Direct Method Based Control System for an Autonomous Quadrotor

This paper proposes a real time control algorithm for autonomous operation of a quadrotor unmanned air vehicle. The quadrotor is a small agile vehicle, which as well as being a excellent test bed for advanced control techniques could also be suitable for internal surveillance, search and rescue and remote inspection. The proposed control scheme incorporates two key aspects of autonomy; trajectory planning and trajectory following. Using the differentially-flat dynamics property of the system, the trajectory optimization is posed as a non-linear constrained optimization within the output space in the virtual domain, not explicitly related to the time domain. A suitable parameterization using a virtual argument as opposed to time is applied, which ensures initial and terminal constraint satisfaction. The speed profile is optimized independently, followed by the mapping to the time domain achieved using a speed factor. Trajectory following is achieved with a standard multi-variable control technique and a digital switch is used to re-optimize the reference trajectory in the event of infeasibility or mission change. The paper includes simulations using a full dynamic model of the quadrotor demonstrating the suitability of the proposed control scheme.

[1]  Robert F. Stengel,et al.  Flight Control Design using Nonlinear Inverse Dynamics , 1986, 1986 American Control Conference.

[2]  Oleg A. Yakimenko,et al.  A Vision Based Navigation Among Multiple Flocking Robots: Modeling And Simulation , 2006 .

[3]  M. V. Cook.  Flight Dynamics Principles , 1997 .

[4]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[5]  Oleg A. Yakimenko,et al.  Computing short-time aircraft maneuvers using direct methods , 2008 .

[6]  Hans Seywald,et al.  Dense-sparse discretization for optimization and real-time guidance , 1996 .

[7]  I. Kaminer,et al.  Path Generation, Path Following and Coordinated Control for TimeCritical Missions of Multiple UAVs , 2006, 2006 American Control Conference.

[8]  A. L. Herman,et al.  Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules , 1996 .

[9]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[10]  A. Chelouah,et al.  Extensions of differential flat fields and Liouvillian systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[11]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[12]  Brian J. Driessen,et al.  A globally convergent tracking controller for the X4 flyer rotor craft for reference trajectories with positive thrust , 2004, Robotica.

[13]  I. Michael Ross,et al.  Pseudospectral Knotting Methods for Solving Optimal Control Problems , 2004 .

[14]  Roland Siegwart,et al.  PID vs LQ control techniques applied to an indoor micro quadrotor , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[15]  S. Shankar Sastry,et al.  Differential flatness based full authority helicopter control design , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[16]  Oleg A. Yakimenko.  Direct method for real-time prototyping of optimal control , 2006 .

[17]  O. Yakimenko.  Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories , 2000 .

[18]  M.J. van Nieuwstadt,et al.  Approximate trajectory generation for differentially flat systems with zero dynamics , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[19]  Renjith R. Kumar,et al.  Should Controls Be Eliminated While Solving Optimal Control Problems via Direct Methods , 1995 .

[20]  Oskar von Stryk,et al.  Direct and indirect methods for trajectory optimization , 1992, Ann. Oper. Res..

[21]  L. Beji,et al.  Streamlined Rotors Mini Rotorcraft : Trajectory Generation and Tracking , 2005 .

[22]  George A. Boyarko,et al.  Time-optimal reorientation of a spacecraft using a direct optimization method based on inverse dynamics , 2010, 2010 IEEE Aerospace Conference.

[23]  Bruce A. Conway,et al.  Discrete approximations to optimal trajectories using direct transcription and nonlinear programming , 1992 .

[24]  S. L. Harris,et al.  Applied Numerical Methods for Engineers Using MATLAB and C , 1999 .

[25]  Oleg A. Yakimenko,et al.  Computing short-time aircraft maneuvers using direct methods , 2010 .

[26]  I. Michael Ross,et al.  Direct trajectory optimization by a Chebyshev pseudospectral method , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[27]  B. Paden,et al.  A different look at output tracking: control of a VTOL aircraft , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[28]  Naira Hovakimyan,et al.  Coordinated Path Following for Time-Critical Missions of Multiple UAVs via L1 Adaptive Output Feedback Controllers , 2007 .

[29]  M. Fliess,et al.  Sur les systèmes non linéaires différentiellement plats , 1992 .

[30]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[31]  Arthur E. Bryson,et al.  Inverse and Optimal Control for Desired Outputs , 1992 .

[32]  Jonathan P. How,et al.  Indoor Multi-Vehicle Flight Testbed for Fault Detection, Isolation, and Recovery , 2006 .

[33]  D. Hull.  Conversion of optimal control problems into parameter optimization problems , 1996 .

[34]  Nathan Slegers,et al.  Optimal Control for Terminal Guidance of Autonomous Parafoils , 2009 .

[35]  Anil V. Rao,et al.  Practical Methods for Optimal Control Using Nonlinear Programming , 1987 .

[36]  B. Conway,et al.  Collocation Versus Differential Inclusion in Direct Optimization , 1998 .

[37]  Riccardo Bevilacquaa,et al.  On-Line Generation of Quasi-Optimal Docking Trajectories , 2007 .

[38]  D. Cooke,et al.  OPTIMAL TRAJECTORY PLANNING AND LQR CONTROL FOR A QUADROTOR UAV , 2006 .

[39]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[40]  O. V. Stryk.  Simulation und Systemoptimierung , 2002 .

[41]  Hans Seywald,et al.  Trajectory optimization based on differential inclusion , 1994 .

[42]  Alastair K. Cooke,et al.  Helicopter test and evaluation , 1994 .

[43]  Ping Lu.  An inverse dynamics approach to trajectory optimization for an aerospace plane , 1992 .

[44]  Mark B. Milam,et al.  A new computational approach to real-time trajectory generation for constrained mechanical systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[45]  I. Michael Ross,et al.  Second Look at Approximating Differential Inclusions , 2001 .

[46]  I.I. Kaminer,et al.  Coordinated control of multiple UAVs for time-critical applications , 2006, 2006 IEEE Aerospace Conference.

[47]  Rogelio Lozano,et al.  Real-time stabilization and tracking of a four rotor mini-rotorcraft , 2003 .