We propose a novel approach for safe tracking of a moving target in cluttered environments using a quadrotor. The key contribution of our work is a formulation that enables the generation of safe and dynamical feasible tracking trajectories that satisfy arbitrary relative motion patterns (circling, parallel tracking, undirectional tracking, etc.) with respect to the target. In our framework, forming the desired relative motion pattern between the quadrotor and the target only requires a generative function that specifies relative positions at different time instants. Our method generates samples to fit a piecewise-polynomial representation of the desired relative motion pattern and embeds it into a cost function for solving valid tracking trajectories via quadratic programming. Collision avoidance is achieved by squeezing the trajectory into a collision-free flight corridor, and dynamical feasibility is achieved by enforcing bounds on corresponding derivatives. Both of which can be written as linear constraints for the quadratic programming. Our approach is lightweight and can be implemented for real-time target tracking. We use a simulated cluttered environment and multiple desired relative motion patterns to demonstrate the performance of the proposed approach.
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