Cartesian Position Research Articles

Learning periodic skills for robotic manipulation: Insights on orientation and impedance

Many daily tasks exhibit a periodic nature, necessitating that robots possess the ability to execute them either alone or in collaboration with humans. A widely used approach to encode and learn such periodic patterns from human demonstrations is through periodic Dynamic Movement Primitives (DMPs). Periodic DMPs encode cyclic data independently across multiple dimensions of multi-degree of freedom systems. This method is effective for simple data, like Cartesian or joint position trajectories. However, it cannot account for various geometric constraints imposed by more complex data, such as orientation and stiffness. To bridge this gap, we propose a novel periodic DMP formulation that enables the encoding of periodic orientation trajectories and varying stiffness matrices while considering their geometric constraints. Our geometry-aware approach exploits the properties of the Riemannian manifold and Lie group to directly encode such periodic data while respecting its inherent geometric constraints. We initially employed simulation to validate the technical aspects of the proposed method thoroughly. Subsequently, we conducted experiments with two different real-world robots performing daily tasks involving periodic changes in orientation and/or stiffness, i.e., operating a drilling machine using a rotary handle and facilitating collaborative human–robot sawing.

A unified formulation of geometry-aware discrete dynamic movement primitives

Learning from demonstration (LfD) is considered as an efficient way to transfer skills from humans to robots. Traditionally, LfD has been used to transfer Cartesian and joint positions and forces from human demonstrations. The traditional approach works well for some robotic tasks, but for many tasks of interest, it is necessary to learn skills such as orientation, impedance, and/or manipulability that have specific geometric characteristics. An effective encoding of such skills can be only achieved if the underlying geometric structure of the skill manifold is considered and the constrains arising from this structure are fulfilled during both learning and execution. However, typical learned skill models such as dynamic movement primitives (DMPs) are limited to Euclidean data and fail in correctly embedding quantities with geometric constraints. In this paper, we propose a novel and mathematically principled framework that uses concepts from Riemannian geometry to allow DMPs to properly embed geometric constrains. The resulting DMP formulation can deal with data sampled from any Riemannian manifold including, but not limited to, unit quaternions and symmetric and positive definite matrices. The proposed approach has been extensively evaluated both on simulated data and real robot experiments. The performed evaluation demonstrates that beneficial properties of DMPs, such as convergence to a given goal and the possibility to change the goal during operation, apply also to the proposed formulation.

The VirTra V-100 Is a Test-Retest Reliable Shooting Simulator for Measuring Accuracy/Precision, Decision-Making, and Reaction Time in Civilians, Police/SWAT, and Military Personnel.

Buga, A, Decker, DD, Robinson, BT, Crabtree, CD, Stoner, JT, Arce, LF, El-Shazly, X, Kackley, ML, Sapper, TN, Anders, JPV, Kraemer, WJ, and Volek, JS. The VirTra V-100 is a test-retest reliable shooting simulator for measuring accuracy/precision, decision-making, and reaction time in civilians, police/SWAT, and military personnel. J Strength Cond Res XX(X): 000-000, 2024-Law-enforcement agencies and the military have increasingly used virtual reality (VR) to augment job readiness. However, whether VR technology captures consistent data for shooting performance evaluation has never been explored. We enrolled 30 adults (24 M/6 F) to examine test-retest reliability of the VirTra shooting simulator. Approximately 30% of the sample had a tactical background (PD/SWAT and military). Trained research staff familiarized subjects with how to shoot the infrared-guided M4 rifle at digitally projected targets. Subjects then performed 3 identical experimental shooting sessions (consecutive or separated by 1-2 days) that assessed accuracy/precision, decision-making, and reaction time. Key metrics comprised projectile Cartesian position ( x , y ), score, time, and throughput (score or accuracy divided by time). Test-retest reliability was measured with intraclass correlation coefficients (ICC). After each visit, subjects completed a perceptual survey to self-evaluate their shooting performance and perceived VR realism. The simulator captured 21 ballistic variables with good to excellent test-retest agreement, producing a global ICC of 0.78. Notable metrics were the individual projectile distances to the center of the target (0.81), shot group radius (0.91), time-to-first decision (0.97), decision-making throughput (0.95), and target transition reaction time (0.91). Subjects had positive self-evaluations about their shooting performance, with "confidence" increasing from baseline to the end of the study ( p = 0.014). The VirTra V-100 virtual ballistic shooting simulator captures data with a high degree of test-retest reliability and is easy to familiarize regardless of starting expertise levels, making it appropriate for use as a method to objectively track progress or a tactical research testing tool.

Homography-Based Visual Servoing of Eye-in-Hand Robots With Exact Depth Estimation

Visual servoing can effectively control robots using visual feedback to improve their intelligence and reliability. For a feature point detected by a monocular camera, the time-varying depth appearing nonlinearly in the Jacobian matrix is difficult to be measured without the prior geometry knowledge of the observed object. Hence, the depth of the feature point is one of the major uncertain parameters in visual servoing. Considering unknown Cartesian feature positions, this study presents a dynamics-based homography-based visual servoing (HBVS) controller for the three-dimensional (3-D) pose regulation of eye-in-hand robot arms with monocular cameras. The uncertain depth is represented as a linear form of its Cartesian feature position, and a composite learning law is applied to estimate position parameters accurately, resulting in exact depth estimation. Compared to existing adaptive HBVS methods, the distinctive feature of the proposed method is that it is a dynamics-based design and guarantees exact depth estimation under a much weaker condition termed interval excitation than persistent excitation. Simulations and experiments on a collaborative robot with 7 degrees of freedom named Franka Emika Panda have verified the effectiveness of the proposed method.

A Self-Adaptive Inertia Hybrid Control of a Fully Constrained Cable-Driven Parallel Robot

A Cable-Driven Parallel Robot (CDPR) is a special type of parallel robot actuated by elastic cables instead of rigid links, which brings uncertainties of model nonlinearities and structural friction depending on the payload variation. A precise motion with minimum control effort against an unknown payload has been a challenging task. To conquer it, we propose an adaptive hybrid control approach for the fully-constrained CDPR with an unknown payload in this paper. A Cartesian space position control and a joint space cable force control are designed through inertia estimation to encounter the effect of the uncertain payload. And then, an artificial neural network (ANN) is employed to estimate the end-effector force in Cartesian space for precise force control and consecutive uncertainties compensation. The stability of the proposed controller is proven based on the Lyapunov method and the efficacy is verified by the experiments. As for feasibility results, the proposed adaptive hybrid control-based cable force estimation was evaluated on the Mini CDPR. Compared to the traditional control scheme, the tracking error was decreased approximately 56% and the utilized tension was significantly reduced for the given trajectory tracking test. Furthermore, the investigation of free movements of the helix trajectory and pick-and-place tasks showed that the proposed hybrid adaptive control can control the position and cable force altogether while being able to estimate the inertia of the end-effector. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The study was motivated by the control problem of adjusting cable tensions of a cable-driven parallel robot (CDPR) against varying payloads at the end-effector. Several advanced control approaches were proposed for but limited to CDPR model parameter estimation and did not consider varying payload. This paper suggests a practical methodology capable of both self-adaptation to unknown payload inertia and consequently improving tracking control performance for a CDPR. In this paper, we derived an adaptive control model and proved stability to ensure safety. In order to encounter unmodeled uncertainties such as pulley friction and cable characteristics, we utilized an artificial neural network (ANN) trained by experiments. The experimental results could confirm that the proposed scheme can estimate the payload inertia and generate minimized cable tension while maintaining good trajectory tracking performance. In future research, we will show more practical validation for a scale-up CDPR with heavy objects toward logistics or pick-and-place application in practice.

A mechanical wave travels along a genetic guide to drive the formation of an epithelial furrow during Drosophila gastrulation

Epithelial furrowing is a fundamental morphogenetic process during gastrulation, neurulation, and body shaping. A furrow often results from a fold that propagates along a line. How fold formation and propagation are controlled and driven is poorly understood. To shed light on this, we study the formation of the cephalic furrow, a fold that runs along the embryo dorsal-ventral axis during Drosophila gastrulation and the developmental role of which is still unknown. We provide evidence of its function and show that epithelial furrowing is initiated by a group of cells. This cellular cluster works as a pacemaker, triggering a bidirectional morphogenetic wave powered by actomyosin contractions and sustained by de novo medial apex-to-apex cell adhesion. The pacemaker's Cartesian position is under the crossed control of the anterior-posterior and dorsal-ventral gene patterning systems. Thus, furrow formation is driven by a mechanical trigger wave that travels under the control of a multidimensional genetic guide.

Cartesian Stiffness Shaping of Compliant Robots—Incremental Learning and Optimization Based on Sequential Quadratic Programming

Emerging robotic systems with compliant characteristics, incorporating nonrigid links and/or elastic actuators, are opening new applications with advanced safety features, as well as improved performance and energy efficiency in contact tasks. However, the complexity of such systems poses challenges in modeling and control due to their nonlinear nature and model variations over time. To address these challenges, the paper introduces Locally Weighted Projection Regression (LWPR) and its online learning capabilities to keep the model of compliant actuators accurate and enable the model-based controls to be more robust. The approach is experimentally validated in Cartesian position and stiffness control for a 4 DoF planar robot driven by Variable Stiffness Actuators (VSA), whose real-time implementation is supported by the Sequential Least Squares Programming (SLSQP) optimization approach.

Perseverare in (suo) Esse: Gassendi and Spinoza against Descartes

Abstract This contribution focuses on the issue of creatures’ conservation in being. The aim is as follows: to demonstrate that the Cartesian position is significantly different from the positions adopted by Gassendi and then by Spinoza. Indeed, both, in contrast to Descartes, adopt a principle of metaphysical inertia, which parallels their principle of physical inertia. If Gassendi can conceive of this principle of metaphysical inertia, it is because he really distinguishes between creation and conservation. If Spinoza, who owes it to his reading of the 5th Objections and Replies, can conceive of his principle, it is because he distinguishes between ideal essence and actual essence.

Trajectory tracking control of nonholonomic wheeled mobile robots using only measurements for position and velocity

This paper studies the trajectory tracking control of nonholonomic wheeled mobile robots, and only measurements for Cartesian position and velocity are used. A full-order observer is proposed to estimate the unmeasurable attitude and filter the position signal. Its effectiveness relies on the persistent excitation (PE) condition of non-zero linear velocity. Using the observer states, we design a local tracking controller that guarantees: (a) the linear velocity input is positive, and (b) the position tracking error is convergent to zero locally asymptotically. Experiments performed on a robot built in-house illustrate the control algorithm.

Soft Pneumatic Muscles: Revolutionizing Human Assistive Devices with Geometric Design and Intelligent Control.

Soft robotics, a recent advancement in robotics systems, distinguishes itself by utilizing soft and flexible materials like silicon rubber, prioritizing safety during human interaction, and excelling in handling complex or delicate objects. Soft pneumatic actuators, a prevalent type of soft robot, are the focus of this paper. A new geometrical parameter for soft artificial pneumatic muscles is introduced, enabling the prediction of actuation behavior using analytical models based on specific design parameters. The study investigated the impact of the chamber pitch parameter and actuation conditions on the deformation direction and internal stress of three tested soft pneumatic muscle (SPM) models. Simulation involved the modeling of hyperelastic materials using finite element analysis. Additionally, an artificial neural network (ANN) was employed to predict pressure values in three chambers at desired Cartesian positions. The trained ANN model demonstrated exceptional performance. It achieved high accuracy with training, validation, and testing residuals of 99.58%, 99.89%, and 99.79%, respectively. During the validation simulations and neural network results, the maximum errors in the x, y, and z coordinates were found to be 9.3%, 7.83%, and 8.8%, respectively. These results highlight the successful performance and efficacy of the trained ANN model in accurately predicting pressure values for the desired positions in the soft pneumatic muscles.

Vision-Based Hierarchical Impedance Control of an Aerial Manipulator

This paper presents an image-based impedance control scheme for an under-actuated aerial manipulator. Unlike the existing Cartesian cascade control (admittance control) scheme, we design an image-space visual servoing controller at the dynamic level to achieve compliant interaction with unknown environments. Furthermore, compared with the state of the art in aerial interaction control, feedback of both the external wrench and the Cartesian position of the aerial manipulator are not required. To cope with the under-actuation property of the system, an attitude tracking control task is designed in such a way that it is dynamically decoupled with the visual impedance control task. Convergence of the task-space tracking error is proven based on the Lyapunov theory. The finite-gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathcal{L}}_2$</tex-math></inline-formula> stability of the system regarding external force/disturbance is also proven. Indoor experiments are conducted to demonstrate the proposed method.

Application of Elliptic Jerk Motion Profile to Cartesian Space Position Control of a Serial Robot

The paper discusses the application of a motion profile with an elliptic jerk to Cartesian space position control of serial robots. This motion profile is obtained by means of a kinematic approach, starting from the jerk profile and then calculating acceleration, velocity and position by successive integrations. Until now, this profile has been compared to other motion laws (trapezoidal velocity, trapezoidal acceleration, cycloidal, sinusoidal jerk, modified sinusoidal jerk) considering single-input single-output systems. In this work, the comparison is extended to nonlinear multi-input multi-output systems, investigating the application to Cartesian space position control of serial robots. As case study, a 4-DOF SCARA-like architecture with elastic balancing is considered; both an integer-order and a fractional-order controller are applied. Multibody simulation results show that, independently of the controller, the behavior of the robot using the elliptic jerk profile is similar to the case of adopting the sinusoidal jerk and modified sinusoidal jerk laws, but with a slight reduction in the position error (−3.8% with respect to the sinusoidal jerk law and −0.8% with respect to the modified sinusoidal jerk law in terms of Integral Square Error) and of the control effort (−8.2% with respect to the sinusoidal jerk law and −1.3% with respect to the modified sinusoidal jerk law in terms of Integral Control Effort).

Unbiased Conversion of 3-D Bistatic Radar Measurements to Cartesian Position

Tracking with bistatic radar measurements is a challenging problem due to the nonlinear relationship between the radar measurements and the Cartesian coordinates, especially for long distances. This nonlinearity leads, for 3-D bistatic radar, to a non-ellipsoidal measurement uncertainty region in Cartesian coordinates, similar to a thin contact lens, that causes consistency problems for a tracking filter. A solution is proposed by developing an unbiased and statistically consistent conversion of the bistatic 3-D sine-space position measurements to Cartesian coordinates, based on second order Taylor expansion. Such an approach was successfully used for monostatic radars but considered impractical for the bistatic case due to the difficulty to derive explicit conversion expressions, as done in this work. The recently developed 2-D approach for the bistatic case could not be successfully extended to 3-D and a different conversion was needed. It is shown that in contrast to the first order conversion and the best nonlinear conversions (based on the cubature method), only the proposed conversion can cover the true uncertainty.

Initial-Pose Self-Calibration for Redundant Cable-Driven Parallel Robot Using Force Sensors Under Hybrid Joint-Space Control

This letter investigates initial-pose estimation (Cartesian position and orientation) for redundant cable-driven parallel robots (CDPRs). As the forward kinematics cannot be performed if the robot is equipped with incremental sensors, a calibration method using force sensors is proposed. The self-calibration problem is formulated as a non-linear least-squares optimization problem based on the hybrid joint-space control strategy. The redundant cables are tension-controlled; the other cables are maintained at a fixed length in the joint space. A position-determined cable adjustable force (P-CAF) performance index and the concept of calibratable space were proposed to maintain the quasi-static conditions. A simulated case study was used to validate the calibration process.

Plant-Inspired Soft Growing Robots: A Control Approach Using Nonlinear Model Predictive Techniques

Soft growing robots, which mimic the biological growth of plants, have demonstrated excellent performance in navigating tight and distant environments due to their flexibility and extendable lengths of several tens of meters. However, controlling the position of the tip of these robots can be challenging due to the lack of precise methods for measuring the robots’ Cartesian position in their working environments. Moreover, classical control techniques are not suitable for these robots because they involve the irreversible addition of materials, which introduces process constraints. In this paper, we propose two optimization-based approaches, combining Moving Horizon Estimation (MHE) with Nonlinear Model Predictive Control (NMPC), to achieve superior performance in point stabilization, trajectory tracking, and obstacle avoidance for these robots. MHE is used to estimate the entire state of the robot, including its unknown Cartesian position, based on available configuration measurements. The proposed NMPC approach considers process constraints by relying on the estimated state to ensure optimal performance. We perform numerical simulations using the nonlinear kinematic model of a vine-like robot, one of the newly introduced plant-inspired growing robots, and achieve satisfactory results in terms of reduced computation times and tracking error.

A Novel Low-Cost ZMP Estimation Method for Humanoid Gait using Inertial Measurement Devices: Concept and Experiments

Estimation and control of zero-moment point (ZMP) is a widely used concept for planning the locomotion of bipedal robots and is commonly measured using integrated joint angle encoders and foot force sensors. Contemporary methods for ZMP measurement involve built-in contact sensors such as joint encoders or instrumented foot force sensors. This paper presents a novel approach for computing ZMP for a humanoid robot using inertial sensor-based wireless foot sensor modules (WFSMs). The developed WFSMs, strapped at different limb segments of a bipedal robot, measure lower limb joint angles in real time. The joint angle trajectories, further transformed into Cartesian position coordinates, are used for estimating the ZMP positions of humanoid robots using the planar biped model. The whole framework is presented through experimental studies for different real-life walking scenarios. Since the modules work based on the limb motion and inclination, any ground unevenness would be automatically reflected in the module output. Hence, this measurement process can be a convenient method for applications requiring humanoid control on uneven surfaces/outdoor terrains. To compare the performance of the proposed model, ZMP is simultaneously measured from inbuilt foot force sensors and joint encoders of the robot. Statistical tests exhibit a high linear correlation between the proposed method with integrated encoders and foot force sensors (Pearson’s coefficient, [Formula: see text]). Results indicate that ZMP estimated by WFSM is a viable method to monitor the dynamic gait balance of a humanoid robot and has potential application in outdoor and uneven terrains.

An Approach to Psychosis: A Psychoanalytical Reading of Franz Kafka’s The Trial

Kafka’s The Trial (1925) provides an intricate narrative, it is enriched with complex feelings and perceptions that are difficult to grasp. Most of Kafka’s works allows the readers to experience states and feelings that go far beyond their normal understanding. Even though this text mainly focuses on the dystopian and totalitarian system of the court, it can also be viewed under a psychoanalytical lens. It narrates the story of Josef K., a bank clerk who’s arrested in a very abrupt manner without any predisposition. He’s never enlightened about the true nature of his crime. As K. tries to unfold the labyrinthine network of bureaucratic traps he slips into a state of complete delusion. This paper is an attempt to inquire as to how The Trial shows the crisis of a modern man in a dystopian world altogether leading him into a state of psychosis. This paper further argues as to how the main character of this text, Josef K. subverts the Cartesian position of being “I think therefore I am” with his constant attempt at making sense of his state as he tries to abject his superego. In the course of the paper through a detailed analysis it shall bring forth instances to appropriate the reason for Josef K.’s psychosis. It will further try to draw a parallel between his psyche and chaos by proving how he tries to conceal his logical inconsistency by presenting himself as someone who is rational and in order while lurking behind it is his pathological illness i.e disorder within order.

КАРТЕЗИАНСКИЕ «ВРОЖДЕННЫЕ ИДЕИ» КАК ПРЕДМЕТ РЕЦЕПЦИИ ДУХОВНО-АКАДЕМИЧЕСКОЙ ФИЛОСОФИИ РЕЛИГИИ

The article deals with a critical analysis of the Cartesian position on the innate idea of God by representatives of the spiritual and academic tradition. The concept of the existence of objective reality, proposed by Descartes, played a key role in the era of the formation of natural science and a new type of philosophizing. At the same time, as an organic part of the Cartesian existence of the world, the idea of innate knowledge of God has undergone significant analysis by the theistic philosophy of religion. Representa-tives of the Moscow and Kazan academies pointed out an error in understanding the knowledge of the Absolute, which involved the reduction of human activity to a minimum.

Warehouse Drone: Indoor Positioning and Product Counter with Virtual Fiducial Markers

The use of robotic systems in logistics has increased the importance of precise positioning, especially in warehouses. The paper presents a system that uses virtual fiducial markers to accurately predict the position of a drone in a warehouse and count items on the rack. A warehouse scenario is created in the simulation environment to determine the success rate of positioning. A total of 27 racks are lined up in the warehouse and in the center of the space, and a 6 × 6 ArUco type fiducial marker is used on each rack. The position of the vehicle is predicted by supervised learning. The inputs are the virtual fiducial marker features from the drone. The output data are the cartesian position and yaw angle. All input and output data required for supervised learning in the simulation environment were collected along different random routes. An image processing algorithm was prepared by making use of fiducial markers to perform rack counting after the positioning process. Among the regression algorithms used, the AdaBoost algorithm showed the highest performance. The R2 values obtained in the position prediction were 0.991 for the x-axis, 0.976 for the y-axis, 0.979 for the z-axis, and 0.816 for the γ-angle rotation.

Application of Half-Derivative Damping to Cartesian Space Position Control of a SCARA-like Manipulator

In classical Cartesian space position control, KD, the end-effector follows the set-point trajectory with a stiffness expressed in the directions of the external coordinates through the stiffness matrix, K, and with a damping proportional to the first-order derivatives of errors of the external coordinates through the damping matrix, D. This work deals with a fractional-order extension of the Cartesian space position control, KDHD, which is characterized by an additional damping term, proportional to the half-order derivatives of the errors of the external coordinates through a second damping matrix, HD. The proposed Cartesian position control scheme is applied to a SCARA-like serial manipulator with elastic compensation of gravity. Multibody simulation results show that the proposed scheme was able to reduce the tracking error, in terms of mean absolute value of the end-effector position error and Integral Square Error, with the same amount of Integral Control Effort and comparable maximum actuation torques.