Flatness-Based Quadcopter Trajectory Planning and Tracking With Continuous-Time Safety Guarantees
Victor Freire, Xiangru Xu
Abstract
This work proposes a convex optimization-based framework for the trajectory planning and tracking of quadcopters that ensures continuous-time safety guarantees. Using the convexity property of B-spline curves and the differential flatness property of quadcopters, a second-order cone program is formulated to generate an optimal nominal trajectory that respects state and input constraints, including position, linear velocity, angle, angular velocity, thrust, waypoints, and obstacle avoidance constraints, rigorously in the continuous-time sense. To ensure safe trajectory tracking, a convex quadratic program is proposed based on control barrier functions, which guarantees that the actual trajectory of the quadcopter remains within a prescribed safe tube of the nominal trajectory in continuous time. Furthermore, conditions that ensure the safe tracking controller respects thrust, roll, and pitch constraints are also presented. Both the planning and control approaches are suitable for online implementation, and the effectiveness of the proposed framework is demonstrated through simulations and experiments with a Crazyflie2.1 nano quadcopter.