Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque

  • Qiang Zhang Automation Department China University of Petroleum(East China)
  • Shu-Rong Li Automation Department China University of Petroleum(East China)
  • Jian-Xin Guo Academy of Mathematics and Systems Science Chinese Academy of Sciences
  • Xiao-Shan Gao Academy of Mathematics and Systems Science Chinese Academy of Sciences


In this paper, the problem of time optimal trajectory planning under confined torque and uncertain dynamics and torque parameters along a predefined geometric path is considered. It is shown that the robust optimal solution to such a problem can be obtained by solving a linear program. Thus a tractable algorithm is given for robust time-optimal path-tracking control under confined torque.


[1] Katzschmann, R.; Kroger, T.; Asfour, T.; Khatib O.(2013); Towards Online Trajectory Generation Considering Robot Dynamics and Torque Limits, in Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on, ISSN 2153-0858, Tokyo, 5644 - 5651.

[2] Verscheure, D.; Demeulenaere, B.; Swevers, J.; De Schutter, J.; Diehl, M.(2009); Timeoptimal path tracking for robots: a convex optimization approach, IEEE Trans. on Automatic Control, ISSN 0018-9286, 54(10): 2318-2327.

[3] Bobrow, J.E.; Dubowsky, S.; Gibson, J.(1985); Time-optimal control of robotic manipulators along specified paths, International Journal of Robotics Research, ISSN 0278-3649, 4(3): 3-17.

[4] Shin, K.; McKay, N.(1985); Minimum-time control of robotic manipulators with geometric path constraints, IEEE Trans. on Automatic Control, ISSN 0018-9286, 30(6): 531-541.

[5] Timar, S.D.; Farouki, R.T.(2007); Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds, Robotics and Computer-Integrated Manufacturing, ISSN 0736-5845, 23(5): 563-579.

[6] Yuan, C.; Zhang, K.; Fan, W.(2013); Time-optimal Interpolation for CNC Machining along Curved Tool Pathes with Confined Chord Error, Journal of Systems Science and Complexity, ISSN 1559-7067, 26(5): 836-870.

[7] Chen, Y.; Desrochers, A.A.(1989); Structure of minimum-time control law for robotic manipulators with constrained paths, in Robotics and Automation, IEEE International Conference on, ISBN 0-8186-1938-4, Scottsdale, USA, 971-976.

[8] Guo, J.X.; Zhang, Q.; Gao, X.S.(2013); Tracking Error Reduction in CNC Machining by Reshaping the Kinematic Trajectory, Journal of Systems Science and Complexity, ISSN 1559-7067, 26(5), 800-817.

[9] Zhang, K.; Yuan, C.M.; Gao, X.S.(2013); Efficient algorithm for feedrate planning and smoothing with confined chord error and acceleration for each axis, The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768 , 66(9): 1685-1697.

[10] Ardeshiri, T.; Norrlof, M.; Lofberg, J.; Hansson, A.(2011); Convex optimization approach for time-optimal path tracking of robots with speed dependent constraint, in Proceedings of the 18th IFAC World Congress, ISSN 1474-6670, Milano, Italy, 14648-14653.

[11] Hauser, K.(2013); Fast Interpolation and Time-Optimization on Implicit Contact Submanifolds, in Proceedings of Robotics: Science and Systems, ISSN 2330-765X, Berlin, Germany.

[12] Shin, K.G.; McKay, N.D.(1987); Robust trajectory planning for robotic manipulators under payload uncertainties, IEEE Trans. on Automatic Control, ISSN 0018-9286, 32(12): 1044- 1054.

[13] Kieffer, J.; Cahill, A.J.; James, M.R.(1997); Robust and accurate time-optimal pathtracking control for robot manipulators, IEEE Trans. on Robotics and Automation, ISSN 1042-296X, 13(6): 880–890.

[14] Diehl, M.; Gerhard, J.; Marquardt, W.; Monnigmann, M.(2008); Numerical solution approaches for robust nonlinear optimal control problems, Computers & Chemical Engineering, ISSN 0098-1354, 32(6): 1279-1292.

[15] Marti, K.; Aurnhammer, A.(2002); Robust optimal trajectory planning for robots by stochastic optimization, Mathematical and Computer Modelling of Dynamical Systems, ISSN 1744-5051, 8(1): 75-116.

[16] Chisci, L.; Rossiter, J.A.; Zappa, G.(2001); Systems with persistent disturbances: Predictive control with restrictive constraints, Automatica, ISSN 0005-1098, 37(7): 1019-1028.

[17] Mayne, D.Q.; Seron, M.M.; Rakovic, S.V.(2005); Robust model predictive control of constrained linear systems with bounded disturbances, Automatica, ISSN 0005-1098, 41(2): 219-224.

[18] Patrikalakis, N.M.; Maekawa, T.(2010); Shape Interrogation for Computer Aided Design and Manufacturing, ISBN 978-3-642-04074-0, Springer Berlin, Heidelberg.

[19] Bertsimas, D.; Brown, D.B.; Caramanis, C.(2011); Theory and applications of robust optimization, SIAM Review, ISSN 0036-1445, 53(3): 464–501.

[20] Karmarkar, N.(1984); A new polynomial time algorithm for linear programming, Combinatorica, ISSN 0209-9683, 4(4): 373-395.

[21] Sirisena, H.R.; Chou, F.S.(1979); Convergence of the control parameterization Ritz method for nonlinear optimal control problems, Journal of Optimization Theory and Applications, ISSN 0022-3239, 29(3): 369-382.

[22] Daniel, J.W.(1973); The Ritz-Galerkin method for abstract optimal control problems, SIAM Journal on Control, ISSN 0036-1402, 11(1): 53-63.

[23] Schwartz, A.L.(1996); Theory and Implementation of Numerical Methods Based on Runge- Kutta Integration for Solving Optimal Control Problems, Ph.D. Thesis, Univ. of California at Berkeley.

[24] Corke, P.(1996); A robotics toolbox for MATLAB, IEEE Robotics and Automation Magazine, ISSN 1070-9932, 3(1): 24-32.

[25] Sturm, J.F.(1999); Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones, Optimization Methods and Software, ISSN 1055-6788, 11(1-4): 625-653.
How to Cite
ZHANG, Qiang et al. Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 10, n. 1, p. 123-135, nov. 2014. ISSN 1841-9844. Available at: <>. Date accessed: 26 sep. 2020. doi:


robust optimal control, time minimum trajectory planning, parameter uncertainties, tractable algorithm