Hugh H. T. Liu

Yi Lok Lo, Longhao Qian, Hugh H. T. Liu

In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.

Chao Qin, Hugh H. T. Liu

We present a perception constrained visual predictive control (PCVPC) algorithm for quadrotors to enable aggressive flights without using any position information. Our framework leverages nonlinear model predictive control (NMPC) to formulate a constrained image-based visual servoing (IBVS) problem. The quadrotor dynamics, image dynamics, actuation constraints, and visibility constraints are taken into account to handle quadrotor maneuvers with high agility. Two main challenges of applying IBVS to agile drones are considered: (i) high sensitivity of depths to intense orientation changes, and (ii) conflict between the visual servoing objective and action objective due to the underactuated nature. To deal with the first challenge, we parameterize a visual feature by a bearing vector and a distance, by which the depth will no longer be involved in the image dynamics. Meanwhile, we settle the conflict problem by compensating for the rotation in the future visual servoing cost using the predicted orientations of the quadrotor. Our approach in simulation shows that (i) it can work without any position information, (ii) it can achieve a maximum referebce speed of 9 m/s in trajectory tracking without losing the target, and (iii) it can reach a landmark, e.g., a gate in drone racing, from varied initial configurations.

Qingrui Zhang, Hugh H. T. Liu

Robust cooperative formation control is investigated in this paper for fixed-wing unmanned aerial vehicles in close formation flight to save energy. A novel cooperative control method is developed. The concept of virtual structure is employed to resolve the difficulty in designing virtual leaders for a large number of UAVs in formation flight. To improve the transient performance, desired trajectories are passed through a group of cooperative filters to generate smooth reference signals, namely the states of the virtual leaders. Model uncertainties due to aerodynamic couplings among UAVs are estimated and compensated using uncertainty and disturbance observers. The entire design, therefore, contains three major components: cooperative filters for motion planning, baseline cooperative control, and uncertainty and disturbance observation. The proposed formation controller could at least secure ultimate bounded control performance for formation tracking. If certain conditions are satisfied, asymptotic formation tracking control could be obtained. Major contributions of this paper lie in two aspects: 1) the difficulty in designing virtual leaders is resolved in terms of the virtual structure concept; 2) a robust cooperative controller is proposed for close formation flight of a large number of UAVs suffering from aerodynamic couplings in between. The efficiency of the proposed design will be demonstrated using numerical simulations of five UAVs in close formation flight.

Qingrui Zhang, Hugh H. T. Liu

This paper investigates the robust nonlinear close formation control problem. It aims to achieve precise position control at dynamic flight operation for a follower aircraft under the aerodynamic impact due to the trailing vortices generated by a leader aircraft. One crucial concern is the control robustness that ensures the boundedness of position error subject to uncertainties and disturbances to be regulated with accuracy. This paper develops a robust nonlinear formation control algorithm to fulfill precise close formation tracking control. The proposed control algorithm consists of baseline control laws and disturbance observers. The baseline control laws are employed to stabilize the nonlinear dynamics of close formation flight, while the disturbance observers are introduced to compensate system uncertainties and formation-related aerodynamic disturbances. The position control performance can be guaranteed within the desired boundedness to harvest enough drag reduction for a follower aircraft in close formation using the proposed design. The efficacy of the proposed design is demonstrated via numerical simulations of close formation flight of two aircraft.