Convexification and real-time on-board optimization for agile quad-rotor maneuvering and obstacle avoidance

Abstract

In this paper, we apply lossless and successive convexification techniques and employ real-time on-board convex optimization to perform constrained motion planning for quadrotors. In general, this problem is challenging for real-time on-board applications due to its non-convex nature. The ability to generate feasible trajectories quickly and reliably is central to operating high-performance aerial robots in populated spaces. Motivated by our earlier research on convexification of non-convex optimal control problems, we use these convexification techniques to cast the problems into one (or a sequence of) Second-Order Cone Programming (SOCP) problem(s). In doing so, we are able to attain our solutions by leveraging modern advances in Interior Point Method (IPM) algorithms. Here, we focus on 3-degree-of-freedom trajectory generation, whereby closed-loop control is used to track a translational trajectory computed on-board at the onset of the maneuver. To the best of our knowledge, this is the first demonstration of convexification techniques used in real-time on-board trajectory generation for high-performance quad-rotor flight. We present two example scenarios: (1) a case where lossless convexification is used to increase the available control envelope, thus enabling an agile flip maneuver, and (2) a case where both convexification techniques are used to compute a path through a flight space containing ellipsoidal keep-out zones. We present flight demonstration results obtained using the Autonomous Control Laboratory's (ACL's) custom quad-rotor platforms and SOCP optimization software. Additionally, computation timing statistics for the example scenarios obtained using a series of mobile ARM and Intel processors show a minimum mean computation time of 36.5 and 122.2 milliseconds, respectively.