Time-Optimal Trajectory Planning for Delta Robot Based on Quintic Pythagorean-Hodograph Curves

Su, Tingting; Cheng, Long; Wang, Yunkuan; Liang, Xu; Zheng, Jinhai; Zhang, Haojian

doi:10.1109/access.2018.2831663

Cited by 50 publications

(22 citation statements)

References 32 publications

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“…The proposed method can be used to generate PPO trajectory of Delta parallel robot to meet a prescribed geometrical constraint, and can quickly and easily solve the relationship between PH curve and the prescribed geometrical constraint. The maximum deviation of the comparison method in reference [35] can be calculated by…”

Section: Discussionmentioning

confidence: 99%

“…In Figure 2, |AG| = w, |HC| = |EI| = k, |BH| = |FI| = m, |AB| = |GF| = j, |AH| = |GI| =h. The quintic PH curves in the PPO path illustrated in Figure 3 are given [35]…”

Section: Path Planningmentioning

confidence: 99%

“…4 m/s. As a comparison method, the trajectory planning based on motion superposition [35] was also simulated. In the comparison method, the maximum velocity in the vertical direction was set to 1.2 m/s, and the maximum velocity in the horizontal direction was set to 2.4 m/s, which were the same as the proposed method.…”

Section: Simulation and Analysismentioning

confidence: 99%

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Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Liang

2019

Applied Sciences

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A new trajectory planning approach on the basis of the quintic Pythagorean–Hodograph (PH) curve is presented and applied to Delta robot for implementing pick-and-place operation (PPO). To satisfy a prescribed geometrical constraint, which indicates the distance between the transition segment curve and right angle of PPO trajectory is no greater than a prescribed value, the quintic PH curve is used to produce a connection segment path for collision avoidance. The relationship between the PH curve and constraint is analyzed, based on which PH curve is calculated simply. Afterwards, the trajectory is planned in different phases with different motion laws, i.e. polynomial motion laws and PH curve parameter-dependent motion laws, to obtain a smooth performance both in Cartesian and joint space. The relationship between the PH curve and constraint is also used to improve the efficiency of calculation, and the trajectory symmetry is used to reduce calculation time by direct symmetric transformation. Thus, real-time performance is improved. The results of simulations and experiments indicate that the approach in this paper can provide smooth motion and meet the real-time requirement under the prescribed geometrical constraint.

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Section: Discussionmentioning

confidence: 99%

“…In Figure 2, |AG| = w, |HC| = |EI| = k, |BH| = |FI| = m, |AB| = |GF| = j, |AH| = |GI| =h. The quintic PH curves in the PPO path illustrated in Figure 3 are given [35]…”

Section: Path Planningmentioning

confidence: 99%

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Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Liang

2019

Applied Sciences

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“…erefore, selecting a suitable curve function to represent the trajectory according to the traffic condition is important. In the relevant trajectory planning studies, the commonly used geometric curves include the spline curve [13][14][15][16][17], trapezoidal acceleration curve [18][19][20][21][22], Bezier curve [23][24][25][26], and polynomial curve [27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

A Universal Trajectory Planning Method for Automated Lane-Changing and Overtaking Maneuvers

Wang

Wei

2020

Mathematical Problems in Engineering

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Lane-changing and overtaking are conventional maneuvers on roads, and the reference trajectory is one of the prerequisites to execute these maneuvers. This study proposes a universal trajectory planning method for automated lane-changing and overtaking maneuvers, in which the trajectory is regarded as the combination of a path and its traffic state profiles. The two-dimensional path is represented by a suitable curve to connect the initial position with final position of the ego vehicle. Based on the planned path, its traffic state profiles are generated by solving a nonlinear mathematical optimization model. Moreover, the study discretizes the time horizon into several time intervals and determines the parameters to obtain the continuous and smooth profiles, which guarantees the safety and comfort of the ego vehicle. Finally, a series of simulation experiments are performed in the MATLAB platform and the results show the feasibility and effectiveness of the proposed universal trajectory planning method.

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“…The minimum time optimization, directly associated with the production efficiency of the robot, was the first of these objectives to be considered, having been widely applied. For instance, in [24], considering three different types of constraints, smooth joint trajectories were constructed with the cubic polynomial function, a genetic algorithm procedure with parallel-populations was applied for the purpose of minimizing time, and finally, the validity of the method was verified; in [25], a time-optimal trajectory planning method was proposed, based on quintic Pythagorean Hodograph (PH) curves, in order to realize a smooth and high-speed operation of a Delta parallel robot. If we blindly pursue the minimum execution time at actual operation, it will easily lead to the discontinuity of torque and acceleration.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Planning and Optimization for a Par4 Parallel Robot Based on Energy Consumption

Zhang

Ming

2019

Applied Sciences

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A study on trajectory planning and optimization for a Par4 parallel robot was carried out, based on energy consumption in high-speed picking and placing. In the end-effector operating space of the Par4 parallel robot, the rectangular transition of the pick-and-place trajectory was rounded by a Lamé curve. A piecewise design method was adopted to accomplish trajectory shape planning for displacement, velocity and acceleration. To make the Par4 robot’s end run more smoothly and to reduce residual vibration, asymmetric fifth-order and sixth-order polynomial motion laws were employed. With the aim of reaching the minimum mechanical energy consumption for the Par4 parallel robot, the recently proposed Grey Wolf Optimizer (GWO) algorithm was adopted to optimize the planning trajectory. The validity of the design method was verified by experiments, and it was found that the minimum mechanical energy consumption of the optimal trajectory planned under the law of fifth-order polynomial motion is lower than that of sixth-order polynomial motion. In addition, the experiments also revealed the optimal values of Parameters e and f, which were the parameters of the Lamé curve function. Parameter e can be calculated as half the pick-up span for the minimum mechanical energy consumption, unlike parameter f, whose optimal value depends on specific circumstances such as the pick-and-place coordinates and the pick-up height.

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Time-Optimal Trajectory Planning for Delta Robot Based on Quintic Pythagorean-Hodograph Curves

Cited by 50 publications

References 32 publications

Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

Quintic Pythagorean-Hodograph Curves Based Trajectory Planning for Delta Robot with a Prescribed Geometrical Constraint

A Universal Trajectory Planning Method for Automated Lane-Changing and Overtaking Maneuvers

Trajectory Planning and Optimization for a Par4 Parallel Robot Based on Energy Consumption

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