This work presents a convex optimization framework for the planning and tracking of quadcopter trajectories with continuous-time safety guarantees. Using B-spline basis functions and the differential flatness property of quadcopters, a second-order cone program is formulated to generate optimal trajectories that respect safe state and input constraints in the continuous-time sense. A quadratic program (QP) based on control barrier functions is proposed to guarantee bounded trajectory tracking in continuous time by filtering a nominal controller, where the QP is shown to be always feasible. Furthermore, conditions that ensure the safe tracking controller respects thrust, roll angle, and pitch angle constraints are also proposed. The effectiveness of the proposed framework is demonstrated by real-world experiments using a Crazyflie2.1 nano quadcopter.The video for the experiments of Section VI is available at https://xu.me.wisc.edu/wp-content/uploads/sites/1196/2021/10/ continuous-safety.mp4.
This paper provides an approach to design control barrier functions (CBFs) using the notion of dynamic safety margins (DSMs). In particular, it is shown that DSMs are CBFs for an augmented system. The proposed approach can handle multiple state and input constraints using the control-sharing property of CBFs. Moreover, it makes no assumption on the relative degree of the constraints. Numerical simulations show that the method outperforms existing DSM-based approaches, while also guaranteeing safety and recursive feasibility.
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