Mediating Between Contact Feasibility and Robustness of Trajectory Optimization Through Chance Complementarity Constraints

As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.

Dynamics of a rotating beam with intermittent contact

A flexible beam that is attached to a rotating hub, and whose tip encounters intermittent contact with a flat rigid surface is modelled. The beam is modelled using Euler-Bernoulli beam theory. Lagrange Equations are used to develop the system governing equations of motion, impact is modelled using the momentum balance method and contact is represented via a Lagrange multiplier and Coulomb friction. The model does not allow penetration of the surface to occur by enforcing a geometric constraint throughout contact. Both flexible and rigid initial beam assumptions before impact were analyzed. The effects of angular velocity, depth of penetration and the friction coefficient were examined. A numerical algorithm is outlined and Matlab software is used to implement the procedure. The results show compliance with expected trends and they show smoother transition from unconstrained to constrained motion for the flexible initial beam configuration compared to the rigid configuration.

Dynamics of a rotating beam with intermittent contact

A flexible beam that is attached to a rotating hub, and whose tip encounters intermittent contact with a flat rigid surface is modelled. The beam is modelled using Euler-Bernoulli beam theory. Lagrange Equations are used to develop the system governing equations of motion, impact is modelled using the momentum balance method and contact is represented via a Lagrange multiplier and Coulomb friction. The model does not allow penetration of the surface to occur by enforcing a geometric constraint throughout contact. Both flexible and rigid initial beam assumptions before impact were analyzed. The effects of angular velocity, depth of penetration and the friction coefficient were examined. A numerical algorithm is outlined and Matlab software is used to implement the procedure. The results show compliance with expected trends and they show smoother transition from unconstrained to constrained motion for the flexible initial beam configuration compared to the rigid configuration.

Scanning Probe Microscopy

Scanning probe microscopy (SPM) scans a fine tip close to a surface and measures the tunneling current (STM) or force (SFM), based on many possible tip-surface interactions. STM provides atomic resolution imaging, or the local electronic structure (spectroscopy) as a function of bias voltage, and is also used to manipulate adsorbed atoms on a clean surface. STM operates in two modes— constant current or height—and requires a conducting specimen. SFM uses a cantilever (force sensor) to measure short range (< 1 nm) chemical, and a variety of long-range (< 100 nm) forces, depending on the tip and the specimen; a conducting specimen is not required. In static mode, the tip height is controlled to maintain a constant force, and measure surface topography. In dynamic mode, changes in the vibrational properties of the cantilever are measured using frequency, amplitude, or phase modulation as feedback to control the tip-surface distance and form the image. Dynamic imaging includes contact and non-contact modes, but intermittent contact or tapping mode is common. SPMs measure properties (optical, acoustic, conductance, electrochemical, capacitance, thermal, magnetic, etc.) using appropriate tips, and find applications in the physical and life sciences. They are also used for nanoscale lithography.

Investigation of transient processes of blade movement of compacted snow vibrocleaver

The lack of the necessary amount of equipment for winter maintenance, significant precipitation in the form of snow, lead to a decrease in the efficiency of roads. Inside, courtyards and sidewalks are also covered with a layer of compacted snow due to untimely snow removal. Mekhanic method of breaking compacted snow is currently insufficiently studied and so far there is no effective equipment to combat snow and ice formations. A peculiarity of the process of compacted snow destruction in the mode of vibration cutting is intermittent contact of the knife with the destroyed medium. Condition of the set mode of vibrocutting is the criterion of an exit of a blade of a vibrocleaver from contact with the destroyed environment. The aim of the study is to establish the time at which the knife comes into contact with compacted snow. The obtained results of the calculations make it possible to set the values at which the mode of «vibration cutting» is set and to select parameters of the hydraulic accumulator, which ensures the movement of the blade of the vibrocleaver of the compacted snow.

On the frequency dependence of viscoelastic material characterization with intermittent-contact dynamic atomic force microscopy: avoiding mischaracterization across large frequency ranges

Atomic force microscopy (AFM) is a widely use technique to acquire topographical, mechanical, or electromagnetic properties of surfaces, as well as to induce surface modifications at the micrometer and nanometer scale. Viscoelastic materials, examples of which include many polymers and biological materials, are an important class of systems, the mechanical response of which depends on the rate of application of the stresses imparted by the AFM tip. The mechanical response of these materials thus depends strongly on the frequency at which the characterization is performed, so much so that important aspects of behavior may be missed if one chooses an arbitrary characterization frequency regardless of the materials properties. In this paper we present a linear viscoelastic analysis of intermittent-contact, nearly resonant dynamic AFM characterization of such materials, considering the possibility of multiple characteristic times. We describe some of the intricacies observed in their mechanical response and alert the reader about situations where mischaracterization may occur as a result of probing the material at frequency ranges or with probes that preclude observation of its viscoelastic behavior. While we do not offer a solution to the formidable problem of inverting the frequency-dependent viscoelastic behavior of a material from dynamic AFM observables, we suggest that a partial solution is offered by recently developed quasi-static force–distance characterization techniques, which incorporate viscoelastic models with multiple characteristic times and can help inform dynamic AFM characterization.

Vascular endothelial function is improved after active mattress use

Objective: Active mattresses are used to prevent, treat and relieve pressure ulcers (PU) by intermittent contact pressure/relief. However, no studies have directly assessed the vascular endothelial response to long-term active mattress use. This study investigated the hypothesis that eight weeks use of an active mattress would lead to improvements in vascular endothelial function in healthy participants. Methods: Physiological parameters of baseline skin temperature (BskT), resting blood flow (RBF) and endothelial function as measured using post-occlusive reactive hyperaemia (PORH), were assessed at baseline (week 0); following eight weeks of sleeping on an active mattress, and after an eight week washout period (at week 16). Results: We recruited 10 healthy participants (four male, age 52.7±8.5 years, six female age 51.8±17.5 years). Following active mattress use RBF, PORH and BskT at the hallux pulp increased by 336%, 197% and 3.5°C, respectively. Mean values increased from 24.3±38.3 perfusion units to 106.0±100.3 perfusion units (p=0.021) and from 13,456±10,225 to 40,252±23,995 perfusion units x seconds (p=0.003) and from 22.9±2.5°C to 26.4±1.9°C (p<0.001), respectively. Conclusion: Active mattress use for eight weeks leads to significant improvements in RBF, PORH, and BskT. These results suggest that active mattress use can improve endothelial function. Future research is required to explore the potential of active mattress use in the treatment and management of diseases and conditions that would benefit from an improved endothelial function.