Motor learning in reaching tasks leads to homogenization of task space error distribution

A human arm, up to the wrist, is often modelled as a redundant 7 degree-of-freedom serial robot. Despite its inherent nonlinearity, we can perform point-to-point reaching tasks reasonably fast and with reasonable accuracy in the presence of external disturbances and noise. In this work, we take a closer look at the task space error during point-to-point reaching tasks and learning during an external force-field perturbation. From experiments and quantitative data, we confirm a directional dependence of the peak task space error with certain directions showing larger errors than others at the start of a force-field perturbation, and the larger errors are reduced with repeated trials implying learning. The analysis of the experimental data further shows that a) the distribution of the peak error is made more uniform across directions with trials and the error magnitude and distribution approaches the value when no perturbation is applied, b) the redundancy present in the human arm is used more in the direction of the larger error, and c) homogenization of the error distribution is not seen when the reaching task is performed with the non-dominant hand. The results support the hypothesis that not only magnitude of task space error, but the directional dependence is reduced during motor learning and the workspace is homogenized possibly to increase the control efficiency and accuracy in point-to-point reaching tasks. The results also imply that redundancy in the arm is used to homogenize the workspace, and additionally since the bio-mechanically similar dominant and non-dominant arms show different behaviours, the homogenizing is actively done in the central nervous system.

Robust Relative Hand Placement for Bi-Manual Tasks

In many bi-manual robotic tasks, like peg-in-a-hole assembly, the success of the task execution depends on the error in achieving the desired relative pose between the peg and the hole in a pre-insertion configuration. Random actuation errors in the joint space usually prevents the two arms from reaching their desired task space poses, which in turn results in random error in relative pose between the two hands. This random error varies from trial to trial, and thus depending on the tolerance between the peg and the hole, the outcome of the assembly task may be random (sometimes the task execution succeeds and sometimes it fails). In general, since the relative pose has 6 degrees-of-freedom, there are an infinite number of joint space solutions for the two arms that correspond to the same task space relative pose. However, in the presence of actuation errors, the joint space solutions are not all identical since they map the joint space error sets differently to the task space. Thus, the goal of this paper is to develop a methodical approach to compute a joint space solution such that the maximum task space error is below a (specified) threshold with high probability. Such a solution is called a robust inverse kinematics solution for the bi-manual robot. Our proposed method also allows the robot to self-evaluate whether it can perform a given bi-manual task reliably. We use a square peg-in-a-hole assembly scenario on the dual-arm Baxter robot for numerical simulations that shows the utility of our approach.

1.5 years of TROPOMI CO measurements: Comparisons to MOPITT and ATom

We have analyzed TROPOspheric Monitoring Instrument (TROPOMI) carbon monoxide (CO) data acquired between November 2017 and March 2019 with respect to other satellite (MOPITT, Measurement Of Pollution In The Troposphere) and airborne (ATom, Atmospheric Tomography mission) datasets to understand better TROPOMI’s contribution to the global tropospheric CO record (2000 to present). TROPOMI and MOPITT are currently the only satellite instruments deriving CO from solar reflected radiances. Therefore, it is particularly important to understand how these two datasets compare. Our results indicate that TROPOMI CO retrievals over land show excellent agreement with respect to MOPITT: relative biases and their standard deviation (i.e., accuracy and precision) are on average −3.73 ± 11.51, −2.24 ± 12.38, and −3.22 ± 11.13 %, compared to the MOPITT TIR (thermal infrared), NIR (near infrared), and TIR+NIR (multispectral) products, respectively. TROPOMI and MOPITT data also show good agreement in terms of temporal and spatial patterns. Despite depending on solar reflected radiances for its measurements, TROPOMI can also retrieve CO over bodies of water if clouds are present, by approximating partial columns under cloud tops using scaled, model-based reference CO profiles. We quantify the bias of TROPOMI total column retrievals over bodies of water with respect to colocated in situ ATom CO profiles after smoothing the latter with the TROPOMI column averaging kernels (AK), which account for signal attenuation under clouds (relative bias and its standard deviation = 3.25 ± 11.46 %). In addition, we quantify enull (the null-space error), which accounts for differences between the shape of the TROPOMI reference profile and that of the ATom true profile (enull = 2.16 ± 2.23 %). For comparisons of TROPOMI and MOPITT retrievals over open water, we adopt a simpler approach, since smoothing with TROPOMI AK does not apply for MOPITT retrievals. To this effect, we compare TROPOMI total CO columns (above and below cloud tops) and partial CO columns (above cloud top) to their colocated MOPITT TIR counterparts. (This approximation would be most accurate for optically thick clouds.) We find very small changes in relative bias between TROPOMI and MOPITT TIR retrievals if total columns are considered instead of partial above-cloud-top columns (

Computing Robust Inverse Kinematics Under Uncertainty

Robotic tasks, like reaching a pre-grasp configuration, are specified in the end effector space or task space, whereas, robot motion is controlled in joint space. Because of inherent actuation errors in joint space, robots cannot achieve desired configurations in task space exactly. Furthermore, different inverse kinematics (IK) solutions map joint space error set to task space differently. Thus for a given task with a prescribed error tolerance, all IK solutions will not be guaranteed to successfully execute the task. Any IK solution that is guaranteed to execute a task (possibly with high probability) irrespective of the realization of the joint space error is called a robust IK solution. In this paper we formulate and solve the robust inverse kinematics problem for redundant manipulators with actuation uncertainties (errors). We also present simulation and experimental results on a 7-DoF redundant manipulator for two applications, namely, a pre-grasp positioning and a pre-insertion positioning scenario. Our results show that the robust IK solutions result in higher success rates and also allows the robot to self-evaluate how successful it might be in any application scenario.

PHASE SPACE ERROR CONTROL WITH VARIABLE TIME-STEPPING ALGORITHMS APPLIED TO THE FORWARD EULER METHOD FOR AUTONOMOUS DYNAMICAL SYSTEMS

We consider a phase space stability error control for numerical simulation of dynamical systems. Standard adaptive algorithm used to solve the linear systems perform well during the finite time of integration with fixed initial condition and performs poorly in three areas. To overcome the difficulties faced the Phase Space Error control criterion was introduced. A new error control was introduced by R. Vigneswaran and Tony Humbries which is generalization of the error control first proposed by some other researchers. For linear systems with a stable hyperbolic fixed point, this error control gives a numerical solution which is forced to converge to the fixed point. In earlier, it was analyzed only for forward Euler method applied to the linear system whose coefficient matrix has real negative eigenvalues. In this paper we analyze forward Euler method applied to the linear system whose coefficient matrix has complex eigenvalues with negative large real parts. Some theoretical results are obtained and numerical results are given.

Signal in Space Error and Ephemeris Validity Time Evaluation of Milena and Doresa Galileo Satellites

In August 2016, Milena (E14) and Doresa (E18) satellites started to broadcast ephemeris in navigation message for testing purposes. If these satellites could be used, an improvement in the position accuracy would be achieved. A small error in the ephemeris would impact the accuracy of positioning up to ±2.5 m, thus orbit error must be assessed. The ephemeris quality was evaluated by calculating the SISEorbit (in orbit Signal In Space Error) using six different ephemeris validity time thresholds (14,400 s, 10,800 s, 7200 s, 3600 s, 1800 s, and 900 s). Two different periods of 2018 were analyzed by using IGS products: DOYs 52–71 and DOYs 172–191. For the first period, two different types of ephemeris were used: those received in IGS YEL2 station and the BRDM ones. Milena (E14) and Doresa (E18) satellites show a higher SISEorbit than the others. If validity time is reduced, the SISEorbit RMS of Milena (E14) and Doresa (E18) greatly decreases differently from the other satellites, for which the improvement, although present, is small. Milena (E14) and Doresa (E18) reach a SISEorbit RMS of about 1 m (comparable to that of the other Galileo satellites reach with the nominal validity time) when validity time of 1800 s is used. Therefore, using this threshold, the two satellites could be used to improve single point positioning accuracy.