Autonomous and Safety-Critical Stair Climbing via Nonlinear Model Predictive Control for Quadrupedal Robots
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Motion planning for quadrupedal robots on unstructured terrains demands the consideration of torso terrain adaptation and safety foothold placement. This paper presents an autonomous and safety stair climbing control strategy, aiming to simultaneously optimize body and leg movements. An improved mobility metric taking into account leg mobility and maintaining stability margin, is introduced. By penalizing deviations from the current joint angle and nominal leg configuration in the cost function, the stance legs can naturally extend to lifting body, and the projection of the center of mass is always inside the support region. Then, the reference climbing velocity is automatically determined based on the geometric information of the stairs. With these reference velocities, we solve a two-layer control framework which couples nonlinear model predictive control (MPC) with whole-body control (WBC), and add several different control barrier functions (CBF) constraints to ensure safety foot placement and edge avoidance. Note that each constrained act on the kinematics or dynamics level depends on the order of the system dynamics. In the simulation, we demonstrate that the robot efficiently climbs several different size stairs with 10 cm height (25% of the maximum leg length) and the maximum climbing velocity reaches 0.64m/s.Keywords:
Model Predictive Control
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Quadrupedalism
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Falls on stairs are a common cause of injury and death among older adults. Although stair climbing is a component of some instruments that assess activities of daily living, normal speeds for safe stairway ambulation have not been established. Furthermore, little is known about which components of functional mobility are most highly associated with stair-climbing speed. The purposes of this study were to determine the range of normal stair-climbing speeds for ambulatory, community-dwelling older adults and identify which functional mobility tests could best explain this speed.Twenty men and 34 women older than 65 years completed 6 functional mobility tests, including timed heel rises, timed chair stands, functional reach, one-legged stance time (OLST), a timed step test (alternately touching a step 10 times), and self-selected gait speed. Participants were then timed as they ascended and descended a flight of 8 to 10 steps. Combined ascent-descent times were used to calculate stair-climbing speed in steps per second. Stepwise regression techniques determined the best functional predictors for stair-climbing speed.Participants ascended and descended stairs at an average speed of 1.3 steps per second; men tended to ambulate stairs more quickly than women. The best predictors of stair-climbing speed were usual gait speed and OLST (R = 0.79; P = .01), which explained 63% of the variance in stair-climbing speed.Our results were similar to others who reported stair-climbing speeds ranging from 1.1 to 1.7 steps per second for older adults. However, the 2 predictors identified in this study provide a simpler and more accurate model for estimating stair-climbing speed than has been previously reported. Further research is needed to determine whether this speed is sufficient for negotiating stairs in an emergency. In addition, further study is needed to determine which tests/measures best differentiate individuals who can and cannot independently climb a typical flight of stairs.An older adult's stair-climbing speed can be accurately estimated by using a model that includes his or her usual gait speed and OLST. This information will help health care professionals and directors of residential facilities make appropriate decisions related to living accommodations for their older adult clients.
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Purpose. Visual improvements have been shown to encourage stair use in worksites independently of written prompts. This study examined whether visual modifications alone can influence behavior in a shopping mall. Climbing one flight of stairs, however, will not confer health benefits. Therefore, this study also assessed whether exposure to the intervention encouraged subsequent stair use. Design. Interrupted time-series design. Settings. Escalators flanked by a staircase on either side. Subjects. Ascending and descending pedestrians (N = 81,948). Interventions. Following baseline monitoring, a colorful design was introduced on the stair risers of one staircase (the target staircase). A health promotion message was superimposed later on top. The intervention was visible only to ascending pedestrians. Thus, any rise in descending stair use would indicate increased intention to use stairs, which endured after initial exposure to the intervention. Measures. Observers inconspicuously coded pedestrians' means of ascent/descent and demographic characteristics. Results. The design alone had no meaningful impact. Addition of the message, however, increased stair climbing at the target and nontarget staircases by 190% and 52%, respectively. The message also produced a modest increase in stair descent at the target (25%) and nontarget (9%) staircases. Conclusions. In public venues, a message component is critical to the success of interventions. In addition, it appears that exposure to an intervention can encourage pedestrians to use stairs on a subsequent occasion.
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Abstract For most older adults, their own homes is the overwhelmingly preferred environment for living and growing older. However, for those living in homes with stairs, the difficulty and risk of injury in stair ascent/descent is a major challenge in their daily life, which may endanger the feasibility of such choice. In this paper, the authors present a novel assistive device, namely RailBot, to help mobility-challenged individuals (including frail older adults) to climb stairs more easily. Unlike the traditional elevators and stair lifts, the RailBot is a highly compact device that can be easily installed in existing stairways, allowing it to benefit a large number of individuals living in homes with stairs. Further, by assisting the users' stair climbing instead of carrying them upstairs, the RailBot enables and encourages the users to maintain and enhance their stair-climbing capabilities, and thus contributes to their long-term physical health. The design details of the RailBot prototype are presented, including the system configuration, the actuation mechanism of the mobile platform, as well as the intuitive control interface for start-stop control and speed regulation. After mounting the prototype in a real-world use environment, a small-scale human study was conducted, with the results clearly demonstrating the effectiveness of the RailBot assistance through the significant reduction of lower-limb muscle activities.
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Increasing physical activity levels among a largely sedentary public is a health priority.1 Lifestyle exercise, such as walking or stair climbing, has been recommended because it provides substantial health benefits and fits easily into daily routines.2 Opportunities for stair climbing in workplaces, public buildings, and the home are frequently available to most population groups.
Studies conducted in both the United States and the United Kingdom have shown that posters at the “point of choice” between escalators and stairs can increase stair use.3–6 As a result, physical activity promoters have championed the use of such posters.
In a recent study, however, messages placed as banners on alternate stair risers were associated with a greater increase in shoppers' stair use than that typically observed with posters.7 To confirm the superiority of these banners in promoting stair climbing, we systematically compared the use of poster prompts and stair-riser banners.
The study was conducted at 2 shopping malls; both sites had 28-step staircases with adjacent escalators. Following a coding system,3 an observer recorded the number of people using the escalators and stairs on alternate days at each location. Observations were made between 11 am and 1 pm to include day and lunchtime shoppers.
At the control site, a 2-week baseline period was followed by 4 weeks during which a poster that read “Stay healthy, use the stairs” was displayed. Use of this poster had been found to be effective in previous research.3 At the experimental site, 2 weeks of baseline observation and 2 weeks of the poster intervention were followed by 2 weeks during which banners, containing mulitple messages, were placed on the stair risers, as in our earlier study.7
Logistic regression analyses were conducted with escalator–stair use as the dichotomous outcome variable. Overall pedestrian traffic volume, a potential confounding variable,3 was calculated as the total number of people using the escalators and stairs during each half-hour period. Traffic volume was entered into the logistic regression models as a continuous variable. Sex, age, and ethnicity were also added to the models, in that previous research had demonstrated their importance.3–6
Figure 1 ▶ illustrates the effects of the poster and banner conditions in the 2 shopping malls. At the control site (n = 12 018), the rate of stair use increased from 2.2% at baseline to 4.8% during the first 2 weeks of the poster exposure but fell slightly to 4.1% during the second 2 weeks. At the experimental site (n = 11 961), stair use increased from 2.4% at baseline to 4.0% when the poster was in place and rose to 6.7% when the banners were displayed on the stair risers.
FIGURE 1—
Stair use at baseline in poster and banner conditions in the control and experimental shopping malls.
Logistic regression analyses revealed that stair use increased at both sites during the first 2 weeks in which the poster was displayed (odds ratio [OR] = 2.18, 95% confidence interval [CI] = 1.69, 2.80), with no significant differences between the sites. During the second intervention period, there was an interaction between the sites (OR = 2.06, 95% CI = 1.48, 2.87) such that rates of stair use were higher with the banners at the experimental site than with the poster at the control site.
There are several reasons why the banners were more effective than the poster in encouraging stair use. First, the banners were highly visible. In our earlier studies, 76% of interviewees reported seeing these banners,7 whereas only a third reported noticing the poster used.8 Second, while the poster included only one health-related message, the banners contained multiple messages, such as “Keep fit,” “Be active,” and “Free exercise.” As such, they are likely to appeal to a broader population range.9
Regular stair climbing has been associated with discernible health gains.10 Accordingly, if large population groups are regularly exposed to motivating stair banners instead of the posters currently used by health promoters, the public health dividends could be considerable.
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The apparent slope of a hill, termed geographical slant perception, is overestimated in explicit awareness. Proffitt (2006) argued that overestimation allows individuals to manage their locomotor resources. Increasing age, fatigue, and wearing a heavy back pack will reduce the available resources and result in steeper reports for a particular hill. In contrast, Durgin and colleagues have proposed an alternative explanation for these effects based on experimental design-particularly, the potential effects of experimental demand. Proffitt's resource-based model would predict that pedestrians with reduced resources should avoid climbing a hill that would further deplete their resources if the opportunity arose. Within the built environment, stairs are the man-made equivalent of relatively steep hills (20°-30°). In many public access settings, pedestrians can avoid climbing the stairs by opting for an adjacent escalator. Observations of pedestrian behavior in shopping malls reveal that 94.5 % do so. This article summarizes the effects of demographic grouping on avoidance of stairs in public health research. Observations in shopping malls (n = 355,069) and travel contexts (n = 711,867) provide data consistent with Proffitt's resource model. Women, the old, and those carrying excess body weight or large bags avoid the stairs more than do their comparison groups. Discussion focuses on differences in physiology that may underlie avoidance of stair climbing in order to highlight the pedestrian behavior that psychology needs to explain.
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The purpose of this study was to describe the relationships between perceived limitations in stair climbing and self-reported stair climbing activity, muscle strength, and adiposity. The study involved the cross-sectional examination of community-dwelling men (n = 32) and women (n = 107) aged at least 65 years. Perceived limitations in climbing one and several flights of stairs were identified by responses to items of the Short-Form 36. Lower limb strength was indicated by the 5 repetition sit-to-stand test. Adiposity was characterized by body mass index. Stair climbing activity was reflected by self-report of flights climbed daily. Stair climbing limitations were common among the participants. Correlational analysis showed low but significant correlations between stair climbing limitations and stair climbing activity, adiposity, and lower limb strength. Regression analysis demonstrated that the 3 independent variables combined together predicted 36.8% of the variance in limitations in climbing a single flight of stairs, and that the stair flights climbed and lower limb strength explained 22.1% of the variance in climbing several flights of stairs. While the design of the study precludes attributing cause, it appears that stair climbing limitations might be assuaged through reduction of adiposity and augmentation of lower limb strength. Stair climbing activity itself may have a direct or indirect effect on stair climbing limitations.
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In terms of self-rated health, the most important activities of daily living are those involving mobility. Of these activities stair climbing is regarded as the most strenuous. A loss of stair climbing ability with age is normally associated with a loss of muscle strength and power, while other factors that influence muscle function, such as fatigue, are often not taken into account. So far no research has been published on how long-lasting fatigue affects activities of daily living, despite the fact that it has been repeatedly proven, in laboratory settings, to influence muscle force production over long periods of time. Technological advances in body sensor networks (BSNs) now provide a method to measure performance during complex real-life situations. In this study the use of a BSN was explored to investigate the effects of long-lasting fatigue on stair climbing performance in 20 healthy adults. Stair climbing performance was measured before and after a fatiguing protocol using a BSN. Performance was defined by temporal and spatial parameters. Long-lasting fatigue was successfully induced in all participants using an exercise protocol. The BSN showed that post-exercise fatigue did not influence stair climbing times (p > 0.2) and no meaningful changes in joint angles were found. No effect on overall stair climbing performance was found, despite a clear presence of long-lasting fatigue. This study shows that physiological paradigms can be further explored using BSNs. Ecological validity of lab-based measurements can be increased by combining them with BSNs.
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Purpose:
The purpose of this research is to validate the stair climbing function of the Fitbit One (tri-axial accelerometer). Currently this is the only commercially available device that records and tracks the number of flights of stairs climbed by an individual. An objective measure of purposeful stair climbing will be a useful tool in future interventions that can focus on this behaviour.
Methods:
Participants. Sixty-six participants (n = 53 female, n = 13 male) were recruited from the University of Alberta.
Procedure. A route was mapped out in a University of Alberta building. This route included two identical staircases each with an elevation of 20 ft. Each staircase represented two flights of stairs (based on 10 ft./flight). Participants walked up the two stair cases ten times each for a total of 20 flights of stairs. The output from the Fitbit One was recorded and compared to the actual flights climbed.
Results:
The internal consistency within the devices was high (α = .86). The percent agreement between the actual flights of stairs climbed and the number reported by the FitBit One was 92.4% with a range of values from 19-21. The absolute percent error was also calculated (APE = -0.23 ± 1.37) and found to be well under the acceptable level of error.
Conclusion:
The overall results of this study suggest that the Fitbit One is an accurate and reliable measure of purposeful stair climbing behaviour and is therefore suitable for use as an objective measure for use in stair climbing interventions.
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[Purpose] The purpose of this study was to investigate the relationship between Probe Reaction Time (P-RT) and fatigue in normal young adults induced by climbing up and down stairs. This study examined how P-RT changes depending on the degree of fatigue. [Subjects] Twelve healthy subjects (4 males, 8 females) participated in this study. [Methods] Subjects were asked to climb up and down stairs while the P-RT and the heart rate (HR) were measured. The speed of climbing up and down stairs was decided by the subjects. [Results] The general ANOVA was significant and showed that P-RT after climbing up and down several times was different from that of the first time. Furthermore, the HR and P-RT were correlated. [Conclusion] The result of this research show that when someone is tired by climbing stairs, their P-RT is likely to be longer.
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