Energy-Optimal Time Allocation of a Series of Point-to-Point Motions

When a system has to perform a series of point-to-point (PTP) motions within a given time, the execution time for each individual motion is, in many cases, free to choose. This letter presents a dynamic programming algorithm to allocate the time to each motion in a series of PTP motions in an energy-optimal way. The algorithm is demonstrated on an xy-positioning stage and the results are compared with an equal time allocation scheme.

[1]  J. S. Park,et al.  Motion profile planning of repetitive point-to-point control for maximum energy conversion efficiency under acceleration conditions , 1996 .

[2]  R. Fung,et al.  Minimum-Energy Point-to-Point Trajectory Planning for a Motor-Toggle Servomechanism , 2012, IEEE/ASME Transactions on Mechatronics.

[3]  Johannes P. Schlöder,et al.  An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. Part 1: theoretical aspects , 2003, Comput. Chem. Eng..

[4]  Panos J. Antsaklis,et al.  Optimal control of switched systems based on parameterization of the switching instants , 2004, IEEE Transactions on Automatic Control.

[5]  Pablo González de Santos,et al.  Minimizing Energy Consumption in Hexapod Robots , 2009, Adv. Robotics.

[6]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[7]  Sebastian Sager,et al.  Numerical methods for mixed-integer optimal control problems , 2006 .

[8]  Anastasios D. Pouliezos,et al.  Optimal Robot Speed Trajectory by Minimization of the Actuator Motor Electromechanical Losses , 2002, J. Intell. Robotic Syst..

[9]  Rahman Saidur,et al.  A review on electrical motors energy use and energy savings , 2010 .

[10]  Akira Abe,et al.  Trajectory planning for saving energy of a flexible manipulator using soft computing methods , 2010, ICCAS 2010.

[11]  Goele Pipeleers,et al.  A Data-Driven Constrained Norm-Optimal Iterative Learning Control Framework for LTI Systems , 2013, IEEE Transactions on Control Systems Technology.

[12]  Alberto Olivares,et al.  Energy-optimal trajectory planning for robot manipulators with holonomic constraints , 2012, Syst. Control. Lett..

[13]  K. Moore,et al.  Iterative Learning Control: Robustness and Monotonic Convergence for Interval Systems , 2010 .

[14]  Frank Körner,et al.  A hybrid method for solving nonlinear knapsack problems , 1989 .

[15]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[16]  Stuart E. Dreyfus,et al.  Applied Dynamic Programming , 1965 .

[17]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[18]  R. E. Marsten,et al.  An Algorithm for Nonlinear Knapsack Problems , 1976 .

[19]  Xuping Xu,et al.  A dynamic programming approach for optimal control of switched systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[20]  Wim Symens,et al.  Badminton playing robot - a multidisciplinary test case in Mechatronics , 2010 .

[21]  M. Benrejeb,et al.  Optimal Switching Instants of Linear Switched Systems Based on Metaheuristic Approaches , 2011 .