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.

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.

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.

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.

Hidden Attractor in a Passive Motion Model of Compass-Gait Robot

2018 ◽  
Vol 28 (14) ◽  
pp. 1850171 ◽  
Author(s):  
Mahdi Nourian Zavareh ◽  
Fahimeh Nazarimehr ◽  
Karthikeyan Rajagopal ◽  
Sajad Jafari
Keyword(s):  
Path Planning ◽  
Basin Of Attraction ◽  
Biped Robot ◽  
Motion Path ◽  
Motion Model ◽  
Hidden Attractor ◽  
Biped Robots ◽  
Sloping Surface ◽  
Dynamical Properties ◽  
Basin Of Attractions

Many studies have been done on different aspects of biped robots such as motion, path planning, control and stability. Dynamical properties of biped robot on a sloping surface such as equilibria and their stabilities, bifurcations and basin of attraction are investigated in this paper. Basin of attraction is an important property since it can determine the unseen conditions which affect the attractor of the system with multistabilities. By the help of basin of attractions, the paper claims that the strange attractors of compass-gait robot are hidden.

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.

scholarly journals How does ankle push-off balance the walking speed and energy efficiency of planar biped robots?

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110119
Author(s):  
Qiaoli Ji ◽  
Zhihui Qian ◽  
Lei Ren ◽  
Luquan Ren
Keyword(s):  
Energy Efficiency ◽  
Gait Cycle ◽  
Walking Speed ◽  
Biped Robot ◽  
Step Length ◽  
Cost Of Transport ◽  
Biped Robots ◽  
Walking Gait ◽  
Motion Performance ◽  
Step Transition

Ankle push-off is defined as the phase in which muscle-tendon units about the ankle joint generate a burst of positive power during the step-to-step transition in human walking. The dynamic walking of a biped robot can be effectively realized through ankle push-off. However, how to use ankle push-off to balance the walking speed and energy efficiency of biped robots has not been studied deeply. In this study, the effects of the step length (the inter-leg angle is 40°, 50°, and 60°), torque and timing of ankle push-off on the walking speed and energy efficiency of biped robots were studied. The results show that when the step length is 50°, the push-off torque is 30 N· m and the corresponding push-off timing occurs at 43% of the gait cycle, the simulated robot obtains a highly economical walking gait. The corresponding maximum normalized walking speed is 0.40, and the minimum mechanical cost of transport is 2.25. To acquire a more economical walking gait of biped robots, the amount of ankle push-off and the push-off timing need to be coordinated. The purpose of this study is to provide a reference for the influence of ankle push-off on the motion performance of biped robots.

scholarly journals The fast and the frugal: Divergent locomotory strategies drive limb lengthening in theropod dinosaurs

2019 ◽  
Author(s):  
T. Alexander Dececchi ◽  
Aleksandra M. Mloszewska ◽  
Thomas R. Holtz ◽  
Michael B. Habib ◽  
Hans C.E. Larsson
Keyword(s):  
Body Size ◽  
Large Body ◽  
Limb Lengthening ◽  
Limb Length ◽  
Energetic Cost ◽  
Energetic Efficiency ◽  
Leg Length ◽  
Distal Limb ◽  
Cost Of Transport ◽  
The Impact

AbstractLimb length, cursoriality and speed have long been areas of significant interest in theropod paleobiology as locomotory capacity, especially running ability, is critical in not just in prey pursuit but also to avoid become prey oneself. One aspect that is traditionally overlooked is the impact of allometry on running ability and the limiting effect of large body size. Since several different non-avian theropod lineages have each independently evolved body sizes greater than any known terrestrial carnivorous mammal, ∼1000kg or more, the effect that such larger mass has on movement ability and energetics is an area with significant implications for Mesozoic paleoecology. Here using expansive datasets, incorporating several different metrics to estimate body size, limb length and running speed, to calculate the effects of allometry running We test both on traditional metrics used to evaluate cursoriality in non-avian theropods such as distal limb length, relative hindlimb length as well as comparing the energetic cost savings of relative hindlimb elongation between members of the Tyrannosauridae and more basal megacarnivores such as Allosauroids or Ceratosauridae. We find that once the limiting effects of body size increase is incorporated, no commonly used metric including the newly suggested distal limb index (Tibia + Metatarsus/ Femur length) shows a significant correlation to top speed. The data also shows a significant split between large and small bodied theropods in terms of maximizing running potential suggesting two distinct strategies for promoting limb elongation based on the organisms’ size. For small and medium sized theropods increased leg length seems to correlate with a desire to increase top speed while amongst larger taxa it corresponds more closely to energetic efficiency and reducing foraging costs. We also find, using 3D volumetric mass estimates, that the Tyrannosauridae show significant cost of transport savings compared to more basal clades, indicating reduced energy expenditures during foraging and likely reduced need for hunting forays. This suggests that amongst theropods while no one strategy dictated hindlimb evolution. Amongst smaller bodied taxa the competing pressures of being both a predator and a prey item dominant while larger ones, freed from predation pressure, seek to maximize foraging ability. We also discuss the implications both for interactions amongst specific clades and Mesozoic paleobiology and paleoecological reconstructions as a whole.

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