Control barrier function-based quadratic program (CBF-QP) provides an avenue for agile and numerically efficient obstacle avoidance algorithms. However, the CBF-QP methods may lead to lengthy detours and undesirable avoidance maneuvers. This paper proposes a bi-level CBF-QP for the safe navigation of quadrotors. A Planning-QP is proposed to create a safe reference trajectory that shadows the actual reference trajectory with prescribed avoidance acceleration, velocity, distance, and direction during the avoidance maneuver. A control Lyapunov function (CLF) ensures that modified reference closely matches the actual reference outside the avoidance regions and multiple control barrier functions (CBFs) ensure the safety and smoothness of the avoidance trajectory. Model uncertainties can undermine the safety of the quadrotor while tracking the modified reference. Hence, a Tracking-QP is designed to achieve accurate tracking with ensured safe maneuvering around obstacles, where a new CBF is constructed to prevent actuator saturation. Prescribed attitude bounds are ensured via additional acceleration constraints in the Tracking-QP. The proposed method is validated using numerous experiments involving various static obstacles where the quadrotor carries different payloads.

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