Multi-Objective Trajectory Planning for Unmanned Aerial Vehicles Using CLF-CBF-Based Quadratic Programs

Control barrier function-based quadratic programs (CBF-based QP) provide an avenue for agile and numerically efficient obstacle avoidance algorithms. However, the CBF-based QP methods may lead to lengthy detours and undesirable transient tracking performance without proper trajectory planning. This paper expands the CBF-based QP concept to create a modified safe reference trajectory with a prescribed avoidance radius and direction, where the modified reference shadows the actual reference during the avoidance maneuver. We use a control Lyapunov function (CLF) to match the modified reference with the actual reference and three CBFs to formulate safety and performance objectives to maintain distance, adjust velocity, and determine the direction of the avoidance maneuver. These formulations produce constraints that are synthesized by means of a quadratic program. The QP generates a desirable velocity profile for the safe reference trajectory. Numerical simulations verify the effectiveness of the proposed trajectory planning method.