An integrated robust probing motion planning and control scheme: A tube-based MPC approach

'This paper introduces the integration of a probing scheme into a robust MPC-based robot motion planning and control algorithm. The proposed solution tackles the output-feedback tube-based MPC problem using the partially-closed loop strategy to incorporate future measurements in a computationally efficient manner. This combination will provide not only a robust controller but also avoids overly conservative planning which is a drawback of the original implementation of the output-feedback tube-based MPC. The proposed solution is composed of two controllers: (i) a nominal MPC controller with probing feature to plan a globally convergent trajectory in conjunction with active localization, and (ii) an ancillary MPC controller to stabilize the robot motion around the planned trajectory. The performance and real-time implementation of the proposed planning and control algorithms have been verified through both extensive numerical simulations and experiments with a mobile robot.

[1]  Francisco Rodríguez,et al.  Robust tube-based predictive control for mobile robots in off-road conditions , 2011, Robotics Auton. Syst..

[2]  Y. Bar-Shalom Stochastic dynamic programming: Caution and probing , 1981 .

[3]  Gamini Dissanayake,et al.  Multi-Step Look-Ahead Trajectory Planning in SLAM: Possibility and Necessity , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[4]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[5]  Calin Belta,et al.  Discrete abstractions for robot motion planning and control in polygonal environments , 2005, IEEE Transactions on Robotics.

[6]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems , 2006, Autom..

[7]  D. Mayne,et al.  Min-max feedback model predictive control for constrained linear systems , 1998, IEEE Trans. Autom. Control..

[8]  Jun Yan,et al.  Incorporating state estimation into model predictive control and its application to network traffic control , 2005, Autom..

[9]  Gamini Dissanayake,et al.  Active SLAM using Model Predictive Control and Attractor based Exploration , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Graham C. Goodwin,et al.  Constrained Control and Estimation: an Optimization Approach , 2004, IEEE Transactions on Automatic Control.

[11]  Javier Civera,et al.  Unified Inverse Depth Parametrization for Monocular SLAM , 2006, Robotics: Science and Systems.

[12]  Joel W. Burdick,et al.  Robot Motion Planning in Dynamic, Uncertain Environments , 2012, IEEE Transactions on Robotics.

[13]  David Q. Mayne,et al.  Robust model predictive control: advantages and disadvantages of tube-based methods ⋆ , 2011 .

[14]  Eduardo Mario Nebot,et al.  Consistency of the EKF-SLAM Algorithm , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  David Q. Mayne,et al.  Tube‐based robust nonlinear model predictive control , 2011 .

[16]  Frank Allgöwer,et al.  Nonlinear model predictive control : towards new challenging applications , 2009 .

[17]  Andrey V. Savkin,et al.  Collision free cooperative navigation of multiple wheeled robots in unknown cluttered environments , 2012, Robotics Auton. Syst..

[18]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[19]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[20]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[21]  Ümit Özgüner,et al.  Robustness analysis on constrained model predictive control for nonholonomic vehicle regulation , 2009, 2009 American Control Conference.

[22]  Frank Allgöwer,et al.  Unconstrained Nonlinear Model Predictive Control and Suboptimality Estimates for Continuous-Time Systems , 2011 .

[23]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[24]  Robert R. Bitmead,et al.  Interaction between Control and State Estimation in Nonlinear MPC , 2004 .

[25]  N. Filatov,et al.  Survey of adaptive dual control methods , 2000 .

[26]  Basil Kouvaritakis,et al.  Stochastic tubes in model predictive control with probabilistic constraints , 2010, Proceedings of the 2010 American Control Conference.

[27]  Nicholas Roy,et al.  Global A-Optimal Robot Exploration in SLAM , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[28]  Frank Allgöwer,et al.  Unconstrained model predictive control and suboptimality estimates for nonlinear continuous-time systems , 2012, Autom..

[29]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[30]  Du Toit,et al.  Robot motion planning in dynamic, cluttered, and uncertain environments: the Partially Closed-Loop Receding Horizon Control approach , 2010 .

[31]  S. Shankar Sastry,et al.  Provably safe and robust learning-based model predictive control , 2011, Autom..

[32]  Zhaodan Kong,et al.  A Survey of Motion Planning Algorithms from the Perspective of Autonomous UAV Guidance , 2010, J. Intell. Robotic Syst..

[33]  Jonathan P. How,et al.  Distributed Robust Receding Horizon Control for Multivehicle Guidance , 2007, IEEE Transactions on Control Systems Technology.

[34]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[35]  Zvi Artstein,et al.  Set invariance under output feedback: a set-dynamics approach , 2011, Int. J. Syst. Sci..

[36]  Gamini Dissanayake,et al.  Active SLAM in structured environments , 2008, 2008 IEEE International Conference on Robotics and Automation.

[37]  Sauro Longhi,et al.  Motion planning for unicycle and car-like robots , 1996, Int. J. Syst. Sci..

[38]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[39]  Homayoun Najjaran,et al.  Unscented predictive motion planning of a nonholonomic system , 2011, 2011 IEEE International Conference on Robotics and Automation.

[40]  Jonathan P. How,et al.  Robust distributed model predictive control , 2007, Int. J. Control.