Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Control Method ◽  
Basin Of Attraction ◽  
Time Derivative ◽  
Energetic Efficiency ◽  
Underactuated Mechanical Systems ◽  
Cost Of Transport ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Step Velocity ◽  
Walking Speeds

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree-of-freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the time derivative of the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by (1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, (2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and (3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the observed trends are consistent across different walking speeds.

Velocity Decomposition-Enhanced Control for Point and Curved-Foot Planar Bipeds Experiencing Velocity Disturbances

2018 ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Control Method ◽  
Basin Of Attraction ◽  
Energetic Efficiency ◽  
Underactuated Mechanical Systems ◽  
Cost Of Transport ◽  
Biped Robots ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Step Velocity ◽  
Walking Speeds

This paper extends the use of velocity decomposition of underactuated mechanical systems to the design of an enhanced hybrid zero dynamics (HZD)-based controller for biped robots. To reject velocity disturbances in the unactuated degree of freedom, a velocity decomposition-enhanced controller implements torso and leg offsets that are proportional to the error in the unactuated velocity. The offsets are layered on top of an HZD-based controller to preserve simplicity of implementation. Simulation results with a point-foot, three-link planar biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. Curved feet are implemented in simulation and show that the proposed control method is valid for both point-foot and curved-foot planar bipeds. Performance of each controller is assessed by 1) the magnitude of the disturbance it can reject by numerically computing the basin of attraction, 2) the speed of return to nominal step velocity following a disturbance at every point of the gait cycle, and 3) the energetic efficiency, which is measured via the specific cost of transport. Several gaits are analyzed to demonstrate that the trends observed in 1) through 3) are consistent across different walking speeds.

scholarly journals Terrain-blind walking of planar underactuated bipeds via velocity decomposition-enhanced control

2019 ◽  
Vol 38 (10-11) ◽  
pp. 1307-1323 ◽  
Author(s):  
Martin Fevre ◽  
Bill Goodwine ◽  
James P Schmiedeler
Keyword(s):  
Feedback Control ◽  
Biped Robot ◽  
Rate Of Change ◽  
Energetic Cost ◽  
Practical Implementation ◽  
Leg Length ◽  
Cost Of Transport ◽  
Velocity Decomposition ◽  
Novel Approach ◽  
Hybrid Zero Dynamics

In this article, we develop and assess a novel approach for the control of underactuated planar bipeds that is based on velocity decomposition. The new controller employs heuristic rules that mimic the functionality of transverse linearization feedback control and that can be layered on top of a conventional hybrid zero dynamics (HZD)-based controller. The heuristics sought to retain HZD-based control’s simplicity and enhance disturbance rejection for practical implementation on realistic biped robots. The proposed control strategy implements a feedback on the time rate of change of the decomposed uncontrolled velocity and is compared with conventional HZD-based control and transverse linearization feedback control for both vanishing and non-vanishing disturbances. Simulation studies with a point-foot, three-link biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. For the non-vanishing case, the velocity decomposition-enhanced controller outperforms HZD-based control, but takes fewer steps on average before failure than transverse linearization feedback control when walking on uneven terrain without visual perception of the ground. The findings were validated experimentally on a planar, five-link biped robot for eight different uneven terrains. The velocity decomposition-enhanced controller outperformed HZD-based control while maintaining a relatively low specific energetic cost of transport (~0.45). The biped robot “blindly” traversed uneven terrains with changes in terrain height accumulating to 5% of its leg length using the stand-alone low-level controller.

scholarly journals A Control Method for the Ultrasonic Spot Welding of Fiber-Reinforced Thermoplastic Laminates through the Weld-Power Time Derivative

2018 ◽  
Vol 3 (1) ◽  
pp. 1 ◽  
Author(s):  
Shahan Tutunjian ◽  
Martin Dannemann ◽  
Fabian Fischer ◽  
Oğuzhan Eroğlu ◽  
Niels Modler
Keyword(s):  
Spot Welding ◽  
Control Method ◽  
Time Derivative ◽  
Welding Process ◽  
Microscopic Analysis ◽  
Fiber Reinforced ◽  
Spot Center ◽  
Computed Tomography Scans ◽  
Time Trace ◽  
Reinforced Thermoplastics

It was found that the ultrasonic spot welding may serve as an efficient method to join relative large thin-walled parts made of fiber-reinforced thermoplastics. In this study, a new control method for the ultrasonic spot-welding process was investigated. It was found that, when welding fiber-reinforced thermoplastic laminates without energy directors, overheating and decomposition of the polymer at the weld spot occurred. The occurrence of the overheating took place at unpredictable times during welding. It was observed that the time trace of the consumed power curve by the welder follows a similar pattern as the time trace of the temperature in the weld spot center. Based on this observation, a control system was developed. The time derivative of the welder power was monitored in real time and, as soon as it exceeded a critical value, the ultrasonic vibration amplitude was actively adjusted through a microcontroller. The controlling of the ultrasonic welding process forced the temperature in the weld spot to remain in an adequate range throughout the welding duration for the polymer diffusion to occur. The results of the controlled welding process were evaluated by means of weld temperature measurements, computed tomography scans, and microscopic analysis of the weld spot fracture surfaces.

Heart energetic efficiency in O2-exposed rats studied in isolated working heart

1992 ◽  
Vol 73 (6) ◽  
pp. 2289-2296 ◽  
Author(s):  
R. Arieli ◽  
S. A. Ben-Haim ◽  
G. Hayam ◽  
Y. Edoute
Keyword(s):  
Exposure Time ◽  
Time Derivative ◽  
Left Ventricular Pressure ◽  
Left Ventricular ◽  
Pulmonary Insufficiency ◽  
Energetic Efficiency ◽  
Normobaric Hyperoxia ◽  
Mechanical Power Output ◽  
The Individual ◽  
Working Heart

Death in normobaric hyperoxia was related in the past to pulmonary insufficiency of the edematous lung. However, high arterial O2 tension on final collapse led to the suggestion that the heart and not the lung is the first organ that fails. We measured aortic flow, coronary flow, left ventricular pressure, affluent and effluent PO2, PCO2, and pH in the working heart excised from control and normobaric O2-exposed rats (51–63 h). The oxygen consumption (VO2) of experimental hearts was not different from control, but mechanical power output (PVAP) (calculated from pressure-volume area) was reduced as a function of O2 exposure time. Myocardial contractility indexes, maximal elastance and maximal time derivative of pressure, increased as a function of O2 exposure time, being below control values after 50 h and above control values after 60 h. The individual slopes for the regression of VO2 vs. PVAP rose as a function of exposure time from values below control after 50 h exposure to values above control after 60 h. Energetic efficiency (PVAP/VO2) decreased as a function of O2 exposure time and points to possible heart failure in the intact animal. After 50 h O2 exposure the heart was energetically more efficient than the control. Possible changes in the heart are discussed.

scholarly journals A new arc-length control method based on the rates of the internal and the dissipated energy

2016 ◽  
Vol 33 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Stefan May ◽  
Julien Vignollet ◽  
René de Borst
Keyword(s):  
Control Method ◽  
Time Derivative ◽  
Phase Field Model ◽  
Second Law Of Thermodynamics ◽  
Dissipated Energy ◽  
Control Procedure ◽  
Arc Length ◽  
Interface Elements ◽  
Content Type ◽  
Two Parameters

Purpose – The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach – In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings – The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-through and/or snap-back phenomena. Originality/value – A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way. The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

Individual Leg Muscle Contributions to the Cost of Walking: Effects of Age and Walking Speed

2017 ◽  
Vol 25 (2) ◽  
pp. 295-304 ◽  
Author(s):  
Patricio A. Pincheira ◽  
Lauri Stenroth ◽  
Janne Avela ◽  
Neil J. Cronin
Keyword(s):  
Energy Cost ◽  
Young Group ◽  
Energetic Cost ◽  
Elderly Subjects ◽  
Older Individuals ◽  
Cost Of Transport ◽  
Leg Muscles ◽  
Lower Limb Muscles ◽  
Walking Speeds ◽  
The Cost

This study examined the contributions of individual muscles to changes in energetic cost of transport (COT) over seven walking speeds, and compared results between healthy young and elderly subjects. Twenty six participants (13 young aged 18–30; 13 old aged 70–80) were recruited. COT (O2/kg body mass/km) was calculated by standardizing the mean oxygen consumption recorded during steady state walking. Electromyography signals from 10 leg muscles were used to calculate the cumulative activity required to traverse a unit of distance (CMAPD) for each muscle at each speed. In the old group CMAPD was correlated with COT, presented higher and more variable values, and showed greater increases around optimal speed for all studied muscles. Soleus CMAPD was independent of speed in the young group, but this was not evident with aging. Greater energy cost of walking in older individuals seems to be attributable to increased energy cost of all lower limb muscles.

CONTROLLING OSCILLATION AMPLITUDES VIA FEEDBACK

2000 ◽  
Vol 10 (12) ◽  
pp. 2815-2822 ◽  
Author(s):  
DANIEL W. BERNS ◽  
JORGE L. MOIOLA ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Nonlinear Systems ◽  
State Feedback ◽  
Control Method ◽  
Classical Model ◽  
Time Derivative ◽  
Control Law ◽  
Derivative Term ◽  
Nonlinear Control Law ◽  
Nonlinear State

This paper studies feedback control of limit cycle amplitudes in nonlinear systems. A graphical approach to bifurcation control is first briefly introduced, followed by the derivation of a nonlinear control law. Then, a suitable implementation of the design is developed via an approximation of the time-derivative term in the nonlinear state feedback controller. A classical model is finally simulated for illustration of the proposed control method.

Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots

2015 ◽  
Author(s):  
David C. Post ◽  
Bill Goodwine ◽  
James P. Schmiedeler
Keyword(s):  
Disturbance Rejection ◽  
Open Loop ◽  
Legged Robots ◽  
Periodic Motions ◽  
Biped Robots ◽  
Velocity Decomposition ◽  
Hybrid Zero Dynamics ◽  
Control Authority ◽  
Flat Ground ◽  
Instantaneous Control

The locomotion of legged robots is inherently underactuated, which creates control challenges in terms of rejecting large disturbances. A detailed understanding of how the control authority of a robot evolves over a gait trajectory has the potential to inform the design of controllers that offer superior disturbance rejection capabilities without compromising the efficiency benefits that typically accompany underactuated legged robots. Previous work has shown how the system velocities of an underactuated mechanical system can be decomposed into directions aligned with the inputs, or controlled directions, and directions orthogonal to the inputs, or uncontrolled directions, and applied that decomposition to drive wheeled robots to rest. This decomposition fundamentally provides a measure of the instantaneous control authority of the robot. This paper examines how the same techniques can be applied to inform the control of biped robots walking with periodic gaits. This problem differs from those previously studied in that it necessarily involves ground impacts and non-zero desired velocities. A representative example of a two-link planar biped walking on flat ground shows how a simple open loop controller that implements heuristics identified through the velocity decomposition to make use of the available control authority can improve disturbance rejection when added to a hybrid zero dynamics-based controller.

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