Differential flatness of a front-steered vehicle with tire force control

A trajectory tracking controller based on differential flatness is presented for a nonlinear bicycle model. This controller maps the bicycle dynamics into a point mass located at a center of oscillation with an additional degree of freedom of yaw dynamics. A state transformation is performed that reveals structure in the yaw dynamics resembling a Liénard system. A candidate Lyapunov function inspired by this structure is used to assess the stability of the yaw dynamics while tracking straight-line trajectories and steady turns. The basin of attraction of the controller is limited by actuator constraints and the presence of unstable equilibrium points during turns with high lateral acceleration. The controller properties and the stability of yaw dynamics are demonstrated in simulation.

[1]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1977 .

[2]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[3]  Jürgen Ackermann.  Robust decoupling, ideal steering dynamics and yaw stabilization of 4WS cars , 1994, Autom..

[4]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[5]  Aníbal Ollero,et al.  Stability analysis of mobile robot path tracking , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[6]  R. Murray,et al.  Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems , 1995 .

[7]  A different look at output tracking: control of a vtol aircraft , 1996, Autom..

[8]  Shun'ichi Doi,et al.  Bifurcation in vehicle dynamics and robust front wheel steering control , 1998, IEEE Trans. Control. Syst. Technol..

[9]  S. Fuchshumer,et al.  Nonlinear Vehicle Dynamics Control - A Flatness Based Approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[10]  R. Isermann,et al.  Nonlinear trajectory following control for automatic steering of a collision avoiding vehicle , 2006, 2006 American Control Conference.

[11]  John R. Wagner,et al.  A trajectory tracking steer-by-wire control system for ground vehicles , 2006, IEEE Transactions on Vehicular Technology.

[12]  Efstathios Velenis,et al.  Modeling aggressive maneuvers on loose surfaces: The cases of Trail-Braking and Pendulum-Turn , 2007, 2007 European Control Conference (ECC).

[13]  Sanjiv Singh,et al.  The 2005 DARPA Grand Challenge , 2007 .

[14]  Brigitte d'Andréa-Novel,et al.  Flatness-Based Vehicle Steering Control Strategy With SDRE Feedback Gains Tuned Via a Sensitivity Approach , 2007, IEEE Transactions on Control Systems Technology.

[15]  Sanjiv Singh,et al.  The 2005 DARPA Grand Challenge: The Great Robot Race , 2007 .

[16]  Francesco Borrelli,et al.  Predictive Active Steering Control for Autonomous Vehicle Systems , 2007, IEEE Transactions on Control Systems Technology.

[17]  Steven C. Peters,et al.  Mobile robot path tracking of aggressive maneuvers on sloped terrain , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  Andreas Kugi,et al.  A new flatness-based control of lateral vehicle dynamics , 2008 .

[19]  Sanjiv Singh,et al.  The DARPA Urban Challenge: Autonomous Vehicles in City Traffic, George Air Force Base, Victorville, California, USA , 2009, The DARPA Urban Challenge.