Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter

This paper presents two types of nonlinear controllers for an autonomous quadrotor helicopter. One type, a feedback linearization controller involves high-order derivative terms and turns out to be quite sensitive to sensor noise as well as modeling uncertainty. The second type involves a new approach to an adaptive sliding mode controller using input augmentation in order to account for the underactuated property of the helicopter, sensor noise, and uncertainty without using control inputs of large magnitude. The sliding mode controller performs very well under noisy conditions, and adaptation can effectively estimate uncertainty such as ground effects. Recommended by Editorial Board member Hyo-Choong Bang under the direction of Editor Hyun Seok Yang. This work was supported by the Korea Research Foundation Grant (MOEHRD) KRF-2005-204-D00002, the Korea Science and Engineering Foundation(KOSEF) grant funded by the Korea government(MOST) R0A-2007-000-10017-0 and Engineering Research Institute at Seoul National University. Daewon Lee received the B.S. degree in Mechanical and Aerospace Engineering from Seoul National University (SNU), Seoul, Korea, in 2005, where he is currently working toward a Ph.D. degree in Mechanical and Aerospace Engineering. He has been a member of the UAV research team at SNU since 2005. His research interests include applications of nonlinear control and vision-based control of UAV. H. Jin Kim received the B.S. degree from Korea Advanced Institute of Technology (KAIST) in 1995, and the M.S. and Ph.D. degrees in Mechanical Engineering from University of California, Berkeley in 1999 and 2001, respectively. From 2002–2004, she was a Postdoctoral Researcher and Lecturer in Electrical Engineering and Computer Science (EECS), University of California, Berkeley (UC Berkeley). From 2004–2009, she was an Assistant Professor in the School of in Mechanical and Aerospace Engineering at Seoul National University (SNU), Seoul, Korea, where she is currently an Associate Professor. Her research interests include applications of nonlinear control theory and artificial intelligence for robotics, motion planning algorithms. Shankar Sastry received the B.Tech. degree from the Indian Institute of Technology, Bombay, in 1977, and the M.S. degree in EECS, the M.A. degree in mathematics, and the Ph.D. degree in EECS from UC Berkeley, in 1979, 1980, and 1981, respectively. He is currently Dean of the College of Engineering at UC Berkeley. He was formerly the Director of the Center for Information Technology Research in the Interest of Society (CITRIS). He served as Chair of the EECS Department from January, 2001 through June 2004. In 2000, he served as Director of the Information Technology Office at DARPA. From 1996 to 1999, he was the Director of the Electronics Research Laboratory at Berkeley (an organized research unit on the Berkeley campus conducting research in computer sciences and all aspects of electrical engineering). He is the NEC Distinguished Professor of Electrical Engineering and Computer Sciences and holds faculty appointments in the Departments of Bioengineering, EECS and Mechanical Engineering. Prior to joining the EECS faculty in 1983 he was a Professor with the Massachusetts Institute of Technology (MIT), Cambridge. He is a member of the National Academy of Engineering and Fellow of the IEEE.     

Decomposition principle in model predictive control for linear systems with bounded disturbances

Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based MPC approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbations to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.     

基于终端滑模的四旋翼飞行器非线性轨迹跟踪控制

考虑到四旋翼飞行器的传统内外环控制策略依赖时标分离假设,稳定性分析复杂,并且控制参数选取困难的缺点,提出了一种与传统内外环控制策略不同的轨迹跟踪控制器;首先将四旋翼飞行器数学模型进行相应的变换,以分解为高度、偏航角和纵横向三个级联的子系统,再使用终端滑模控制方法设计高度和偏航角子系统的控制器,使两个子系统的状态误差可以在有限时间内收敛到原点,之后基于变量非线性变换设计纵横向子系统的控制器,分析了闭环系统稳定性,证明了所设计的轨迹跟踪控制器可以保证闭环系统跟踪误差渐近稳定到原点,最后仿真实验的结果验证了所设计的控制器的有效性。     

Robust model predictive control of constrained linear systems with bounded disturbances

This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances. The optimal control problem that is solved online includes, uniquely, the initial state of the model employed in the problem as a decision variable. The associated value function is zero in a disturbance invariant set that serves as the ‘origin’ when bounded disturbances are present, and permits a strong stability result, namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances, to be obtained. The resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control.     

Experimental quadrotor flight performance using computationally efficient and recursively feasible linear model predictive control

A new linear model predictive control (MPC) algorithm in a state-space framework is presented based on the fusion of two past MPC control laws: steady-state optimal MPC (SSOMPC) and Laguerre optimal MPC (LOMPC). The new controller, SSLOMPC, is demonstrated to have improved feasibility, tracking performance and computation time than its predecessors. This is verified in both simulation and practical experimentation on a quadrotor unmanned air vehicle in an indoor motion-capture testbed. The performance of the control law is experimentally compared with proportional-integral-derivative (PID) and linear quadratic regulator (LQR) controllers in an unconstrained square manoeuvre. The use of soft control output and hard control input constraints is also examined in single and dual constrained manoeuvres.     

Precision flight control for a multi-vehicle quadrotor helicopter testbed

Quadrotor helicopters continue to grow in popularity for unmanned aerial vehicle applications. However, accurate dynamic models for deriving controllers for moderate to high speeds have been lacking. This work presents theoretical models of quadrotor aerodynamics with non-zero free-stream velocities based on helicopter momentum and blade element theory, validated with static tests and flight data. Controllers are derived using these models and implemented on the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC), demonstrating significant improvements over existing methods. The design of the STARMAC platform is described, and flight results are presented demonstrating improved accuracy over commercially available quadrotors.     

An enhanced anti-disturbance attitude control law for flexible spacecrafts subject to multiple disturbances

As well-known disturbance rejection methods, active disturbance rejection control and disturbance observer-based control can effectively improve the control performances of complex systems in the presence of disturbances. However, the accurate rejection of multiple disturbances for control systems of practical engineering, for example, the attitude control system of flexible spacecraft, is still a bottleneck problem. In order to further improve the anti-disturbance capability and reduce the conservativeness, this paper proposes a novel enhanced anti-disturbance control law for the attitude control system of flexible spacecraft by combining active disturbance rejection control and disturbance observer-based control in a unified framework. More specifically, the disturbance from flexible vibration is described by an uncertain exogenous system based on the partially known information including elastic damping ratios and modal frequencies. The disturbance observer-based control is utilized to estimate and thereby reject this disturbance. On the other hand, the other disturbances such as external environmental disturbance and complex model nonlinearity are merged into a equivalent disturbance with bounded derivative, which is compensated by using the active disturbance rejection control law. Stability and robustness analysis are carried out for the disturbance observer and extended state observer. Finally, simulation results of low-earth-orbit flexible satellite are presented to verify the effectiveness of proposed methods.     

Constraint-softening in model predictive control with off-line-optimized admissible sets for systems with additive and multiplicative disturbances

An approach to the softening of constraints is explored for a class of MPC algorithms that employ off-line-computed constraint-admissible sets for simplified on-line computations. The proposed approach relies on the use of exact penalty functions to ensure that the solution coincides with the actual optimal solution if the original MPC problem is feasible and that there are constraint violations at minimum possible levels if the original problem is infeasible. The approach is implemented for a class of linear systems with additive and multiplicative disturbances using a dynamic-policy-based MPC algorithm. Results specific to the cases of non-stochastic and stochastic disturbances are explored and assessed with simulation examples.     

输入饱和与姿态受限的四旋翼无人机反步姿态控制

本文针对四旋翼无人机研究了鲁棒反步姿态控制策略.由于四旋翼无人机结构复杂,其非线性数学模型难以精确建立,因此在控制器设计过程中需要综合考虑模型不确定性、未知外部干扰、输入饱和以及姿态受限等因素.针对模型中的不确定项,使用神经网络进行逼近;对于外部未知干扰,使用非线性干扰观测器进行补偿;使用双曲正切函数逼近饱和函数,解决输入饱和问题;同时使用界限Lyapunov函数设计控制器,确保姿态满足限制条件.最后,设计四旋翼无人机反步姿态控制器,并根据Lyapunov稳定性定理证明了闭环控制系统的有界稳定.仿真结果表明了所研究控制方法的有效性.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.