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 Online adaptation for humanoids walking on uncertain surfaces

2017 ◽  
Vol 231 (4) ◽  
pp. 245-258 ◽  
Author(s):  
Majid Khadiv ◽  
S Ali A Moosavian ◽  
Aghil Yousefi-Koma ◽  
Hessam Maleki ◽  
Majid Sadedel
Keyword(s):  
Dynamic Balance ◽  
Bipedal Walking ◽  
Maximum Height ◽  
Task Space ◽  
Adaptation Algorithm ◽  
Double Support ◽  
Online Adaptation ◽  
Two Stages ◽  
Single Support Phase ◽  
Support Phase

In this article, an online adaptation algorithm for bipedal walking on uneven surfaces with height uncertainty is proposed. To generate walking patterns on flat terrains, the trajectories in the task space are planned to satisfy the dynamic balance and slippage avoidance constraints and also to guarantee smooth landing of the swing foot. To ensure smooth landing of the swing foot on surfaces with height uncertainty, the preplanned trajectories in the task space should be adapted. The proposed adaptation algorithm consists of two stages. In the first stage, once the swing foot reaches its maximum height, the supervisory control is initiated until the touch is detected. After the detection, the trajectories in the task space are modified to guarantee smooth landing. In the second stage, this modification is preserved during the double support phase and released in the next single support phase. Effectiveness of the proposed online adaptation algorithm is experimentally verified through realization of the walking patterns on the SURENA III humanoid robot, designed and fabricated at Center of Advanced Systems and Technologies. The walking is tested on a surface with various flat obstacles, where the swing foot is prone to land on the ground either soon or late.

Effect of Heel to Toe Walking on Time Optimal Walking of a Biped During Single Support Phase

2014 ◽  
Author(s):  
Tara Farizeh ◽  
Mohammad Jafar Sadigh
Keyword(s):  
Whole Body ◽  
Maximum Speed ◽  
Flat Foot ◽  
Double Support ◽  
Time Optimal ◽  
Foot Model ◽  
Two Phases ◽  
Single Support Phase ◽  
Toe Walking ◽  
Support Phase

Dynamic modeling of a biped has gained lots of attention during past few decades. While stability and energy consumption were among the first issues which were considered by researchers, nowadays achieving maximum speed and improving pattern of motion to reach that speed are the important targets in this field. Walking model of bipeds usually includes two phases, single support phase (SSP), in which only the stance foot is in contact with the ground while the opposite leg is swinging; and double support phase (DSP) in which the swing leg is in contact with the ground in addition to the rear foot. It is common in the simplified model of walking to assume the stance leg foot, flat during the entire SSP; but one may know that for human walking, there is also a sub-phase during SSP in which the heel of stance foot leaves the ground while the whole body is supported by toe link. Actually in this sub phase the stance leg foot rotates around the toe joint. This paper is trying to study the effect of toe-link and heel to toe walking model on dynamic and specially speed of walking compare to flat foot model.

scholarly journals Walking Gait of a Biped with a Wearable Walking Assist Device

2015 ◽  
Vol 12 (04) ◽  
pp. 1550018 ◽  
Author(s):  
Yannick Aoustin
Keyword(s):  
Dynamic Model ◽  
Unique Solution ◽  
Energy Cost ◽  
Assist Device ◽  
Double Support ◽  
Kinematic Chains ◽  
Walking Gait ◽  
Time Period ◽  
Single Support Phase ◽  
Support Phase

A ballistic walking gait is designed for a planar biped equipped with a wearable walking assist device. The biped is a seven-link planar biped with two legs, two feet, and a trunk. The wearable walking assist device is composed of a bodyweight support, two upper legs, two lower legs, and two shoes. The dynamic model of the biped with its walking assist device, containing two closed kinematic chains, is calculated by virtually cutting each of both loops at one of their point. In the single support phase, the biped with its assist device moves due to the existence of a momentum, produced mechanically, without applying active torques in the inter-link joints. The biped and this assist device are controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the six inter-link joints of the biped and in several inter-link joints of the wearable walking assist device. The following distributions of impulsive torques, in the knees or the ankles, hips and knees, hips and ankles, or knees and ankles and the fully assist device, are compared with the case of no assistance for the biped. Each time, an infinity of solutions exists to find the impulsive torques. An energy cost functional defined from these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, the assistance of the hips is a good compromise to help the biped.

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.

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.

scholarly journals Implementation and Integration of Fuzzy Algorithms for Descending Stair of KMEI Humanoid Robot

2020 ◽  
pp. 372-388
Author(s):  
Wulandari Puspita Sari ◽  
R. Sanggar Dewanto ◽  
Dadet Pramadihanto
Keyword(s):  
Humanoid Robot ◽  
Fuzzy Logic Controller ◽  
Integrated Control ◽  
Step Length ◽  
Smooth Transition ◽  
Double Support ◽  
Walking Gait ◽  
Single Support Phase ◽  
Support Phase ◽  
Double Support Phase

Locomotion of humanoid robot depends on the mechanical characteristic of the robot. Walking on descending stairs with integrated control systems for the humanoid robot is proposed. The analysis of trajectory for descending stairs is calculated by the constrains of step length stair using fuzzy algorithm. The established humanoid robot on dynamically balance on this matter of zero moment point has been pretended to be consisting of single support phase and double support phase. Walking transition from single support phase to double support phase is needed for a smooth transition cycle. To accomplish the problem, integrated motion and controller are divided into two conditions: motion working on offline planning and controller working online walking gait generation. To solve the defect during locomotion of the humanoid robot, it is directly controlled by the fuzzy logic controller. This paper verified the simulation and the experiment for descending stair of KMEI humanoid robot. 

scholarly journals Assessing Gait Stability before and after Cochlear Implantation

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Katarzyna Kaczmarczyk ◽  
Michalina Błażkiewicz ◽  
Ida Wiszomirska ◽  
Katarzyna Pietrasik ◽  
Agnieszka Zdrodowska ◽  
...  
Keyword(s):  
Cochlear Implantation ◽  
Research Question ◽  
Center Of Mass ◽  
Strong Stability ◽  
Control Group ◽  
Gait Stability ◽  
Risk Of Falls ◽  
Single Support Phase ◽  
Experimental Group ◽  
Support Phase

Background. It is known that cochlear implantation may alter the inner ear and induce vestibular disorders. Research Question. How does cochlear implantation influence gait stability? Material and Methods. An experimental group of twenty-one subjects scheduled for cochlear implantation underwent gait testing twice, on the day before cochlear implantation (BCI) and three months after cochlear implantation (ACI), using a motion capture system. A control group of 30 age-matched healthy individuals were also tested. Results. In the experimental group, the gait stability ratio (GSR) was found to improve in 17 subjects after implantation, by an average of 6%. Certain other parameters also showed statistically significant improvement between the two experimental group tests: step time (p<0.001), single-support phase walking speed (p<0.05), and center of mass (CoM) (p<0.05). Using the CoM results of the control group, we devised a stability classification system and applied it to the pre- and postimplantation subjects. After implantation, increases were seen in the number of subjects classified in interval II (strong stability) and III (weak stability). The number of subjects in interval I (perfect stability) decreased by 1 and in interval IV (no stability) by 4. Significance. (1) Although cochlear implantation intervenes in the vestibular area, we found evidence that gait stability improves in most subjects after the surgery, reducing the risk of falls. (2) We found statistically significant improvements in individual parameters (such as single-support phase time), in GSR, and in CoM. (3) Based on CoM results, we proposed a new rule-of-thumb way of classifying patients into gait stability intervals, for use in rehabilitation planning and monitoring.

CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250004 ◽  
Author(s):  
GUSTAVO MEDRANO CERDA ◽  
HOUMAN DALLALI ◽  
MARTIN BROWN
Keyword(s):  
Energy Efficiency ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Research Problem ◽  
Bipedal Walking ◽  
Constrained Motion ◽  
Double Support ◽  
Compliant Actuators ◽  
Support Phase ◽  
Double Support Phase

Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan.

scholarly journals Angular momentum regulation may dictate the slip severity in young adults

2019 ◽  
Author(s):  
Mohammad Moein Nazifi ◽  
Kurt Beschorner ◽  
Pilwon Hur
Keyword(s):  
Young Adults ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Upper Body ◽  
Group Differences ◽  
Normal Gait ◽  
Double Phase ◽  
Single Support Phase ◽  
Time Lead ◽  
Support Phase

AbstractFalls vastly affect the economy and the society with their high cost, injuries, and mortalities. Slipping is the main trigger for falling. Yet, individuals differ in their ability to recover from slips. Mild slippers can accommodate slips without falling, whereas severe slippers indicate inadequate or slow pre-or post-slip control that make them more prone to fall after a slip. Knowing the discrepancies in different kinematic and kinetic variables in mild and severe slippers helps pinpoint the adverse control responsible for severe slipping and falling. This study examined Center of Mass (COM) height, sagittal angular momentum (H), upper body kinematics, and the duration of single/double phase in mild and severe slippers for both normal walking and slipping to identify their differences and possible relationships. Possible causality of such relationships were also studied by observing the time-lead of the deviations. Twenty healthy young adults walked in a long walkway for several trials and were slipped unexpectedly. They were classified into mild and severe slippers based on their slip severity. No inter-group differences were observed in the upper extremity kinematics. It was found that mild and severe slippers do not differ in the studied variables during normal gait; however, they do show significant differences through slipping. Compared to mild slippers, sever slippers lowered their COM height following a slip, presented higher H, and shortened their single support phase (p-value<0.05 for all). Based on the time-lead observed in H over all other variables suggests that angular momentum may be the key variable in controlling slips.

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