Navigating Discrete Difference Equation Governed WMR by Virtual Linear Leader Guided HMPC

In this paper, we revisit model predictive control (MPC) for the classical wheeled mobile robot (WMR) navigation problem. We prove that the reachable set based hierarchical MPC (HMPC), a state-of-the-art MPC, cannot handle WMR navigation in theory due to the non-existence of non-trivial linear system with an under-approximate reachable set of WMR. Nevertheless, we propose a virtual linear leader guided MPC (VLL-MPC) to enable HMPC structure. Different from current HMPCs, we use a virtual linear system with an under-approximate path set rather than the traditional trace set to guide the WMR. We provide a valid construction of the virtual linear leader. We prove the stability of VLL-MPC, and discuss its complexity. In the experiment, we demonstrate the advantage of VLL-MPC empirically by comparing it with NMPC, LMPC and anytime RRT* in several scenarios.

[1]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[2]  Angela P. Schoellig,et al.  Learning‐based Nonlinear Model Predictive Control to Improve Vision‐based Mobile Robot Path Tracking , 2016, J. Field Robotics.

[3]  Shengchao Qin,et al.  Switched Linear Multi-Robot Navigation Using Hierarchical Model Predictive Control , 2017, IJCAI.

[4]  Sayan Mitra,et al.  A verification framework for hybrid systems , 2007 .

[5]  Xin Chen,et al.  A Linear Programming Relaxation Based Approach for Generating Barrier Certificates of Hybrid Systems , 2016, FM.

[6]  Renquan Lu,et al.  Trajectory-Tracking Control of Mobile Robot Systems Incorporating Neural-Dynamic Optimized Model Predictive Approach , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[7]  F. Borrelli,et al.  A study on decentralized receding horizon control for decoupled systems , 2004, Proceedings of the 2004 American Control Conference.

[8]  Howie Choset,et al.  M*: A complete multirobot path planning algorithm with performance bounds , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[9]  Emilio Frazzoli,et al.  Anytime Motion Planning using the RRT* , 2011, 2011 IEEE International Conference on Robotics and Automation.

[10]  Tor Arne Johansen,et al.  MPC-based Collision Avoidance Strategy for Existing Marine Vessel Guidance Systems , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[11]  Riccardo Scattolini,et al.  Hierarchical Model Predictive Control of independent systems with joint constraints , 2016, Autom..

[12]  Raymond Hemmecke,et al.  Nonlinear Integer Programming , 2009, 50 Years of Integer Programming.

[13]  Tim Miller,et al.  Real-Time UAV Maneuvering via Automated Planning in Simulations , 2017, IJCAI.

[14]  Giuseppe Oriolo,et al.  Closed-loop MPC with Dense Visual SLAM - Stability through Reactive Stepping , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[15]  Richard L. Church,et al.  Finding shortest paths on real road networks: the case for A* , 2009, Int. J. Geogr. Inf. Sci..

[16]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..

[17]  Insup Lee,et al.  Compositional Refinement for Hierarchical Hybrid Systems , 2001, HSCC.

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

[19]  Walter Fetter Lages,et al.  MOBILE ROBOT TRAJECTORY TRACKING USING MODEL PREDICTIVE CONTROL , 2005 .

[20]  Mike Stilman,et al.  Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete , 2014, WAFR.

[21]  Alberto Rodriguez,et al.  Reactive Planar Manipulation with Convex Hybrid MPC , 2017, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[22]  Erez Karpas,et al.  Mixed Discrete-Continuous Heuristic Generative Planning Based on Flow Tubes , 2015, IJCAI.

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

[24]  Eduard Vidal,et al.  Online path planning for autonomous underwater vehicles in unknown environments , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[25]  Shengchao Qin,et al.  Hierarchical Model Predictive Control for Multi-Robot Navigation , 2016, IJCAI.

[26]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[27]  Eric Goubault,et al.  Inner approximated reachability analysis , 2014, HSCC.

[28]  Kenneth Holmström,et al.  The TOMLAB Optimization Environment , 2004 .

[29]  Xin Chen,et al.  Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier Certificates , 2017, ACM Trans. Embed. Comput. Syst..

[30]  H. Nijmeijer,et al.  Non-linear model predictive control for constrained mobile robots , 2001, 2001 European Control Conference (ECC).

[31]  Nolan Wagener,et al.  Information theoretic MPC for model-based reinforcement learning , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[32]  Y. Kuwata,et al.  Stable trajectory design for highly constrained environments using receding horizon control , 2004, Proceedings of the 2004 American Control Conference.

[33]  Olivier Bournez,et al.  Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems , 2000, HSCC.

[34]  Karl Worthmann,et al.  Stability and feasibility of state constrained MPC without stabilizing terminal constraints , 2014, Syst. Control. Lett..