Optimal Trajectory Planning for Parallel Robots Considering Time-Jerk

2013 ◽  
Vol 390 ◽  
pp. 471-477 ◽  
Author(s):  
Sajad Rashidnejhad ◽  
Amir Hossein Asfia ◽  
Kambiz Ghaemi Osgouie ◽  
Ali Meghdari ◽  
Aydin Azizi
Keyword(s):  
Objective Function ◽  
Trajectory Planning ◽  
Execution Time ◽  
Optimal Trajectory ◽  
Parallel Robots ◽  
Total Execution Time ◽  
Planning Techniques ◽  
Kinematic Constraints ◽  
Upper Limits ◽  
Optimal Trajectory Planning

A method for optimization in trajectory planning of 3RUU robot manipulators is presented in this paper. At first, to get the optimal trajectory, position analyses has been done on the 3RUU robot, then an objective function which have two terms is minimized: first term relevant to the total execution time and another one relevant to the integral of the squared jerk (defined as the derivative of the acceleration toward time) along the trajectory and this Guarantees that the obtained trajectory is smooth. This technique let to calculate the kinematic constraints on the motion of the robot, defined as upper limits on the absolute values of velocity, acceleration and jerk. , the total execution time does not require to be set priori. The algorithm has been tested in simulation and in comparison with other important trajectory planning techniques it has been given good results.

Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully Specified Paths With G1-Discontinuities

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Eric Barnett ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Optimal Solution ◽  
Test System ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Cable Tension ◽  
Time Optimal ◽  
Optimal Trajectory Planning

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is converted to a dynamic technique and adapted for use with cable-driven parallel robots, which exhibit cable tension and motor torque constraints. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the cable-tension constraints are imposed directly and fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. MTTS is applied to a test system and path, and compared to the bang–bang technique. With the same constraints, the results obtained with both techniques are found to be very close. However, MTTS can be applied to a wider variety of paths, and accepts constraints on jerk and total acceleration that would be difficult to apply using the bang–bang approach.

Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully-Specified Paths With G1 Discontinuities

2013 ◽  
Author(s):  
Eric Barnett ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Optimal Solution ◽  
Vertical Direction ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Time Optimal ◽  
Time Required ◽  
Optimal Trajectory Planning

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully-specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is adapted for use with cable-driven parallel robots, which exhibit the additional constraint that all cable tensions remain positive along a path to be followed. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the minimum-tension constraint is imposed directly and is fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. This approach is relevant for cable-driven mechanism applications that involve high accelerations, particularly in the vertical direction.

scholarly journals Solving the Time-Jerk Optimal Trajectory Planning Problem of a Robot Using Augmented Lagrange Constrained Particle Swarm Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Shaotian Lu ◽  
Jingdong Zhao ◽  
Li Jiang ◽  
Hong Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Objective Function ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Particle Swarm ◽  
Planning Problem ◽  
Swarm Optimization ◽  
Best Value ◽  
Augmented Lagrange Multiplier ◽  
Optimal Trajectory Planning

The problem of minimum time-jerk trajectory planning for a robot is discussed in this paper. The optimal objective function is composed of two segments along the trajectory, which are the proportional to the total execution time and the proportional to the integral of the squared jerk (which denotes the derivative of the acceleration). The augmented Lagrange constrained particle swarm optimization (ALCPSO) algorithm, which combines the constrained particle swarm optimization (CPSO) with the augmented Lagrange multiplier (ALM) method, is proposed to optimize the objective function. In this algorithm, falling into a local best value can be avoided because a new particle swarm is generated per initial procedure, and the best value gained from the former generation is saved and delivered to the next generation during the iterative search procedure to enable the best value to be found more easily and more quickly. Finally, the proposed algorithm is tested on a planar 3-degree-of-freedom (DOF) robot; the simulation results show that the algorithm is effective, offering a solution to the time-jerk optimal trajectory planning problem of a robot under nonlinear constraints.

scholarly journals Time-jerk optimal trajectory planning of hydraulic robotic excavator

2021 ◽  
Vol 13 (7) ◽  
pp. 168781402110346
Author(s):  
Yunyue Zhang ◽  
Zhiyi Sun ◽  
Qianlai Sun ◽  
Yin Wang ◽  
Xiaosong Li ◽  
...  
Keyword(s):  
Angular Velocity ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
High Efficiency ◽  
Optimal Solution ◽  
Optimal Time ◽  
Target Point ◽  
Robotic Excavator ◽  
The Impact ◽  
Optimal Trajectory Planning

Due to the fact that intelligent algorithms such as Particle Swarm Optimization (PSO) and Differential Evolution (DE) are susceptible to local optima and the efficiency of solving an optimal solution is low when solving the optimal trajectory, this paper uses the Sequential Quadratic Programming (SQP) algorithm for the optimal trajectory planning of a hydraulic robotic excavator. To achieve high efficiency and stationarity during the operation of the hydraulic robotic excavator, the trade-off between the time and jerk is considered. Cubic splines were used to interpolate in joint space, and the optimal time-jerk trajectory was obtained using the SQP with joint angular velocity, angular acceleration, and jerk as constraints. The optimal angle curves of each joint were obtained, and the optimal time-jerk trajectory planning of the excavator was realized. Experimental results show that the SQP method under the same weight is more efficient in solving the optimal solution and the optimal excavating trajectory is smoother, and each joint can reach the target point with smaller angular velocity, and acceleration change, which avoids the impact of each joint during operation and conserves working time. Finally, the excavator autonomous operation becomes more stable and efficient.

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