scholarly journals Multiphase Trajectory Generation for Planar Biped Robot Using Direct Collocation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Yubin Liu ◽  
Shuai Heng ◽  
Xizhe Zang ◽  
Zhenkun Lin ◽  
Jie Zhao
Keyword(s):  
Energy Efficiency ◽  
Collocation Method ◽  
Biped Robot ◽  
Contact Forces ◽  
Two Phase ◽  
Double Support ◽  
Direct Collocation ◽  
Direct Collocation Method ◽  
The Stability ◽  
Support Phase

Stability and energy efficiency are the main focuses in the bipedal robot field. In this paper, we apply a multiphase gait, which is different from the widely used two-phase gait, to improve the stability at the moment, when a biped robot transfers from the double support phase to the single support phase. Then, we create dynamic equations with contact forces in each phase using Lagrangian formulation. Furthermore, the direct collocation method is utilized to generate the optimal trajectory toward both stability and energy efficiency. Finally, the comparison between multiphase gait and two-phase gait is performed with numerical simulations. The results prove that multiphase gait increases the stability margin in the cost of slightly decreasing energy efficiency. Besides, both gaits show a similar human-like characteristic in hip height variation during walking.

scholarly journals Effects of Torso Pitch Motion on Energy Efficiency of Biped Robot Walking

2021 ◽  
Vol 11 (5) ◽  
pp. 2342
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Biped Robot ◽  
Gait Pattern ◽  
Pattern Generation ◽  
Biped Robots ◽  
Pitch Motion ◽  
Double Support ◽  
Gait Parameters ◽  
Support Phase

Gait pattern generation has an important influence on the walking quality of biped robots. In most gait pattern generation methods, it is usually assumed that the torso keeps vertical during walking. It is very intuitive and simple. However, it may not be the most efficient. In this paper, we propose a gait pattern with torso pitch motion (TPM) during walking. We also present a gait pattern with torso keeping vertical (TKV) to study the effects of TPM on energy efficiency of biped robots. We define the cyclic gait of a five-link biped robot with several gait parameters. The gait parameters are determined by optimization. The optimization criterion is chosen to minimize the energy consumption per unit distance of the biped robot. Under this criterion, the optimal gait performances of TPM and TKV are compared over different step lengths and different gait periods. It is observed that (1) TPM saves more than 12% energy on average compared with TKV, and the main factor of energy-saving in TPM is the reduction of energy consumption of the swing knee in the double support phase and (2) the overall trend of torso motion is leaning forward in double support phase and leaning backward in single support phase, and the amplitude of the torso pitch motion increases as gait period or step length increases.

GA Based Trajectory Generation for a 7-DOF Biped Robot by Considering Feet Rotation during Double Support Phase

2012 ◽  
Vol 463-464 ◽  
pp. 1252-1255 ◽  
Author(s):  
Farsam Farzadpour ◽  
Mohammad Danesh
Keyword(s):  
High Speed ◽  
Trajectory Generation ◽  
Biped Robot ◽  
Bipedal Walking ◽  
Double Support ◽  
Straight Line ◽  
Zero Moment ◽  
The Stability ◽  
Support Phase ◽  
Double Support Phase

This paper presents a trajectory generation approach for a 7-DOF biped robot on level ground. Simultaneously rotation of feet in double support phase is considered which leads to high-speed and more similar to human being walking. The zero moment point (ZMP) stability criterion is used to ensure the stability of the bipedal walking robot. Since ZMP trajectory in human walking does not stay fixed, it needs to be a straight line shaped forward ZMP trajectory to have a natural walk. A genetic algorithm based method is proposed to obtain key parameters in trajectory generation such that the ZMP follows a predefined trajectory while minimizing power consumption. Simulation results demonstrate the effectiveness of the proposed method.

The Effect of the Toe on the Biped Robot

2013 ◽  
Vol 325-326 ◽  
pp. 1076-1082
Author(s):  
Seyed Mehdi Torklarki ◽  
Mohammad Danesh
Keyword(s):  
Reaction Force ◽  
Stability Margin ◽  
Biped Robot ◽  
Body Motion ◽  
Upper Body ◽  
Biped Robots ◽  
Double Support ◽  
The Stability ◽  
Single Support Phase ◽  
Support Phase

Evaluation of 9-DOF biped robots based on designated smooth and stable trajectories with two added toes is a challenging problem that is the focus of this paper. Simultaneously rotation of feet and toes is considered, which allows the robot to walk more efficiently and like a human being. A desired trajectory for the lower body is designed to increase the stability margin. This obtained by fitting proper polynomials at appropriate break points. Then, the upper body motion is planned based on the Zero Moment Point (ZMP) criterion to provide a stable motion for the biped robot. Next, dynamics equations are obtained for both single support phase (SSP) and double support phase (DSP). On the other hand, two biped robots, which one accompanied by toes, are also compared. Simulation results reveal that the biped robots with toes have better stability margin, less power consumption and more vertical reaction force.

A force-resisting balance control strategy for a walking biped robot under an unknown, continuous force

Robotica ◽  
2014 ◽  
Vol 34 (7) ◽  
pp. 1495-1516
Author(s):  
Yeoun-Jae Kim ◽  
Joon-Yong Lee ◽  
Ju-Jang Lee
Keyword(s):  
External Force ◽  
Control Strategy ◽  
Balance Control ◽  
Biped Robot ◽  
Second Step ◽  
Double Support ◽  
Zero Moment ◽  
External Forces ◽  
Single Support Phase ◽  
Support Phase

SUMMARYIn this paper, we propose and examine a force-resisting balance control strategy for a walking biped robot under the application of a sudden unknown, continuous force. We assume that the external force is acting on the pelvis of a walking biped robot and that the external force in the z-direction is negligible compared to the external forces in the x- and y-directions. The main control strategy involves moving the zero moment point (ZMP) of the walking robot to the center of the robot's sole resisting the externally applied force. This strategy is divided into three steps. The first step is to detect an abnormal situation in which an unknown continuous force is applied by examining the position of the ZMP. The second step is to move the ZMP of the robot to the center of the sole resisting the external force. The third step is to have the biped robot convert from single support phase (SSP) to double support phase (DSP) for an increased force-resisting capability. Computer simulations and experiments of the proposed methods are performed to benchmark the suggested control strategy.

Trajectory Optimization for Spacecraft Proximity Rendezvous Using Direct Collocation Method

2012 ◽  
Vol 433-440 ◽  
pp. 6652-6656 ◽  
Author(s):  
Tao Liu ◽  
Yu Shan Zhao ◽  
Peng Shi ◽  
Bao Jun Li
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Collocation Method ◽  
Trajectory Optimization ◽  
Collocation Methods ◽  
Nonlinear Programming Problem ◽  
Reference Orbit ◽  
Direct Collocation ◽  
Direct Collocation Method

Trajectory optimization problem for spacecraft proximity rendezvous with path constraints was discussed using direct collocation method. Firstly, the model of spacecraft proximity rendezvous in elliptic orbit optimization control problem was presented, with the dynamic equations established in the target local orbital frame, and the performance index was minimizing the total fuel consumption. After that the optimal control problem was transcribed into a large scale problem of Nonlinear Programming Problem (NLP) by means of Hermite-Simpson discretization, which was one of the direct collocation methods. Then the nonlinear programming problem was solved using MATLAB software package SNOPT. Finally, to verify this method, the fuel-optimal trajectory for finite thrust was planned for proximity rendezvous with elliptic reference orbit. Numerical simulation results demonstrate that the proposed method was feasible, and was not sensitive to the initial condition, having good robustness.

Development of multi-phase dynamic equations for a seven-link biped robot with improved foot rotation in the double support phase

2014 ◽  
Vol 229 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Farsam Farzadpour ◽  
Mohammad Danesh ◽  
Seyed M TorkLarki
Keyword(s):  
Power Consumption ◽  
Trajectory Generation ◽  
Biped Robot ◽  
Dynamic Equations ◽  
Total Power ◽  
Phase Dynamic ◽  
Double Support ◽  
Multi Phase ◽  
Support Phase ◽  
Double Support Phase

Gait generation plays a significant role in the quality of locomotion of legged robots. This paper presents the development of multi-phase dynamic equations and optimal trajectory generation for a seven-link planar-biped robot walking on the ground level with consideration of feet rotation in the double support phase. The main contribution of this paper is to increase the stability margin at the phase transition time for simultaneous feet rotation in double support phase by introducing a new style of feet rotation. First, the derivation of the dynamics equations, which is a challenging problem due to the existence of the holonomic constraints, is performed using the Lagrangian formulation. Then, an analytical solution to inverse kinematics is proposed to determine the angles of each joint. A multi-objective genetic algorithm-based optimization technique is proposed to obtain the key parameters in trajectory generation so that the zero moment point tracks a predefined stable trajectory and additionally minimizes the power consumption, which is subjected to actuators’ powers limitations. The effect of the hip height on the total power consumption is also investigated. The numerical simulations demonstrate the effectiveness of the proposed method.

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