Stability Region-Based Analysis of Walking and Push Recovery Control

2021 ◽  
Vol 13 (3) ◽  
Author(s):  
William Z. Peng ◽  
Hyunjong Song ◽  
Joo H. Kim
Keyword(s):  
Sagittal Plane ◽  
Center Of Mass ◽  
Biped Robot ◽  
Optimization Method ◽  
Order System ◽  
Double Support ◽  
Push Recovery ◽  
One Step ◽  
To Come ◽  
Time Required

Abstract To achieve walking and push recovery successfully, a biped robot must be able to determine if it can maintain its current contact configuration or transition into another one without falling. In this study, the ability of a humanoid robot to maintain single support (SS) or double support (DS) contact and to achieve a step are represented by balanced and steppable regions, respectively, as proposed partitions of an augmented center-of-mass-state space. These regions are constructed with an optimization method that incorporates full-order system dynamics, system properties such as kinematic and actuation limits, and contact interactions with the environment in the two-dimensional sagittal plane. The SS balanced, DS balanced, and steppable regions are obtained for both experimental and simulated walking trajectories of the robot with and without the swing foot velocity constraint to evaluate the contribution of the swing leg momentum. A comparative analysis against one-step capturability, the ability of a biped to come to a stop after one step, demonstrates that the computed steppable region significantly exceeds the one-step capturability of an equivalent reduced-order model. The use of balanced regions to characterize the full balance capability criteria of the system and benchmark controllers is demonstrated with three push recovery controllers. The implemented hip–knee–ankle controller resulted in improved stabilization with respect to decreased foot tipping and time required to balance, relative to an existing hip–ankle controller and a gyro balance feedback controller.

Stability Region-Based Analysis of Walking and Push Recovery Control

2020 ◽  
Author(s):  
William Z. Peng ◽  
Hyunjong Song ◽  
Joo H. Kim
Keyword(s):  
Biped Robot ◽  
Step Length ◽  
Stability Control ◽  
Human Gait ◽  
Biped Robots ◽  
Reduced Order ◽  
Double Support ◽  
Push Recovery ◽  
The Stability ◽  
Time Required

Abstract Push recovery is a vital aspect of balance stability control in biped robots. In this work, the response of a biped system to unexpected external perturbations is analyzed for different tasks and controllers using stability criteria based on balanced and steppable regions. The steppable region for a given step length and the balanced regions for single and double support contacts are constructed for a biped robot using optimization with its system dynamics, kinematic limits, actuation limits, and contact interactions with the environment. The regions are compared with those of a human subject to demonstrate that human gait exhibits unbalanced (but steppable) phases largely absent in robotic gait. These regions are also applied to a comparative analysis against capturability, where the computed steppable region is significantly larger than the capture region of an equivalent reduced-order model. The stability regions are also used to compare the performance of controllers during a double support balancing task. The implemented hip, knee, and ankle strategy-based controller led to improved stabilization — i.e., decreased foot tipping and time required to balance — relative to an existing hip and ankle controller and a gyro feedback controller. The proposed approaches are applicable to the analysis of any bipedal task and stability controller in general.

scholarly journals Simulation of Disturbance Recovery Based on MPC and Whole-Body Dynamics Control of Biped Walking

Sensors ◽  
2020 ◽  
Vol 20 (10) ◽  
pp. 2971 ◽  
Author(s):  
Xuanyang Shi ◽  
Junyao Gao ◽  
Yizhou Lu ◽  
Dingkui Tian ◽  
Yi Liu
Keyword(s):  
Large Scale ◽  
Center Of Mass ◽  
Biped Robot ◽  
Optimization Method ◽  
Stability Control ◽  
Body Motion ◽  
Whole Body ◽  
Human Beings ◽  
Foot Placement ◽  
Body Dynamics

Biped robots are similar to human beings and have broad application prospects in the fields of family service, disaster rescue and military affairs. However, simplified models and fixed center of mass (COM) used in previous research ignore the large-scale stability control ability implied by whole-body motion. The present paper proposed a two-level controller based on a simplified model and whole-body dynamics. In high level, a model predictive control (MPC) controller is implemented to improve zero moment point (ZMP) control performance. In low level, a quadratic programming optimization method is adopted to realize trajectory tracking and stabilization with friction and joint constraints. The simulation shows that a 12-degree-of-freedom force-controlled biped robot model, adopting the method proposed in this paper, can recover from a 40 Nm disturbance when walking at 1.44 km/h without adjusting the foot placement, and can walk on an unknown 4 cm high stairs and a rotating slope with a maximum inclination of 10°. The method is also adopted to realize fast walking up to 6 km/h.

Validating Determinants for an Alternate Foot Placement Selection Algorithm During Human Locomotion in Cluttered Terrain

2007 ◽  
Vol 98 (4) ◽  
pp. 1928-1940 ◽  
Author(s):  
Renato Moraes ◽  
Fran Allard ◽  
Aftab E. Patla
Keyword(s):  
Dynamic Stability ◽  
Center Of Mass ◽  
Frontal Plane ◽  
Human Locomotion ◽  
The Body ◽  
Selection Algorithm ◽  
Foot Placement ◽  
Double Support ◽  
One Step ◽  
Base Of Support

The goal of this study was to validate dynamic stability and forward progression determinants for the alternate foot placement selection algorithm. Participants were asked to walk on level ground and avoid stepping, when present, on a virtual white planar obstacle. They had a one-step duration to select an alternate foot placement, with the task performed under two conditions: free (participants chose the alternate foot placement that was appropriate) and forced (a green arrow projected over the white planar obstacle cued the alternate foot placement). To validate the dynamic stability determinant, the distance between the extrapolated center of mass (COM) position, which incorporates the dynamics of the body, and the limits of the base of support was calculated in both anteroposterior (AP) and mediolateral (ML) directions in the double support phase. To address the second determinant, COM deviation from straight ahead was measured between adaptive and subsequent steps. The results of this study showed that long and lateral choices were dominant in the free condition, and these adjustments did not compromise stability in both adaptive and subsequent steps compared with the short and medial adjustments, which were infrequent and adversely affected stability. Therefore stability is critical when selecting an alternate foot placement in a cluttered terrain. In addition, changes in the plane of progression resulted in small deviations of COM from the endpoint goal. Forward progression of COM was maintained even for foot placement changes in the frontal plane, validating this determinant as part of the selection algorithm.

scholarly journals Dynamic and static stability in hexapedal runners.

1994 ◽  
Vol 197 (1) ◽  
pp. 251-269 ◽  
Author(s):  
L H Ting ◽  
R Blickhan ◽  
R J Full
Keyword(s):  
Dynamic Stability ◽  
Center Of Pressure ◽  
Center Of Mass ◽  
Stability Margin ◽  
Static Stability ◽  
Double Support ◽  
Wide Range ◽  
One Step ◽  
Energy And Momentum ◽  
Base Of Support

Stability is fundamental to the performance of terrestrial locomotion. Running cockroaches met the criteria for static stability over a wide range of speeds, yet several locomotor variables changed in a way that revealed an increase in the importance of dynamic stability as speed increased. Duty factors (the fraction of time that a leg spends on the ground relative to the stride period) decreased to 0.5 and below with an increase in speed. The duration of double support (i.e. when both tripods, or all six legs, were on the ground) decreased significantly with an increase in speed. All legs had similar touch-down phases in the tripod, but the shortest leg, the front one, lifted off before the middle and the rear leg, so that only two legs of the tripod were in contact with the ground at the highest speeds. Per cent stability margin (the shortest distance from the center of gravity to the boundaries of support, normalized to the maximum possible stability margin) decreased with increasing speed from 60% at 10 cms-1 to values less than zero at speeds faster than 50 cms-1, indicating instances of static instability at fast speeds. The center of mass moved rearward or posteriorly with respect to the base of support as speed increased. Moments about the center of mass, as shown by the center of pressure (the equivalent of a single 'effective' leg), were variable, but were balanced by opposing moments over a stride. Thus, hexapods can exploit the advantages of both static and dynamic stability. Static or quasi-static assumptions alone were insufficient to explain straight-ahead, constant-speed locomotion and may hinder discovery of behaviors that are dynamic, where kinetic energy and momentum can act as a bridge from one step to the next.

scholarly journals Arms Swing Effects on a Walking Planar Biped

2012 ◽  
Author(s):  
Bassel Kaddar ◽  
Yannick Aoustin ◽  
Christine Chevallereau
Keyword(s):  
Energy Consumption ◽  
Parametric Optimization ◽  
Energy Criterion ◽  
Biped Robot ◽  
Optimization Method ◽  
Robot Kinematics ◽  
Kinematics And Dynamics ◽  
Flat Foot ◽  
Walking Gait ◽  
One Step

A walking gait is designed for a planar biped with two identical three-link legs, a trunk and two one-link arms. This nine-link biped is controlled via eight torques to obtain one step of a cyclic gait. The scope of this paper is to investigate the effects of arms swing on the energy consumption during walking of a fully actuated planar biped robot. Kinematics and dynamics of a biped, HYDROID, are used for this study. Desired gaits are considered to be cyclic having single support phases separated by flat foot impacts. Different evolutions of the arms: arms held, arms bound and arms swing are compared. For each case, we use a parametric optimization method with constraints to produce reference cyclic trajectories according to an energy criterion. The numerical results show that this criterion is lower in the case where the arms swing.

scholarly journals Sliding Balance Control of a Point-Foot Biped Robot Based on a Dual-Objective Convergent Equation

2021 ◽  
Vol 11 (9) ◽  
pp. 4016
Author(s):  
Yizhou Lu ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Dingkui Tian ◽  
Yi Liu
Keyword(s):  
Balance Control ◽  
Center Of Mass ◽  
Biped Robot ◽  
Optimization Method ◽  
Contact Forces ◽  
Joint Torque ◽  
Whole Body ◽  
Physical Constraints ◽  
Equilibrium Control ◽  
Control Framework

The point-foot biped robot is highly adaptable to and can move rapidly on complex, non-structural and non-continuous terrain, as demonstrated in many studies. However, few studies have investigated balance control methods for point-foot sliding on low-friction terrain. This article presents a control framework based on the dual-objective convergence method and whole-body control for the point-foot biped robot to stabilize its posture balance in sliding. In this control framework, a dual-objective convergence equation is used to construct the posture stability criterion and the corresponding equilibrium control task, which are simultaneously converged. Control tasks are then carried out through the whole-body control framework, which adopts an optimization method to calculate the viable joint torque under the physical constraints of dynamics, friction and contact forces. In addition, this article extends the proposed approach to balance control in standing recovery. Finally, the capabilities of the proposed controller are verified in simulations in which a 26.9-kg three-link point-foot biped robot (1) slides over a 10∘ trapezoidal terrain, (2) slides on terrain with a sinusoidal friction coefficient between 0.05 and 0.25 and (3) stands and recovers from a center-of-mass offset of 0.02 m.

Generating globally optimised sagittal gait cycles of a biped robot

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 199-210 ◽  
Author(s):  
Tarik Saidouni ◽  
Guy Bessonnet
Keyword(s):  
Dynamic Models ◽  
Sagittal Plane ◽  
Biped Robot ◽  
Step Length ◽  
Gait Pattern ◽  
Double Support ◽  
Locomotion System ◽  
Motion Time ◽  
Joint Coordinates ◽  
Finite Set

The paper is aimed at generating optimal gait cycles in the sagittal plane of a biped, the locomotion system of which has anthropomorphic characteristics. Both single and double support phases are globally optimised, considering incompletely specified transition postural configurations from one phase to the other. An impactless heel-touch is prescribed. Full dynamic models are developed for both gait phases. They are completed by specific constraints attached to the unilaterality of contact with the supporting ground.A parametric optimisation method is implemented. The biped joint coordinates are approximated by cubic splines functions connected at uniformly distributed knots along the motion time. The finite set of unknowns consists of the joint coordinate values at knots, some gait pattern parameters at phase transitions, and the motion time of each phase. The step length is adjusted to the prescribed gait speed by the optimisation process. Numerical simulations concerning slow and fast optimal gaits are presented and discussed.

An optimization method for the reference trajectory of parametric excitation walking

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 585-593 ◽  
Author(s):  
Kouichi Taji ◽  
Yoshihisa Banno ◽  
Yuji Harata
Keyword(s):  
Parametric Excitation ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Biped Robot ◽  
Optimization Method ◽  
Search Method ◽  
Walking Ability ◽  
Reference Trajectory ◽  
Spline Curves ◽  
Walking Performance

SUMMARYIn parametric excitation walking, up-and-down motion of the center of mass restores mechanical energy and sustainable gait is generated. Not only walking performance but also walking ability strongly depends on the reference trajectory of the center of mass. In this paper, we propose an optimization method for the reference trajectory, in which the reference trajectory is confined to the quartic spline curves and the parameters of spline curves are optimized by a local search method usually used in combinatorial optimization. We apply the proposed method to a kneed biped robot and find some remarkably interesting results by numerical simulations.

scholarly journals Trajectory Planning of Flexible Walking for Biped Robots Using Linear Inverted Pendulum Model and Linear Pendulum Model

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1082
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Trajectory Planning ◽  
Inverted Pendulum ◽  
Negative Impact ◽  
Center Of Mass ◽  
Biped Robot ◽  
Biped Robots ◽  
Double Support ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Support Phase

Linear inverted pendulum model (LIPM) is an effective and widely used simplified model for biped robots. However, LIPM includes only the single support phase (SSP) and ignores the double support phase (DSP). In this situation, the acceleration of the center of mass (CoM) is discontinuous at the moment of leg exchange, leading to a negative impact on walking stability. If the DSP is added to the walking cycle, the acceleration of the CoM will be smoother and the walking stability of the biped will be improved. In this paper, a linear pendulum model (LPM) for the DSP is proposed, which is similar to LIPM for the SSP. LPM has similar characteristics to LIPM. The dynamic equation of LPM is also linear, and its analytical solution can be obtained. This study also proposes different trajectory-planning methods for different situations, such as periodic walking, adjusting walking speed, disturbed state recovery, and walking terrain-blind. These methods have less computation and can plan trajectory in real time. Simulation results verify the effectiveness of proposed methods and that the biped robot can walk stably and flexibly when combining LIPM and LPM.

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