  This paper presents a scalable online algorithm to generate safe and
kinematically feasible trajectories for quadrotor swarms. Existing approaches
rely on linearizing Euclidean distance-based collision constraints and on
axis-wise decoupling of kinematic constraints to reduce the trajectory
optimization problem for each quadrotor to a quadratic program (QP). This
conservative approximation often fails to find a solution in cluttered
environments. We present a novel alternative that handles collision constraints
without linearization and kinematic constraints in their quadratic form while
still retaining the QP form. We achieve this by reformulating the constraints
in a polar form and applying an Alternating Minimization algorithm to the
resulting problem. Through extensive simulation results, we demonstrate that,
as compared to Sequential Convex Programming (SCP) baselines, our approach
achieves on average a 72% improvement in success rate, a 36% reduction in
mission time, and a 42 times faster per-agent computation time. We also show
that collision constraints derived from discrete-time barrier functions (BF)
can be incorporated, leading to different safety behaviours without significant
computational overhead. Moreover, our optimizer outperforms the
state-of-the-art optimal control solver ACADO in handling BF constraints with a
31 times faster per-agent computation time and a 44% reduction in mission time
on average. We experimentally validated our approach on a Crazyflie quadrotor
swarm of up to 12 quadrotors. The code with supplementary material and video
are released for reference.

Robotics