Smooth and time-optimal S-curve trajectory planning for automated robots and machines

Abstract In this paper, a smooth and time-optimal S-curve trajectory planning method is proposed to meet the requirements of high-speed and ultra-precision operation for robotic manipulators in modern industrial applications. This method utilizes a piecewise sigmoid function to establish a jerk profile with suitably chosen phase durations such that the generated trajectories are infinitely continuously differentiable under the given constraints on velocity, acceleration and jerk. All the trajectory parameters are derived with an analytical algorithm to ensure an acceptable computational cost. This S-curve model achieves a greater efficiency than the trigonometric models, while avoiding the high complexity presented by conventional high order polynomial models. The trade-off between efficiency and smoothness can be modulated by the limit value of the snap (the derivative of jerk), this feature is advantageous for adapting to different task requirements. Furthermore, a synchronization strategy is suggested to coordinate multi-axis motions, enabling the full capabilities of the actuators to be exploited. The feasibility and practicality of the proposed approach is evaluated by the simulation and experimental studies in comparison with other benchmark techniques in the literature.

[1]  Vahid Azimirad,et al.  Maximum load determination of nonholonomic mobile manipulator using hierarchical optimal control , 2012, Robotica.

[2]  Serdar Kucuk,et al.  Optimal trajectory generation algorithm for serial and parallel manipulators , 2017 .

[3]  M. Boryga,et al.  Planning of manipulator motion trajectory with higher-degree polynomials use , 2009 .

[4]  Rene de Jesus Romero-Troncoso,et al.  Design methodology for fully dynamic-controlled polynomial profiles and reduced tracking error in CNC machines , 2010 .

[5]  Youdong Chen,et al.  Combined S-curve feedrate profiling and input shaping for glass substrate transfer robot vibration suppression , 2018, Ind. Robot.

[6]  Huashan Liu,et al.  Time-optimal and jerk-continuous trajectory planning for robot manipulators with kinematic constraints , 2013 .

[7]  Fares J. Abu-Dakka,et al.  Statistical evaluation of an evolutionary algorithm for minimum time trajectory planning problem for industrial robots , 2017 .

[8]  Sijie Yan,et al.  Third-order trajectory planning for high accuracy point-to-point motion , 2009 .

[9]  M Maarten Steinbuch,et al.  Trajectory planning and feedforward design for electromechanical motion systems , 2005 .

[10]  Xin Chen,et al.  A Generic Method to Generate AS-Curve Profile in Commercial Motion Controller , 2017 .

[11]  Ali Kireçci,et al.  Improved Trajectory Planning using Arbitrary Power Polynomials , 1994 .

[12]  A. Gasparetto,et al.  A new method for smooth trajectory planning of robot manipulators , 2007 .

[13]  Alessandro Gasparetto,et al.  Experimental Validation of Minimum Time-jerk Algorithms for Industrial Robots , 2011, J. Intell. Robotic Syst..

[14]  Alois Knoll,et al.  An Efficient and Time-Optimal Trajectory Generation Approach for Waypoints Under Kinematic Constraints and Error Bounds , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[15]  G. Oriolo,et al.  Robotics: Modelling, Planning and Control , 2008 .

[16]  Sibi Chacko,et al.  Polynomial joint angle arm robot motion planning in complex geometrical obstacles , 2013, Appl. Soft Comput..

[17]  Kevin M. Lynch,et al.  Modern Robotics - Mechanics, Planning, and Control: Video supplements and software , 2017 .

[18]  Hsien-I Lin,et al.  A Fast and Unified Method to Find a Minimum-Jerk Robot Joint Trajectory Using Particle Swarm Optimization , 2013, Journal of Intelligent & Robotic Systems.

[19]  Moharam Habibnejad Korayem,et al.  Path planning algorithm in wheeled mobile manipulators based on motion of arms , 2015 .

[20]  Hongbin Leng,et al.  Research on cubic polynomial acceleration and deceleration control model for high speed NC machining , 2008 .

[21]  Kyung-Soo Kim,et al.  A Closed-Form Solution to Asymmetric Motion Profile Allowing Acceleration Manipulation , 2010, IEEE Transactions on Industrial Electronics.

[22]  A. Gasparetto,et al.  A technique for time-jerk optimal planning of robot trajectories , 2008 .

[23]  M. H. Korayem,et al.  Maximum payload path planning for redundant manipulator using indirect solution of optimal control problem , 2009 .

[24]  Huaizhong Li,et al.  Motion profile planning for reduced jerk and vibration residuals , 2007 .

[25]  Wang,et al.  Algorithm for Smooth S-curve Feedrate Profiling Generation , 2011 .

[26]  Elizabeth A. Croft,et al.  Jerk-bounded manipulator trajectory planning: design for real-time applications , 2003, IEEE Trans. Robotics Autom..

[27]  Juvenal Rodriguez Resendiz,et al.  Assessment of jerk performance s-curve and trapezoidal velocity profiles , 2017 .

[28]  Tao Chen,et al.  Research on CNC simulation system with instruction interpretations possessed of wireless communication , 2015, The Journal of Supercomputing.

[29]  S. Liu,et al.  An on-line reference-trajectory generator for smooth motion of impulse-controlled industrial manipulators , 2002, 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No.02TH8623).

[30]  Moharam Habibnejad Korayem,et al.  Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller , 2011 .

[31]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[32]  Helge J. Ritter,et al.  On-line planning of time-optimal, jerk-limited trajectories , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  Huaizhong Li.  A jerk-constrained asymmetric motion profile for high-speed motion stages to reduce residual vibration , 2016, Int. J. Comput. Appl. Technol..

[34]  P.H. Meckl,et al.  Optimized s-curve motion profiles for minimum residual vibration , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[35]  Shyh-Leh Chen,et al.  Genetic algorithm-based S-curve acceleration and deceleration for five-axis machine tools , 2016 .

[36]  Zhijun Yang,et al.  Time-Optimal Freeform S-Curve Profile Under Positioning Error and Robustness Constraints , 2018, IEEE/ASME Transactions on Mechatronics.

[37]  Jingdong Zhao,et al.  Solving the Time-Jerk Optimal Trajectory Planning Problem of a Robot Using Augmented Lagrange Constrained Particle Swarm Optimization , 2017 .

[38]  Xueshan Gao,et al.  Optimal trajectory planning for robotic manipulators using improved teaching-learning-based optimization algorithm , 2016, Ind. Robot.

[39]  Moharam Habibnejad Korayem,et al.  Trajectory optimization of flexible mobile manipulators , 2005, Robotica.

[40]  Shurong Li,et al.  Smooth time-optimal tool trajectory generation for CNC manufacturing systems , 2012 .

[41]  R. Saravanan,et al.  Evolutionary Minimum Cost Trajectory Planning for Industrial Robots , 2008, J. Intell. Robotic Syst..

[42]  Youngjin Choi,et al.  Smooth trajectory planning methods using physical limits , 2015 .

[43]  Saravana Perumaal,et al.  Synchronized trigonometric S-Curve trajectory for jerk-Bounded Time-Optimal pick and Place Operation , 2012, Int. J. Robotics Autom..

[44]  Bertrand Tondu,et al.  The Three-Cubic Method: An Optimal Online Robot Joint Trajectory Generator under Velocity, Acceleration, and Wandering Constraints , 1999, Int. J. Robotics Res..

[45]  Jun Wu,et al.  Mechatronics modeling and vibration analysis of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool , 2018 .

[46]  Jin-Tsu Sun,et al.  An S-curve Acceleration/Deceleration Design for CNC Machine Tools Using Quintic Feedrate Function , 2011 .

[47]  Kim Doang Nguyen,et al.  On Algorithms for Planning S-Curve Motion Profiles , 2008 .

[48]  Kaiyuan Wu,et al.  Optimal time-jerk trajectory planning for industrial robots , 2018 .

[49]  H. Lehtihet,et al.  Minimum cost trajectory planning for industrial robots , 2004 .

[50]  Huifeng Wu,et al.  High precision control in PTP trajectory planning for nonlinear systems using on high‐degree polynomial and cuckoo search , 2018, Optimal Control Applications and Methods.

[51]  Mehmet Çevik,et al.  Improved trajectory planning of an industrial parallel mechanism by a composite polynomial consisting of Bézier curves and cubic polynomials , 2019, Mechanism and Machine Theory.

[52]  Huaizhong Li,et al.  Motion Profile Design to Reduce Residual Vibration of High-Speed Positioning Stages , 2009, IEEE/ASME Transactions on Mechatronics.

[53]  Claudio Melchiorri,et al.  Trajectory Planning for Automatic Machines and Robots , 2010 .

[54]  Derek G. Chetwynd,et al.  An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines , 2018, Mechanism and Machine Theory.

[55]  Richard P. Paul,et al.  An On-Line Dynamic Trajectory Generator , 1984 .

[56]  Rene de Jesus Romero-Troncoso,et al.  FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors , 2009 .

[57]  Jun Wu,et al.  Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy , 2009 .