Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

Our trajectory planner can tackle different requirements or constraints uniformly.Our proposal is systematically tested on a wide range of simulation cases.A Hamiltonian-based index is utilized to judge the optimality of an obtained solution.Differences between min-time and min-length trajectories are investigated. Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal.

[1]  Raymond Chiong,et al.  Search-evasion path planning for submarines using the Artificial Bee Colony algorithm , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[2]  Lars Karlsson,et al.  Autonomous Transport Vehicles: Where We Are and What Is Missing , 2015, IEEE Robotics & Automation Magazine.

[3]  T. Martinez-Marfn.  Learning Optimal Motion Planning for Car-like Vehicles , 2005 .

[4]  P. V. Manivannan,et al.  Control of truck-trailer mobile robots: a survey , 2014, Intell. Serv. Robotics.

[5]  Shiho Kim,et al.  A trajectory planning method based on forward path generation and backward tracking algorithm for Automatic Parking Systems , 2014, 17th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[6]  Dogan Ibrahim,et al.  Navigation of mobile robots in the presence of obstacles , 2010, Adv. Eng. Softw..

[7]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[8]  Hamid Salimi,et al.  Stochastic Fractal Search: A powerful metaheuristic algorithm , 2015, Knowl. Based Syst..

[9]  Yasar Ayaz,et al.  Intelligent bidirectional rapidly-exploring random trees for optimal motion planning in complex cluttered environments , 2015, Robotics Auton. Syst..

[10]  Pawit Pharpatara,et al.  Missile trajectory shaping using sampling-based path planning , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  Byung Kook Kim,et al.  Efficient time-optimal two-corner trajectory planning algorithm for differential-driven wheeled mobile robots with bounded motor control inputs , 2015, Robotics Auton. Syst..

[12]  L. Biegler.  An overview of simultaneous strategies for dynamic optimization , 2007 .

[13]  Alessandro Gasparetto,et al.  Optimal trajectory planning for industrial robots , 2010, Adv. Eng. Softw..

[14]  Yahui Yu,et al.  The Exponential Diophantine Equation 2x + b y = c z , 2014, TheScientificWorldJournal.

[15]  Tomás Martínez-Marín.  Learning Optimal Motion Planning for Car-like Vehicles , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[16]  Lorenz T. Biegler,et al.  Nonlinear Waves in Integrable and Nonintegrable Systems , 2018 .

[17]  Leandro Fleck Fadel Miguel,et al.  Search group algorithm , 2015 .

[18]  Saïd Mammar,et al.  Automatic Parallel Parking in Tiny Spots: Path Planning and Control , 2015, IEEE Transactions on Intelligent Transportation Systems.

[19]  Zhijiang Shao,et al.  A unified motion planning method for parking an autonomous vehicle in the presence of irregularly placed obstacles , 2015, Knowl. Based Syst..

[20]  Zhijiang Shao,et al.  Time-Optimal Maneuver Planning in Automatic Parallel Parking Using a Simultaneous Dynamic Optimization Approach , 2016, IEEE Transactions on Intelligent Transportation Systems.

[21]  J. Latombe,et al.  On nonholonomic mobile robots and optimal maneuvering , 1989, Proceedings. IEEE International Symposium on Intelligent Control 1989.

[22]  Geoffrey A. Hollinger,et al.  Search and pursuit-evasion in mobile robotics , 2011, Auton. Robots.

[23]  Weijun Huang,et al.  Optimal Multi-Impulse Orbit Transfer Using Nonlinear Relative Motion Dynamics , 2012 .

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

[25]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[26]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[27]  Philippe Souères,et al.  Optimal trajectories for nonholonomic mobile robots , 1998 .

[28]  Zdzislaw Kowalczuk,et al.  Autonomous Driver Based on an Intelligent System of Decision-Making , 2015, Cognitive Computation.

[29]  Devin J. Balkcom,et al.  Time Optimal Trajectories for Bounded Velocity Differential Drive Vehicles , 2002, Int. J. Robotics Res..

[30]  Dirk Schulz,et al.  Towards Autonomous Robotic Systems for Remote Gas Leak Detection and Localization in Industrial Environments , 2012, FSR.

[31]  D. Alejo,et al.  Collision-Free 4D Trajectory Planning in Unmanned Aerial Vehicles for Assembly and Structure Construction , 2014, J. Intell. Robotic Syst..

[32]  Saïd Mammar,et al.  Geometric continuous-curvature path planning for automatic parallel parking , 2013, 2013 10th IEEE INTERNATIONAL CONFERENCE ON NETWORKING, SENSING AND CONTROL (ICNSC).

[33]  Marc Carreras,et al.  A survey on coverage path planning for robotics , 2013, Robotics Auton. Syst..

[34]  P. Souéres,et al.  Shortest paths synthesis for a car-like robot , 1996, IEEE Trans. Autom. Control..

[35]  Saïd Mammar,et al.  Automatic parallel parking with geometric continuous-curvature path planning , 2014, 2014 IEEE Intelligent Vehicles Symposium Proceedings.

[36]  Raymond Chiong,et al.  A two-layer optimization framework for UAV path planning with interval uncertainties , 2014, 2014 IEEE Symposium on Computational Intelligence in Production and Logistics Systems (CIPLS).

[37]  Milan Simic,et al.  Continuous Path Smoothing for Car-Like Robots Using B-Spline Curves , 2015, J. Intell. Robotic Syst..

[38]  SalimiHamid.  Stochastic Fractal Search , 2015 .

[39]  Jungwon Yoon,et al.  Haptic assisted aircraft optimal assembly path planning scheme based on swarming and artificial potential field approach , 2014, Adv. Eng. Softw..

[40]  Bai Li,et al.  An Improved Artificial Bee Colony Algorithm Based on Balance-Evolution Strategy for Unmanned Combat Aerial Vehicle Path Planning , 2014, TheScientificWorldJournal.

[41]  Amar Khoukhi,et al.  Data-driven multi-stage multi-objective motion planning of mobile robots, application to near minimum power fuzzy parking , 2015, Comput. Electr. Eng..

[42]  Ching-Hung Lee,et al.  Efficient collision-free path-planning of multiple mobile robots system using efficient artificial bee colony algorithm , 2015, Adv. Eng. Softw..

[43]  Emmanuel G. Collins,et al.  Robust automatic parallel parking in tight spaces via fuzzy logic , 2005, Robotics Auton. Syst..

[44]  Konstantin Kondak,et al.  Computation of time optimal movements for autonomous parking of non-holonomic mobile platforms , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[45]  Andrew A. Goldenberg,et al.  Neural network architecture for trajectory generation and control of automated car parking , 1996, IEEE Trans. Control. Syst. Technol..

[46]  Yong Xie,et al.  Path planning for multiple mobile robots under double-warehouse , 2014, Inf. Sci..

[47]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[48]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

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

[50]  Xin Wang,et al.  An adaptive parametric interpolator for trajectory planning , 2010, Advances in Engineering Software.