Quadrotor motion planning in complex environments leverage the concept of safe flight corridor (SFC) to facilitate static obstacle avoidance. Typically, SFCs are constructed through convex decomposition of the environment's free space into cuboids, convex polyhedra, or spheres. However, when dealing with a quadrotor swarm, such SFCs can be overly conservative, substantially limiting the available free space for quadrotors to coordinate. This paper presents an Alternating Minimization-based approach that does not require building a conservative free-space approximation. Instead, both static and dynamic collision constraints are treated in a unified manner. Dynamic collisions are handled based on shared position trajectories of the quadrotors. Static obstacle avoidance is coupled with distance queries from the Octomap, providing an implicit non-convex decomposition of free space. As a result, our approach is scalable to arbitrary complex environments. Through extensive comparisons in simulation, we demonstrate a 60% improvement in success rate, an average 1.8× reduction in mission completion time, and an average 23× reduction in per-agent computation time compared to SFC-based approaches. We also experimentally validated our approach using a Crazyflie quadrotor swarm of up to 12 quadrotors in obstaclerich environments. The code, supplementary materials, and videos are released for reference.
This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex trajectory optimization. The result is an MPC algorithm that runs real-time on laptops and embedded hardware devices such as Jetson TX2. Our approach relies on novel reformulations for the tracking, collision, and occlusion constraints that induce a multi-convex structure in the resulting trajectory optimization. We exploit these mathematical structures using the split Bregman Iteration technique, eventually reducing our MPC to a series of convex Quadratic Programs solvable in a few milliseconds. The fast re-planning of our MPC allows for occlusion and collision-free tracking in complex environments even while considering a simple constant-velocity prediction for the target trajectory and dynamic obstacles. We perform extensive bench-marking in a realistic physics engine and show that our MPC outperforms the state-of-the-art algorithms in visibility, smoothness, and computation-time metrics.
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