Dynamic Walking on Uneven Terrain Using the Time-Varying Divergent Component of Motion

2015 ◽  
Vol 12 (03) ◽  
pp. 1550027 ◽  
Author(s):  
Michael A. Hopkins ◽  
Dennis W. Hong ◽  
Alexander Leonessa
Keyword(s):  
Time Integration ◽  
Whole Body ◽  
Time Varying ◽  
Dynamic Walking ◽  
Reverse Time ◽  
Double Support ◽  
Uneven Terrain ◽  
Finite Time Horizon ◽  
Smooth Transitions ◽  
Toe Walking

This paper presents a framework for dynamic walking on uneven terrain using a novel time-varying extension of the divergent component of motion (DCM). By varying the natural frequency of the DCM, we are able to achieve generic CoM height trajectories during stepping. The proposed approach computes admissible DCM reference trajectories given desired zero moment point (ZMP) plans for single and double support, permitting both flat-footed and heel-toe walking. Real-time planning is accomplished using reverse-time integration of the discretized DCM dynamics over a finite time horizon. To account for discontinuities during replanning, linear model predictive control (MPC) is implemented over a short preview window, enabling smooth transitions between steps. DCM tracking control is achieved using a time-varying proportional-integral controller based on the virtual repellent point (VRP). The effectiveness of the combined approach is verified in simulation using a 30 DOF model of THOR, a compliant torque-controlled humanoid. We demonstrate dynamic locomotion on uneven terrain and heel-toe walking using a complementary whole-body controller to track the corresponding VRP forces.

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.

OPTIMIZING FOOT CENTERS OF PRESSURE THROUGH FORCE DISTRIBUTION IN A HUMANOID ROBOT

2013 ◽  
Vol 10 (03) ◽  
pp. 1350027 ◽  
Author(s):  
PATRICK M. WENSING ◽  
GHASSAN BIN HAMMAM ◽  
BEHZAD DARIUSH ◽  
DAVID E. ORIN
Keyword(s):  
Contact Forces ◽  
Whole Body ◽  
Force Distribution ◽  
Objective Functions ◽  
Distribution Problem ◽  
Double Support ◽  
Uneven Terrain ◽  
Analytical Approaches ◽  
Convex Formulation

The force distribution problem (FDP) in robotics requires the determination of multiple contact forces to match a desired net contact wrench. For the double support case encountered in humanoids, this problem is underspecified, and provides the opportunity to optimize desired foot centers of pressure (CoPs) and forces. In different contexts, we may seek CoPs and contact forces that optimize actuator effort or decrease the tendency for foot roll. In this work, we present two formulations of the FDP for humanoids in double support, and propose objective functions within a general framework to address the variety of competing requirements for the realization of balance. As a key feature, the framework is capable to optimize contact forces for motions on uneven terrain. Solutions for the formulations developed are obtained with a commercial nonlinear optimization package and through analytical approaches on a simplified problem. Results are shown for a highly dynamic whole-body humanoid reaching motion performed on even terrain and on a ramp. A convex formulation of the FDP provides real-time solutions with computation times of a few milliseconds. While the convex formulation does not include CoPs explicitly as optimization variables, a novel objective function is developed which penalizes foot CoP solutions that approach the foot boundaries.

scholarly journals Stable dynamic walking over uneven terrain

2011 ◽  
Vol 30 (3) ◽  
pp. 265-279 ◽  
Author(s):  
Ian R Manchester ◽  
Uwe Mettin ◽  
Fumiya Iida ◽  
Russ Tedrake
Keyword(s):  
Dynamic Walking ◽  
Uneven Terrain

Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

2019 ◽  
Vol 29 (09) ◽  
pp. 1930024
Author(s):  
Sergej Čelikovský ◽  
Volodymyr Lynnyk
Keyword(s):  
Stability Region ◽  
Inverted Pendulum ◽  
Chaotic Behavior ◽  
Mechanical Systems ◽  
Small Time ◽  
Time Varying ◽  
External Forcing ◽  
Double Support ◽  
Lateral Dynamics ◽  
Detailed Mathematical Analysis

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unperturbed undamped hybrid inverted pendulum behaves inside a certain stability region periodically and its respective frequencies range from zero (close to the boundary of that stability region) to infinity (close to its double support equilibrium). Secondly, the constant lateral forcing less than a certain threshold does not affect the periodic behavior of the hybrid inverted pendulum and preserves its equilibrium at the origin. The latter is due to the hybrid nature of the equilibrium at the origin, which exists only in the Filippov sense. It is actually a trivial example of the so-called pseudo-equilibrium [Kuznetsov et al., 2003]. Nevertheless, such an observation holds only for constant external forcing and even arbitrary small time-varying external forcing may destabilize the origin. As a matter of fact, one can observe many, possibly even infinitely many, distinct chaotic attractors for a single system when the forcing amplitude does not exceed the mentioned threshold. Moreover, some general properties of the hybrid inverted pendulum are characterized through its topological equivalence to the classical pendulum. Extensive numerical experiments demonstrate the chaotic behavior of the harmonically perturbed hybrid inverted pendulum.

scholarly journals Acrophobia and visual height intolerance: advances in epidemiology and mechanisms

2020 ◽  
Vol 267 (S1) ◽  
pp. 231-240
Author(s):  
Doreen Huppert ◽  
Max Wuehr ◽  
Thomas Brandt
Keyword(s):  
Motor Behavior ◽  
Behavioral Therapy ◽  
Critical Factor ◽  
Epidemiological Studies ◽  
Visual Exploration ◽  
Whole Body ◽  
Bilateral Vestibulopathy ◽  
Double Support ◽  
Roman Antiquity ◽  
Visual Height Intolerance

AbstractHistorical descriptions of fear at heights date back to Chinese and Roman antiquity. Current definitions distinguish between three different states of responses to height exposure: a physiological height imbalance that results from an impaired visual control of balance, a more or less distressing visual height intolerance, and acrophobia at the severest end of the spectrum. Epidemiological studies revealed a lifetime prevalence of visual height intolerance including acrophobia in 28% of adults (32% in women; 25% in men) and 34% among prepubertal children aged 8–10 years without gender preponderance. Visual height intolerance first occurring in adulthood usually persists throughout life, whereas an early manifestation in childhood usually shows a benign course with spontaneous relief within years. A high comorbidity was found with psychiatric disorders (e.g. anxiety and depressive syndromes) and other vertigo syndromes (e.g. vestibular migraine, Menière’s disease), but not with bilateral vestibulopathy. Neurophysiological analyses of stance, gait, and eye movements revealed an anxious control of postural stability, which entails a co-contraction of anti-gravity muscles that causes a general stiffening of the whole body including the oculomotor apparatus. Visual exploration is preferably reduced to fixation of the horizon. Gait alterations are characterized by a cautious slow walking mode with reduced stride length and increased double support phases. Anxiety is the critical factor in visual height intolerance and acrophobia leading to a motor behavior that resembles an atavistic primitive reflex of feigning death. The magnitude of anxiety and neurophysiological parameters of musculoskeletal stiffening increase with increasing height. They saturate, however, at about 20 m of absolute height above ground for postural symptoms and about 40 m for anxiety (70 m in acrophobic participants). With respect to management, a differentiation should be made between behavioral recommendations for prevention and therapy of the condition. Recommendations for coping strategies target behavioral advices on visual exploration, control of posture and locomotion as well as the role of cognition. Treatment of severely afflicted persons with distressing avoidance behavior mainly relies on behavioral therapy.

Dynamic Analysis of Handling Compliant Sheet-Metal Blanks

2007 ◽  
Author(s):  
Gene Y. Liao
Keyword(s):  
Sheet Metal ◽  
Stiffness Matrix ◽  
Material Handling ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonlinear Finite Element ◽  
Time Varying ◽  
End Effector ◽  
Part Quality ◽  
Element Technique

Automating material handling of flexible sheet-metal blanks in stamping process requires attention due to its significant impact on product quality and productivity. This paper investigated the capability of a fully dynamic and nonlinear finite element technique in developing virtual material handling process of compliant sheet-metal blanks subject to time varying movability conditions. The technique used explicit time integration to avoid the formulation of stiffness matrix by a direct integration of the equations of motion. The influence of holding end-effector layout scheme and movability conditions on the final part quality was investigated.

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