A Novel Algorithm for Time Optimal Trajectory Planning

2014 ◽  
Author(s):  
Mingxing Yuan ◽  
Bin Yao ◽  
Dedong Gao ◽  
Xiaocong Zhu ◽  
Qingfeng Wang
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Optimal Solution ◽  
Problem Of Time ◽  
High Productivity ◽  
Hard Constraints ◽  
Time Optimal ◽  
Rate Optimization ◽  
Feed Rate Optimization ◽  
Optimal Trajectory Planning

Time optimal trajectory planning under various hard constraints plays a significant role in simultaneously meeting the requirements on high productivity and high accuracy in the fields of both machining tools and robotics. In this paper, the problem of time optimal trajectory planning is first formulated. A novel back and forward check algorithm is subsequently proposed to solve the minimum time feed-rate optimization problem. The basic idea of the algorithm is to search the feasible solution in the specified interval using the back or forward operations. Four lemmas are presented to illustrate the calculating procedure of optimal solution and the feasibility of the proposed algorithm. Both the elliptic curve and eight profile are used as case studies to verify the effectiveness of the proposed algorithm.

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 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.

Time-optimal trajectory planning method for six-legged robots under actuator constraints

2019 ◽  
Vol 233 (14) ◽  
pp. 4990-5002
Author(s):  
Zhijun Chen ◽  
Feng Gao
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Optimization Problem ◽  
The Body ◽  
Planning Method ◽  
Legged Robots ◽  
Legged Robot ◽  
Time Optimal ◽  
Actuator Constraints ◽  
Optimal Trajectory Planning

Current studies on time-optimal trajectory planning centers on cases with fixed base and only one end-effector. However, the free-floating body and the multiple legs of the legged robot make the current methods inapplicable. This paper proposes a time-optimal trajectory planning method for six-legged robots. The model of the optimization problem for six-legged robots is built by considering the base and the end-effectors separately. Both the actuator constraints and the gait cycle constraints are taken into account. A novel two-step optimization method is proposed to solve the optimization problem. The first step solves the time-optimal trajectory of the body and the second step solves the time-optimal trajectory of the swinging legs. Finally, the method is applied to a six-parallel-legged robot and validated by experiments on the prototype. The results show that the velocity of the optimized gait is improved by 17.8% in contrast to the non-optimized one.

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