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This paper presents a scalable online algorithm to generate safe andkinematically feasible trajectories for quadrotor swarms. Existing approachesrely on linearizing Euclidean distance-based collision constraints and onaxis-wise decoupling of kinematic constraints to reduce the trajectoryoptimization problem for each quadrotor to a quadratic program (QP). Thisconservative approximation often fails to find a solution in clutteredenvironments. We present a novel alternative that handles collision constraintswithout linearization and kinematic constraints in their quadratic form whilestill retaining the QP form. We achieve this by reformulating the constraintsin a polar form and applying an Alternating Minimization algorithm to theresulting problem. Through extensive simulation results, we demonstrate that,as compared to Sequential Convex Programming (SCP) baselines, our approachachieves on average a 72% improvement in success rate, a 36% reduction inmission time, and a 42 times faster per-agent computation time. We also showthat collision constraints derived from discrete-time barrier functions (BF)can be incorporated, leading to different safety behaviours without significantcomputational overhead. Moreover, our optimizer outperforms thestate-of-the-art optimal control solver ACADO in handling BF constraints with a31 times faster per-agent computation time and a 44% reduction in mission timeon average. We experimentally validated our approach on a Crazyflie quadrotorswarm of up to 12 quadrotors. The code with supplementary material and videoare released for reference.

AMSwarm: An Alternating Minimization Approach for Safe Motion Planning of Quadrotor Swarms in Cluttered Environments