Optimal Trajectory Generation for Robotic Manipulators Using Dynamic Programming

1987 ◽  
Vol 109 (2) ◽  
pp. 88-96 ◽  
Author(s):  
S. Singh ◽  
M. C. Leu
Keyword(s):  
Dynamic Programming ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Robotic Manipulators ◽  
Planning Algorithm ◽  
Manipulator Link ◽  
On Line ◽  
And Performance ◽  
Two Stages ◽  
Optimal Trajectory Planning

The problem of optimal control of robotic manipulators is dealt with in two stages: (1) optimal trajectory planning, which is performed off-line and results in the prescription of the position and velocity of each link as a function of time along a “given” path and (2) on-line trajectory tracking, during which the manipulator is guided along the planned trajectory using a feedback control algorithm. In order to obtain a general trajectory planning algorithm which could account for various constraints and performance indices, the technique of dynamic programming is adopted. It is shown that for a given path, this problem is reduced to a search over the velocity of one moving manipulator link. The design of the algorithm for optimal trajectory planning and the relevant computational issues are discussed. Simulations are performed to test the effectiveness of this method. The use of this algorithm in conjunction with an on-line controller is also presented.

The method of minimal neighborhood: a new and most effective iterative method for minimum cost trajectory planning in robot manipulators

Robotica ◽  
1995 ◽  
Vol 13 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Ignacy Duleba
Keyword(s):  
Dynamic Programming ◽  
Iterative Method ◽  
Trajectory Planning ◽  
Iterative Procedure ◽  
Optimal Trajectory ◽  
Phase Plane ◽  
Robot Manipulators ◽  
Minimum Cost ◽  
Optimal Trajectory Planning

SummaryIn this paper a method of minimal neighborhood for cost optimal trajectory planning along prescribed paths is introduced. The method exploits the phase-plane approach. In the phase-plane, in an iterative procedure, subareas of search are built, called neighborings, which surround the current-best trajectory. In each iteration, in order to find the next-best trajectory, the dynamic programming (pruned to the subarea) is used. The method of minimal neighborhood makes the neighborings as small as possible and therefore speeds up computations maximally. The tests carried out on a model of the IRb-6 ASEA robot have shown that the method of minimal neighborhood is much faster than dynamic programming applied to the whole phase-plane, while preserving the quality of the resulting trajectory.

Time Optimal Path Planning of Palletizing Robot

2013 ◽  
Vol 470 ◽  
pp. 658-662
Author(s):  
Yong Pan Xu ◽  
Ying Hong
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Optimal Path ◽  
Straight Path ◽  
Optimal Path Planning ◽  
Quintic Polynomial ◽  
Time Optimal ◽  
Acceleration And Deceleration ◽  
Planning Algorithm ◽  
Optimal Trajectory Planning

In order to improve the efficiency and reduce the vibration of Palletizing Robot, a new optimal trajectory planning algorithm is proposed. This algorithm is applied to the trajectory planning of Palletizing manipulators. The S-shape acceleration and deceleration curve is adopted to interpolate joint position sequences. Considering constraints of joint velocities, accelerations and jerks, the traveling time of the manipulator is minimized. The joint interpolation confined by deviation is used to approximate the straight path, and the deviation is decreased significantly by adding only small number of knots. Traveling time is solved by using quintic polynomial programming strategy between the knots, and then time-jerk optimal trajectories which satisfy constraints are planned. The results show that the method can avoid the problem of manipulator singular points and improve the palletize efficiency.

An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

Robotica ◽  
2017 ◽  
Vol 35 (12) ◽  
pp. 2400-2417 ◽  
Author(s):  
Ming-Yong Zhao ◽  
Xiao-Shan Gao ◽  
Qiang Zhang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Original Problem ◽  
Robotic Manipulators ◽  
Linear Optimal Control ◽  
Time Optimal ◽  
Optimal Trajectory Planning

SUMMARYThis paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound κ. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of κ = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.

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