Tracking a joint path for the walk of an underactuated 
biped

This paper presents a control law for the tracking of a cyclic reference path by an under-actuated biped robot. The robot studied is a five-link planar biped. The degree of under-actuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. To achieve this objective, we consider a parametrized control. When a joint path is given, a five degree of freedom biped in single support becomes similar to a one degree of freedom inverted pendulum. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple analytical conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced. These conditions are defined on the reference trajectory path. The analytical considerations are illustrated with some simulation results.

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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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Effect of circular arc feet on a control law for a biped

Robotica ◽

10.1017/s0263574708005006 ◽

2009 ◽

Vol 27 (4) ◽

pp. 621-632 ◽

Cited By ~ 8

Author(s):

T. Kinugasa ◽

C. Chevallereau ◽

Y. Aoustin

Keyword(s):

Degrees Of Freedom ◽

Temporal Evolution ◽

Contact Point ◽

Basin Of Attraction ◽

Control Law ◽

Leg Length ◽

Circular Arc ◽

Geometric Evolution ◽

Cyclic Motion ◽

The Stability

SUMMARYThe purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincaré map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.

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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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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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Stable walking control of a 3D biped robot with foot rotation

Robotica ◽

10.1017/s0263574713000866 ◽

2013 ◽

Vol 32 (4) ◽

pp. 551-570 ◽

Cited By ~ 9

Author(s):

Ting Wang ◽

Christine Chevallereau ◽

David Tlalolini

Keyword(s):

Linear Combination ◽

Biped Robot ◽

Control Law ◽

Reference Trajectory ◽

Joint Angles ◽

Flat Foot ◽

Loop Control ◽

Walking Gait ◽

Initial Errors ◽

Rotation Phase

SUMMARYIn order to obtain a more human-like walking and less energy consumption, ait foot rotation phaseis considered in the single support phase of a 3D biped robot, in which the stance heel lifts from the ground and the stance foot rotates about the toe. Since there is no actuation at the toe, a walking phase of the robot is composed of a fully actuated phase and an under-actuated phase. The objective of this paper is to present an asymptotically stable walking controller that integrates these two phases. To get around the under-actuation issue, a strict monotonic parameter of the robot is used to describe the reference trajectory instead of using the time parameter. The overall control law consists of a zero moment point (ZMP) controller, a swing ankle rotation controller and a partial joint angles controller. The ZMP controller guarantees that the ZMP follows the desired ZMP. The swing ankle rotation controller assures a flat-foot impact at the end of the swinging phase. Each of these controllers creates two constraints on joint accelerations. In order to determine all the desired joint accelerations from the control law, a partial joint angles controller is implemented. A word “partial” emphasizes the fact that not all the joint angles can be controlled. The outputs controlled by a partial joint angles controller are defined as a linear combination of all the joint angles. The most important question addressed in this paper is how this linear combination can be defined in order to ensure walking stability. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. Finally, simulation results validate the effectiveness of the control law even in presence of initial errors and modelling errors.

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