Fig 1.
The relationships of trajectory planning.
Fig 2.
(a) The research subject: 5 DoFs manipulator. (b) The system model of manipulator.
Table 1.
DH parameters of manipulator.
Fig 3.
The whole control scheme of trajectory optimization.
Fig 4.
The program flow chart of trajectory optimization.
Table 2.
Simulation parameters.
Table 3.
Simulation sets.
Fig 5.
The trajectory planning results of Simulation 1 based on fifth order polynomial interpolation.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 6.
The trajectory planning results of Simulation 2 based on fifth order polynomial interpolation.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 7.
The trajectory planning results of Simulation 3 based on fifth order polynomial interpolation.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 8.
The trajectory planning results of Simulation 4 based on fifth order polynomial interpolation.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 9.
The trajectory planning results of Simulation 5 based on the proposed optimization method.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 10.
The trajectory planning results of Simulation 6 based on the proposed optimization method.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Table 4.
Comparisons of simulations.
Fig 11.
The optimization process of planning time T = tf − t0 in Simulation 5.
(a) With initial value T = tf − t0 = 10s in Simulation 1, (b) With initial value T = tf − t0 = 20s in Simulation 2.
Fig 12.
The optimization process of planning time T = tf − t0 in Simulation 6.
(a) With initial value T = tf − t0 = 10s in Simulation 3, (b) With initial value T = tf − t0 = 20s in Simulation 4.
Fig 13.
The planning trajectory based on the proposed optimization method in Simulation 5.
Table 5.
Simulation parameters.
Fig 14.
The trajectory planning results of experiment based on the proposed optimization method.
(a) Planning position, (b) Planning attitude, (c) Joint angle, (d) Joint angular velocity, (e) Joint angular acceleration, (f) Joint angular jerk.
Fig 15.
The optimization process of planning time T = tf − t0 in experiment.
Fig 16.
The velocity curves of trajectory planing based on third order polynomial interpolation with planning time t1 and t2.