Balancing inverted pendulum cart on inclines using accelerometers

The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback.

Distinct behavior of the little finger during the vertical translation of an unsteady thumb platform while grasping

Object stabilization while grasping is a common topic of research in motor control and robotics. Forces produced by the peripheral fingers (index and little) play a crucial role in sustaining the rotational equilibrium of a handheld object. In this study, we examined the contribution of the peripheral fingers towards object stabilization when the rotational equilibrium is disturbed. For this purpose, the thumb was placed over an unsteady platform and vertically translated. The task was to trace a trapezoid or an inverted trapezoid pattern by moving the thumb platform in the vertical direction. The thumb displacement data served as visual feedback to trace the pattern displayed. Participants were instructed to maintain the handle in static equilibrium at all times. We observed that the change in the normal force of the little finger due to the downward translation of the thumb was significantly greater than the change in the normal force of the index finger due to the upward translation. We speculate that morphological correlations (between thumb and little finger) during the displacement of the thumb might be a reason for such large increases in the little finger forces.

Gaia-DR2 extended kinematical maps

Context. The Gaia Collaboration has used Gaia-DR2 sources with six-dimensional (6D) phase space information to derive kinematical maps within 5 kpc of the Sun, which is a reachable range for stars with relative error in distance lower than 20%. Aims. Here we aim to extend the range of distances by a factor of two to three, thus adding the range of Galactocentric distances between 13 kpc and 20 kpc to the previous maps, with their corresponding error and root mean square values. Methods. We make use of the whole sample of stars of Gaia-DR2 including radial velocity measurements, which consists in more than seven million sources, and we apply a statistical deconvolution of the parallax errors based on the Lucy’s inversion method of the Fredholm integral equations of the first kind, without assuming any prior. Results. The new extended maps provide lots of new and corroborated information about the disk kinematics: significant departures of circularity in the mean orbits with radial Galactocentric velocities between −20 and +20 km s−1 and vertical velocities between −10 and +10 km s−1; variations of the azimuthal velocity with position; asymmetries between the northern and the southern Galactic hemispheres, especially towards the anticenter that includes a larger azimuthal velocity in the south; and others. Conclusions. These extended kinematical maps can be used to investigate the different dynamical models of our Galaxy, and we will present our own analyses in the forthcoming second part of this paper. At present, it is evident that the Milky Way is far from a simple stationary configuration in rotational equilibrium, but is characterized by streaming motions in all velocity components with conspicuous velocity gradients.

A simple method for the prediction of the orientation of H2O molecules in ionic crystals

A robust and fast method is presented that provides a simple real-space convergent solution for identifying equilibrium orientations of crystallization H2O molecules in ionic crystals, on the basis of zero net torque. The predicted H2O orientations constrained by rotational equilibrium are compared with neutron scattering experiments and/or ab initio density functional theory (DFT) calculations. The comparison shows that predicted and observed H2O orientations are consistent, demonstrating the reliability of the reported torque method. Moreover, the rotational equilibrium conditions predict an alternative, not previously observed, H2O orientation in kernite [Na2B4O6(OH)2·3H2O], and this may explain anomalously large displacement parameters that have been reported for this mineral. Complementary DFT computations corroborate that the two orientations are geometrically distinct and energetically near degenerate.

The Subtalar Joint Axis Palpation Technique

Background Clinically locating the point of no rotation to determine the subtalar joint axis location by applying pressure on the plantar surface of the foot was described by Kirby in 1987 but was never validated. We sought to extend a previously validated mechanical model to cadaver feet and to examine the intratester and intertester reliability. Methods Four testers with different levels of experience determined the subtalar joint axis location and moved the subtalar joint through its range of motion, capturing the movement using kinematic analysis. The comparison of the spatial subtalar joint axis location as determined by palpation between and within testers determined the intertester and intratester reliability. The helical axis method was performed to validate the model. Results The intrarater reliability varied from a high of α = 0.96 to a low of α = 0.26 for the slope and was, in general, high (α = 0.78–0.95) for the intersection. The interrater reliability scored moderate to high, depending on the specific cadaver specimen. Concerning the exact location of the subtalar joint axis, no significant difference was found between the results determined by different testers and the helical axis method. Conclusions The palpation technique as part of the subtalar joint axis location and rotational equilibrium theory proposed by Kirby is a reliable and valid clinical tool. Experience in performing the palpation technique has a positive influence on the accuracy of the results. In the context of evidence-based practice, this technique could be a standard tool in the examination of patients with lower-limb–related pathologic disorders.

New serinolic amino-s-triazines by chemoselective amination of cyanuric chloride and their (pro)diastereomerism in restricted rotational phenomena

The highly chemoselective preparation of new elaborated N-unsymmetrically substituted chlorodiamino-s-triazines and melamines, seen as building-blocks for iterative synthesis, is reported. It consisted of amination of cyanuric chloride with commercial C-2-substituted 2-aminopropane-1,3-diols (“serinols”), playing the role as “open-chain” unit and enantiopure (1S,2S)-2-amino-1-(4-nitrophenyl)propane-1,3-diols (“p-nitrophenylserinols”) based amino-1,3-dioxanes (“closed-chain” unit). Issued from the restricted rotation about C(s-triazine)-N(exocyclic) partial double bonds, seen as axes of (pro)diastereomerism, a global four-component rotational equilibrium involving the title compounds is discussed based on DFT computation and (VT) NMR data. Depending on π-deficiency of the s-triazine core, an (un)synchronised deblocking of the generated rotational diastereomers was observed. They are discussed as influence of intra-vs. intermolecular NH...OH (dynamic) interactions occurring in the “open-chain” unit and the anancomeric, axial vs. equatorial, amino-anchorage of the “closed-chain” unit.

Prehension Stability: Experiments With Expanding and Contracting Handle

We studied adjustments in digit forces and moments during holding a vertically oriented handle under slow, externally imposed changes in the width of the grasp. Subjects ( n = 8) grasped a customized motorized handle with five digits and held it statically in the air. The handle width either increased (expanded) or decreased (contracted) at a rate of 1.0, 1.5, or 2.0 mm/s, while the subjects were asked to ignore the handle width changes, and their attention was distracted. External torques of 0.0, 0.25, and 0.5 Nm were applied to the handle in two directions. Forces and moments at the digit tips were measured with six-component sensors. The analysis was performed at the virtual finger (VF) and individual finger (IF) levels (VF is an imagined finger that produces the same wrench, i.e., the force and moment, as several fingers combined). In all the tasks, the normal VF and thumb forces increased with the handle expansion and decreased with the handle contraction. Similar behavior was seen for the thumb tangential force. In contrast, the VF tangential force decreased with the handle expansion and increased with the handle contraction. The changes in the tangential forces assisted the perturbations in the tasks requiring exertion of the supination moments and annulled the perturbation in the pronation effort tasks. In the former tasks, the equilibrium was maintained by the changes of the moments of normal forces, whereas in the latter tasks, the equilibrium was maintained by the changes of the moments of the tangential forces. Analysis at the IF level has shown that the resultant force and moment exerted on the object could arise from dissimilar adjustments of individual fingers to the same handle width change. The complex adjustments of digit forces to handle width change may be viewed as coming from two sources. First, there are local spring-like adjustments of individual digit forces and moments caused by both mechanical properties of the digits and the action of spinal reflexes. These stiffness-like reactions mainly assist in perturbing the rotational equilibrium of the object rather than in maintaining it. Second, there are tilt-preventing adjustments defined by the common task constraints that unite the digits into a task-specific synergy. The “virtual springs theory” developed in robotics literature is insufficient for describing the phenomena observed in human grasping.