MPC on manifolds with an application to SE(3)

The paper considers formulations of constrained model predictive control (MPC) problems for systems with dynamics defined on smooth manifolds. Generalizations of conventional nonlinear MPC stabilization techniques based on the terminal set and terminal penalty approaches are presented based on recent work by the authors. The significance of the results includes the possibility of systematically generating globally stabilizing, discontinuous, time-invariant feedback laws in situations when smooth, or even continuous, globally stabilizing, time-invariant stabilizers do not exist. To illustrate the development of nonlinear MPC on manifolds, the paper considers an example of a system with dynamics evolving on SE(3). Such systems emerge in many applications, such as quadrotor and quadcopter flight control. In the example, the paper demonstrates semi-global stabilization properties of the nonlinear MPC feedback law.

[1]  N. McClamroch,et al.  A lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[2]  Taeyoung Lee.  Computational geometric mechanics and control of rigid bodies , 2008 .

[3]  N. McClamroch,et al.  Lie group variational integrators for the full body problem in orbital mechanics , 2007 .

[4]  S. Bhat,et al.  A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , 2000 .

[5]  Stefano Di Cairano,et al.  MPC on manifolds with applications to the control of systems on matrix Lie groups , 2015, ArXiv.

[6]  F. Leite,et al.  The Moser-Veselov equation , 2003 .

[7]  F. Allgower,et al.  Real-time feasibility of nonlinear predictive control for large scale processes-a case study , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[8]  M. A. Henson,et al.  Receding horizon control and discontinuous state feedback stabilization , 1995 .

[9]  Stefano Di Cairano,et al.  Constrained spacecraft attitude control on SO(3) using reference governors and nonlinear model predictive control , 2014, 2014 American Control Conference.

[10]  Mario Zanon,et al.  Nonlinear MPC and MHE for Mechanical Multi-Body Systems with Application to Fast Tethered Airplanes , 2012 .

[11]  B. Dundas,et al.  DIFFERENTIAL TOPOLOGY , 2002 .

[12]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .