ZMP-Based Trajectory Generation for Bipedal Robots Using Quadratic Programming

2020 ◽  
pp. 266-285
Author(s):  
Sergei Savin
Keyword(s):  
Numerical Simulation ◽  
Quadratic Programming ◽  
Center Of Mass ◽  
Trajectory Generation ◽  
Bipedal Walking ◽  
Walking Robots ◽  
Bipedal Robots ◽  
Change Of Variables ◽  
Viable Solution ◽  
Modern Optimization

In this chapter, the problem of trajectory generation for bipedal walking robots is considered. A number of modern techniques are discussed, and their limitations are shown. The chapter focuses on zero-moment point methods for trajectory generation, where the desired trajectory of that point can be used to allow the robot to keep vertical stability if followed, and presents an instrument to calculate the desired trajectory for the center of mass for the robot. The chapter presents an algorithm based on quadratic programming, with an introduction of a slack variable to make the problem feasible and a change of variables to improve the numeric properties of the resulting optimization problem. Modern optimization tools allow one to solve such problems in real time, making it a viable solution for trajectory planning for the walking robots. The chapter shows a few results from the numerical simulation made for the algorithm, demonstrating its properties.

Biped Walking Control Based on Quadratic Programming and Differential Inequalities

2020 ◽  
Author(s):  
Stella Diniz Urban ◽  
Bruno Vilhena Adorno
Keyword(s):  
Quadratic Programming ◽  
Center Of Mass ◽  
Bipedal Walking ◽  
Differential Inequalities ◽  
Double Support ◽  
Cycle Simulation ◽  
Minimum Height ◽  
Joint Limits ◽  
Single Support Phase ◽  
Support Phase

This paper presents a novel method to control a bipedal walking based on quadratic programming and differential inequalities using geometric primitives. We allow the center of mass to move anywhere inside the support polygon during the walking cycle, as opposed to classic methods, which usually rely on tracking a desired trajectory for the zero moment point. The constraints keep the robot balance, the pelvis above a minimum height, and prevent the violation of joint limits during the complete walking cycle. Simulation results using the legs of the Poppy humanoid robot show that the trajectories of the closed-loop system converge to the desired center of mass position during the double support phase and the swing foot's trajectories converge to the desired pose during the single support phase while all constraints are obeyed.

scholarly journals Bipedal Walking Trajectory Generation Using Tchebychev Method

2011 ◽  
Vol 2-3 ◽  
pp. 414-418 ◽  
Author(s):  
Yeoun Jae Kim ◽  
Joon Yong Lee ◽  
Ju Jang Lee
Keyword(s):  
Quadratic Programming ◽  
Hip Joint ◽  
Sequential Quadratic Programming ◽  
Trajectory Generation ◽  
Biped Robot ◽  
Bipedal Walking ◽  
Cost Functions ◽  
The Given

It is still important and difficult for a biped robot to optimally generate the stable walking trajectory, because the mechanical limitations of the given biped robot should be also considered carefully. In this paper, we assume that different walking trajectories enable to be generated according to various set of weights of torques loaded in each partial joint (e.g., ankle, knee, and hip joint). We present a method for generating various bipedal walking trajectories corresponding to a set of weighted torques. For this purpose, Tchebychev method and sequential quadratic programming are employed to optimize single cost functions consisting in a set of weight torques. Some notations and constraints introduced in [1] are used and modified in this paper.

scholarly journals Vertical Jumping for Legged Robot Based on Quadratic Programming

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3679
Author(s):  
Dingkui Tian ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Yizhou Lu ◽  
Chuzhao Liu
Keyword(s):  
Quadratic Programming ◽  
Stance Phase ◽  
Center Of Mass ◽  
Maximum Error ◽  
Legged Robot ◽  
Flight Phase ◽  
Programming Framework ◽  
Vertical Jumping ◽  
Control Schemes ◽  
And Control

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

Contact-Dependent Balance Stability of Walking Robots

2017 ◽  
Author(s):  
Carlotta Mummolo ◽  
William Z. Peng ◽  
Carlos Gonzalez ◽  
Joo H. Kim
Keyword(s):  
Stability Region ◽  
Balance Control ◽  
Center Of Mass ◽  
Biped Robot ◽  
Walking Robots ◽  
Ground Contact ◽  
Robotic Platform ◽  
Contact Configuration ◽  
The Stability ◽  
Balance Stability

A novel theoretical framework for the identification of the balance stability regions of biped systems is implemented on a real robotic platform. With the proposed method, the balance stability capabilities of a biped robot are quantified by a balance stability region in the state space of center of mass (COM) position and velocity. The boundary of such a stability region provides a threshold between balanced and falling states for the robot by including all possible COM states that are balanced with respect to a specified feet/ground contact configuration. A COM state outside of the stability region boundary is the sufficient condition for a falling state, from which a change in the specified contact configuration is inevitable. By specifying various positions of the robot’s feet on the ground, the effects of different contact configurations on the robot’s balance stability capabilities are investigated. Experimental walking trajectories of the robot are analyzed in relationship with their respective stability boundaries, to study the robot balance control during various gait phases.

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