Planar Five-link Biped Robot Movement over a Stepped Surface

Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.Modeling the anthropomorphic robot movement is of great interest to researchers all over the world. At the same time, the movement control of a walking mechanism is always a high dimension challenge. The difficulty with the anthropomorphic robot control is also caused by the fact that such a mechanism has always a hybrid dynamics and represents a sequential change of two phases – the single support phase and the double support phase (phase of changing robot’s leg). At the single support phase and at another phase the behavior of the biped robot is described by a system of ordinary differential equations and by a system of linear algebraic equations, respectively.The task of biped robot movement control has been studied in detail for the case when the robot moves over the horizontal surface. Obstacles make the task significantly complicated. The paper considers the movement control of the biped robot over the surface that is a periodic alternation of horizontal sections and obstacles. The obstacles represent steps of the same height known. It is assumed that the lengths of horizontal sections and steps are known as well. The objective is to create a control that provides robot’s periodic movement over the specified surface according to inherent characteristics of a walking human.For the single support phase, the outputs are proposed, the equality of which to zero corresponds to the robot’s movement with a given set of characteristics. The paper presents the feedback controls that stabilize the proposed outputs for a finite amount of time. By choosing the feedback parameters, it is possible to adjust the stabilization time so that the outputs become equal to zero when reached the end of each step.It is shown that for the chosen control law, the problem of constructing the control of robot’s periodic movement is reduced to the solution of a nonlinear equation. In the paper, we discuss the approaches to solving this equation and present the results of numerical simulation.The results obtained can be used to solve the problem of providing control of the biped robot movement over the surfaces with obstacles of a more complicated shape.

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

Robotica ◽

10.1017/s0263574714002616 ◽

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.

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Optimal reference trajectories for walking and running of a biped robot

Robotica ◽

10.1017/s0263574701003307 ◽

2001 ◽

Vol 19 (5) ◽

pp. 557-569 ◽

Cited By ~ 182

Author(s):

C. Chevallereau ◽

Y. Aoustin

Keyword(s):

Biped Robot ◽

Physical Parameters ◽

Polynomial Functions ◽

Minimal Energy ◽

Double Support ◽

Cyclic Motion ◽

Under Construction ◽

Single Support Phase ◽

Reference Trajectories ◽

Support Phase

The objective of this study is to obtain optimal cyclic gaits for a biped robot without actuated ankles. Two types of motion are studied: walking and running. For walking, the gait is composed uniquely of successive single support phases and instantaneous double support phases that are modelled by passive impact equations. The legs swap their roles from one single support phase to the next one. For running, the gait is composed of stance phases and flight phases. A passive impact with the ground exists at the end of flight. During each phase the evolution of m joints variables is assumed to be polynomial functions, m is the number of actuators. The evolution of the other variables is deduced from the dynamic model of the biped. The coefficients of the polynomial functions are chosen to optimise criteria and to insure cyclic motion of the biped. The chosen criteria are: maximal advance velocity, minimal torque, and minimal energy. Furthermore, the optimal gait is defined with respect to given performances of actuators: The torques and velocities at the output of the gear box are bounded. For this study, the physical parameters of a prototype, which is under construction, are used. Optimal walking and running are defined. The running is more efficient for high velocities than the walking with respect to the studied criteria.

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The Effect of the Toe on the Biped Robot

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.325-326.1076 ◽

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.

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Referential ZMP Trajectory for Minimizing Variation of COG Velocity in Single Support Phase of Biped Robot

IEEJ Transactions on Industry Applications ◽

10.1541/ieejias.128.661 ◽

2008 ◽

Vol 128 (5) ◽

pp. 661-668 ◽

Cited By ~ 4

Author(s):

Tomoya Sato ◽

Kouhei Ohnishi

Keyword(s):

Biped Robot ◽

Single Support Phase ◽

Support Phase

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

Applied Sciences ◽

10.3390/app11052342 ◽

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.

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

Volume 3: Biomedical and Biotechnology Engineering ◽

10.1115/imece2014-38214 ◽

2014 ◽

Cited By ~ 1

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.

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Walking Gait of a Biped with a Wearable Walking Assist Device

International Journal of Humanoid Robotics ◽

10.1142/s0219843615500188 ◽

2015 ◽

Vol 12 (04) ◽

pp. 1550018 ◽

Cited By ~ 6

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.

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