Formation control and collision avoidance for multi-UAV systems based on Voronoi partition

This paper deals with the formation control problem of multiple unmanned aerial vehicles(UAVs) with collision avoidance. A distributed formation control and collision avoidance method is proposed based on Voronoi partition and conventional artificial potential field. The collision avoidance is achieved by partitioning the whole space into non-overlapping regions based on Voronoi partition theory, which is taken as the task region to confine the movement of each UAV. The general motion control law is designed based on the conventional artificial potential field. As this often leads to local optimum when two UAVs are going to collide with each other and they may stay still where the repulsive force is adversely equivalent to the attractive force. To address this problem,the destination switch scheme is further proposed to let UAVs switch destinations when they reach the local equilibrium. Finally,the effectiveness of proposed formation control algorithm is validated by simulations and experiments.

Asymptotic uniformity of the quantization error for the Ahlfors-David probability measures

Let μ be an Ahlfors-David probability measure on Rq;therefore,there exist some constants s0> 0 and ε0,C1,C2> 0 such that C1εs0≤μ(B(x,ε))≤C2εs0 for all ε∈(0,ε0) and x ∈ supp(μ).For n≥ 1,let αn be an n-optimal set for μ of order r;furthermore,let {Pa(αn)}a∈αn be an arbitrary Voronoi partition with respect to αn.The n-th quantization error en,r(μ) for μ of order r can be defined as en,rr(μ):=∫ d(x,αn)r dμ(x).We define Ia(αn,μ):=∫Pa(αn) d(x,αn)r dμ(x),a ∈αn,and prove that,the three quantities ■ are of the same order as that of 1/nen,rr(μ).Thus,our result exhibits that,a weak version of Gersho’s conjecture holds true for the Ahlfors-David probability measures on Rq.