Accuracy analysis of optimal trajectory planning methods based, on function approximation for a four-DOF biped walking model

2005 ◽  
Vol 19 (S1) ◽  
pp. 452-460 ◽  
Author(s):  
Chunye Peng ◽  
Kyosuke Ono
2002 ◽  
Vol 124 (4) ◽  
pp. 554-565 ◽  
Author(s):  
Kyosuke Ono ◽  
Rongqiang Liu

This paper describes an optimal trajectory planning of walking locomotion for a planar biped walking mechanism which has thighs, shanks and small feet. The biped mechanism was modeled to be a 3-degree-of-freedom (dof) link system composed of a stance leg and a 2-dof swing leg. The one step walking locomotion is divided into two phases, i.e., the swing motion of 2-dof swing until knee collision and the swing motion of the straight leg until toe collision. It is assumed that the knee collision of the swing leg and the toe collision at the foot exchange are plastic and occur instantly. The motion of the swing and stance legs in the first phase is solved by the optimal trajectory planning based on the function approximation method. Under the full-actuated condition at the hip, knee and ankle joints, we obtained the optimal trajectory solution with a minimum square integral of input torque. We also obtained a sub-optimal walking locomotion for an under-actuated system whose ankle is a passive joint. The validity of the optimal trajectory solution is confirmed by a forward dynamic simulation. The optimal trajectory solution for the human body parameter values exhibits a natural and stable walking locomotion with the step length of 0.33 m and a step period of 0.62 s.


2021 ◽  
Vol 13 (7) ◽  
pp. 168781402110346
Author(s):  
Yunyue Zhang ◽  
Zhiyi Sun ◽  
Qianlai Sun ◽  
Yin Wang ◽  
Xiaosong Li ◽  
...  

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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