Sub-Optimal Moving Horizon Estimation in Feedback Control of Linear Constrained Systems

Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power, we propose to solve the optimization problem underlying MHE sub-optimally for a fixed number of optimization iterations per time step. The stability of the closed-loop system is analyzed using the small-gain theorem by considering the closed-loop controlled system, the optimization algorithm dynamics, and the estimation error dynamics as three interconnected subsystems. By assuming incremental input/output-to-state stability ({\delta}- IOSS) of the system and imposing standard ISS conditions on the controller, we derive conditions on the iteration number such that the interconnected system is input-to-state stable (ISS) w.r.t. the external disturbances. A simulation using an MHE- MPC estimator-controller pair is used to validate the results.Comment: 6 page journal paper with 2 figure

A Real-Time Game Theoretic Planner for Autonomous Two-Player Drone Racing

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms amodel predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others'' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25m/s