Nonlinear Double-Integral Observer and Application to Quadrotor Aircraft

This paper presents a nonlinear double-integral observer based on finite-time stability. The proposed double-integral observer can estimate the onefold and double integrals of a signal synchronously, and the stability in time domain is analyzed. The merits of the presented double-integral observer include its finite-time stability, ease of parameter selection, sufficient stochastic noise rejection, and almost no drift phenomenon. The theoretical results are confirmed by the simulations and an experiment on a quadrotor aircraft: (1) the estimation of position and velocity from the acceleration measurement and (2) a control law is designed based on the double-integral observer to track a reference trajectory.

[1]  Nicolas Boizot,et al.  A Real-Time Adaptive High-Gain EKF, Applied to a Quadcopter Inertial Navigation System , 2014, IEEE Transactions on Industrial Electronics.

[2]  Nam Quoc Ngo,et al.  A New Approach for the Design of Wideband Digital Integrator and Differentiator , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[4]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[5]  Eric Monmasson,et al.  Fully FPGA-Based Sensorless Control for Synchronous AC Drive Using an Extended Kalman Filter , 2012, IEEE Transactions on Industrial Electronics.

[6]  Hai Lin,et al.  Design and frequency analysis of continuous finite-time-convergent differentiator , 2011, ArXiv.

[7]  Xinhua Wang,et al.  Rapid-convergent nonlinear differentiator , 2011, ArXiv.

[8]  Chien-Cheng Tseng,et al.  Digital IIR integrator design using recursive Romberg integration rule and fractional sample delay , 2008, Signal Process..

[9]  Honghai Shen,et al.  Improving the Rapidity of Nonlinear Tracking Differentiator via Feedforward , 2014, IEEE Transactions on Industrial Electronics.

[10]  Nicholas Roy,et al.  Stereo vision and laser odometry for autonomous helicopters in GPS-denied indoor environments , 2009, Defense + Commercial Sensing.

[11]  Robert E. Mahony,et al.  A Practical Visual Servo Control for an Unmanned Aerial Vehicle , 2008, IEEE Transactions on Robotics.

[12]  Mohamad Adnan Al-Alaoui,et al.  Low-frequency differentiators and integrators for biomedical and seismic signals , 2001 .

[13]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[14]  David Potter.  Computational physics , 1973 .

[15]  In-Joong Ha,et al.  A novel approach to control of nonminimum-phase nonlinear systems , 2002, IEEE Trans. Autom. Control..

[16]  Farid Golnaraghi,et al.  A Kalman/Particle Filter-Based Position and Orientation Estimation Method Using a Position Sensor/Inertial Measurement Unit Hybrid System , 2010, IEEE Transactions on Industrial Electronics.

[17]  R. Lozano,et al.  Real-Time Nonlinear Embedded Control for an Autonomous Quadrotor Helicopter , 2007 .

[18]  R. Lozano,et al.  Embedded control system for a four‐rotor UAV , 2007 .

[19]  Jonathan P. How,et al.  Autonomous aircraft flight control for constrained environments , 2008, 2008 IEEE International Conference on Robotics and Automation.

[20]  Tarek Hamel,et al.  Image based visual servo control for a class of aerial robotic systems , 2007, Autom..

[21]  A. N. Atassi,et al.  Separation results for the stabilization of nonlinear systems using different high-gain observer designs ☆ , 2000 .

[22]  Geng Yang,et al.  Finite-Time-Convergent Differentiator Based on Singular Perturbation Technique , 2007, IEEE Transactions on Automatic Control.

[23]  Baris Fidan,et al.  Distributed Cohesive Motion Control of Flight Vehicle Formations , 2013, IEEE Transactions on Industrial Electronics.

[24]  B. Onaral,et al.  Fractal system as represented by singularity function , 1992 .

[25]  Wolfram Burgard,et al.  Towards a navigation system for autonomous indoor flying , 2009, 2009 IEEE International Conference on Robotics and Automation.

[26]  Robert E. Mahony,et al.  Control of a quadrotor helicopter using visual feedback , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[27]  Josep M. Guerrero,et al.  Industrial Applications of the Kalman Filter: A Review , 2013, IEEE Transactions on Industrial Electronics.

[28]  Claire J. Tomlin,et al.  Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment , 2007 .