calculated flight formation (50 vehicles)
The above model is a 2D model, so it cannot be applied to the control of air vehicles which fly in a 3D space. Here, the 3D interaction model is proposed as shown in a figure below. The interaction field is devided into two sub-fields, i.e. attraction and repulsion fields. The attraction and repulsion vecror Aij is determined as follows:
Aij orients to the neighbor when a distance to the neighbor is smaller than rn, where rn is a neutral distance. Aij orients to the opposite direction of the neighbor when the distance is smaller than rn.
The parallel orientation vector Pij is determined as follows:
where vj is the velocity vector of the neighbor. The moving direction of the central individual αij is then determined by the summation of Aij and Pij as follows:
indicating that the central individual moves in the direction which is determined by the combination of approach, repulsion, and parallel orientation. The parameters A and P are used for the weighting. So A is called "attraction- repulsion gain" and P is called "parallel orientation gain". When multiple neighbors exist, the vectors αij determined by each of the neighbors are summarized and the central individual moves to the direction of the summed vector. The calculated motion is shown below showing that 50 vehicles fly in a formation.
Interaction model
Calculated flight formation (50 vehicles)
Development of formation flight system
Formation flight system of real air vehicles is developed based on the simulation research above. The following pictures show the air plane and control system for the formation flight. Each vehicle needs to know the relative position and the moving direction of its neighbors. The position is taken by the GPS sensor and the moving direction is taken by the geomagnetic sensor. The position and the moving direction of each vehicle are transfered to its neighbors by using wireless communication device to realize the formation flight.
Air plane used for the formation flight (MULTIPLEX Fun Cub)
Control system（Xenocross AP-CUB DIY LITE）
Drones used for the formation flight（DJI Phantom2）
Controller Board on the Drone
Flight Test
Flight tests were conducted using developed airplanes and drones.
Formation flight system of real air vehicles is developed based on the simulation research above. The following pictures show the air plane and control system for the formation flight. Each vehicle needs to know the relative position and the moving direction of its neighbors. The position is taken by the GPS sensor and the moving direction is taken by the geomagnetic sensor. The position and the moving direction of each vehicle are transfered to its neighbors by using wireless communication device to realize the formation flight.
Air plane used for the formation flight (MULTIPLEX Fun Cub)
Control system（Xenocross AP-CUB DIY LITE）
Drones used for the formation flight（DJI Phantom2）
Controller Board on the Drone
Flight Test
Flight tests were conducted using developed airplanes and drones.