Robust Trajectory Tracking by a Quadcopter: A Game Theoretic Approach

Authors: Ujjawal Gupta, Bhargav Jha
Supervisor: Prof. Tal Shima

In typical motion planning and tracking, an outer planning loop generates a reference trajectory for some finite time interval in the future, which is tracked by the inner loop in the presence of disturbances and modeling errors. We have proposed a robust controller for aggressive trajectory tracking by a multicopter platform using a linear-quadratic differential game formulation. With flat outputs comprising of spatial position and yaw angle, we reconstruct all the nominal states using the differential flatness property of the multicopter dynamics. A linear time-varying error dynamics is obtained by Jacobian linearization of the nonlinear dynamics about the nominal trajectory. Using the error dynamics, a two-player differential game against nature is formulated. A major advantage of this approach is that the two-game parameters are the only tuning parameters for calculating the controller gains, which can be efficiently calculated offline for a given reference trajectory. Experimental validation of this control method resulted in highly accurate tracking of high-speed trajectories in confined lab spaces as can be seen from the video