Cartesian Control Research Articles

A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows

This paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows, interacting with moving solid obstacles. A simplified incompressible Baer-Nunziato type model is considered for two-phase flows containing a liquid phase, a solid phase, and the surrounding void. According to the so-called diffuse interface approach, the different phases and consequently the void are described by means of a scalar volume fraction function for each phase. In our numerical scheme, the dynamics of the liquid phase and the motion of the solid are decoupled. The solid is assumed to be a moving rigid body, whose motion is prescribed. Only after the advection of the solid volume fraction, the dynamics of the liquid phase is considered. As usual in semi-implicit schemes, we employ staggered Cartesian control volumes and treat the nonlinear convective terms explicitly, while the pressure terms are treated implicitly. The non-conservative products arising in the transport equation for the solid volume fraction are treated by a path-conservative approach. The resulting semi-implicit FV discretization of the mass and momentum equations leads to a mildly nonlinear system for the pressure which can be efficiently solved with a nested Newton-type technique. The time step size is only limited by the velocities of the two phases contained in the domain, and not by the gravity wave speed nor by the stiff algebraic relaxation source term, which requires an implicit discretization. The resulting semi-implicit algorithm is first validated on a set of classical incompressible Navier-Stokes test problems and later also adds a fixed and moving solid phase.

Self-Collision Detection and Avoidance for Dual-Arm Concentric Tube Robots

Recent studies on concentric tube robots (CTRs) have shown that they are well-suited for minimally invasive endoscopic surgeries. However, typical surgical procedures require the use of multiple tools simultaneously which has led to the development of dual-arm CTRs that are susceptible to self-collision. In this paper, a closed-loop control system for dual-arm CTRs is proposed to detect and avoid the inter-collision between arms along their entire body. The collision detection module finds the minimum distance between the manipulators in the Cartesian space. To avoid self-collision, the proposed control system using differential Jacobian-based inverse kinematics is developed with three tasks with different priorities; physical constraints, self-collision avoidance, and end-effector tracking. The performance of the proposed control scheme is investigated through implementation for Cartesian control of a dual-arm CTR to reach pre-defined target points in a simulated scenario similar to epilepsy surgery. The self-collision detection module successfully predicted all 359 self-collision cases in the target region. The experimental results demonstrated the efficacy of the controller in handling inter-collision between arms over their entire body by keeping the minimum distance between arms at 1.542 mm.

Multi-Log Grasping Using Reinforcement Learning and Virtual Visual Servoing

We explore multi-log grasping using reinforcement learning and virtual visual servoing for automated forwarding in a simulated environment. Automation of forest processes is a major challenge, and many techniques regarding robot control pose different challenges due to the unstructured and harsh outdoor environment. Grasping multiple logs involves various problems of dynamics and path planning, where understanding the interaction between the grapple, logs, terrain, and obstacles requires visual information. To address these challenges, we separate image segmentation from crane control and utilise a virtual camera to provide an image stream from reconstructed 3D data. We use Cartesian control to simplify domain transfer to real-world applications. Because log piles are static, visual servoing using a 3D reconstruction of the pile and its surroundings is equivalent to using real camera data until the point of grasping. This relaxes the limits on computational resources and time for the challenge of image segmentation, and allows for data collection in situations where the log piles are not occluded. The disadvantage is the lack of information during grasping. We demonstrate that this problem is manageable and present an agent that is 95% successful in picking one or several logs from challenging piles of 2–5 logs.

Active 6 DoF Force/Torque Control Based on Dynamic Jacobian for Free-Floating Space Manipulator

Abstract In-orbit capture of a non-cooperative satellite will be a major challenge in the proposed servicing and active debris removal missions. The contact forces between the manipulator end-effector and the elements of the target object will occur in the grasping phase. In this paper, an active 6 Degrees of Freedom (DoF) force/torque control method for manipulator mounted on a free-floating servicing satellite is proposed. The main aim of the presented method is to balance the relation between end-effector position and force along each direction in the Cartesian space. The control law is based on the Dynamic Jacobian, which takes into account the influence of the manipulator motion on the state of the servicing satellite. The proposed approach is validated in numerical simulations with a simplified model of contact. Comparison with the classical Cartesian control shows that the active 6 DoF force/torque control method allows to obtain better positioning accuracy of the end-effector and lower control torques in manipulator joints in the presence of external forces.

Application of Impedance Control of the Free Floating Space Manipulator for Removal of Space Debris

A broad and significant class of space debris can be mitigated by means of a satellite, capable of capturing a large non-cooperating object by using a robotized arm with a gripper. The capture operation typically comprises of an approach, a close-on manoeuvre, establishing contact between the robotic grappler arm and a suitable feature on the target satellite, and finally it is concluded when a positive mechanical connection is achieved by the gripper closed on that feature. The phase of establishing contact poses a critical challenge in this scenario, since the target typically will be tumbling with respect to the chaser satellite causing high forces on the gripper and the robotic arm. A family of control methods known collectively as impedance control is typically employed in terrestrial robots for tasks involving an interaction with an environment, especially the dynamic contact. In this work, we present the model-based impedance control applied to a robotic manipulator on a free floating base. The derivation of impedance control law for a robotic manipulator on a free floating satellite, involving Generalized Jacobian Matrix (GJM), is presented, followed by simulation results comparing the loads in the manipulator joints against a classical GJM-based Cartesian controller. The simulation results show that the impedance controlled free floating robotic manipulator completes the task of trajectory following amid contact with unknown target with lower torques in the robot joints.

Mechanical Design of a Biped Robot FORREST and an Extended Capture-Point-Based Walking Pattern Generator

In recent years, many studies have shown that soft robots with elastic actuators enable robust interaction with the environment. Compliant joints can protect mechanical systems and provide better dynamic performance, thus offering huge potential for further developments of humanoid robots. This paper proposes a new biped robot. The new robot combines a torque sensor-based active elastic hip and a spring-based passive elastic knee/ankle. In the first part, the mechanical design is introduced, and in the second part, the kinematics and dynamics capabilities are described. Furthermore, we introduce a new extended capture-point-based walking pattern generator that calculates footstep positions, which are used as input for the controller of our new biped robot. The main contribution of this article is the novel mechanical design and an extended walking pattern generator. The new design offers a unique solution for cable-driven bipeds to achieve both balancing and walking. Meanwhile, the new walking pattern generator can generate smooth desired curves, which is an improvement over traditional generators that use a constant zero-moment-point (ZMP). A simple cartesian controller is applied to test the performance of the walking pattern generator. Although the robot has been built, all experiments regarding the pattern generator are still simulated using MATLAB/Simulink. The focus of this work is to analyze the mechanical design and show the capabilities of the robot by applying a new pattern generator.

Neural-learning-enhanced Cartesian Admittance control of robot with moving RCM constraints

AbstractIn this manuscript, a scheme for neural-learning-enhanced Cartesian Admittance control is presented for a robotic manipulator to deal with dynamic environments with moving remote center of motion (RCM) constraints. Although some research has been implemented to address fixed constrained motion, the dynamic moving movement constraint is still challenging. Indeed, the moving active RCM constraints generate uncertain disturbance on the robot tool shaft with unknown dynamics. The neural-learning-enhanced decoupled controller with disturbance optimisation is employed and implemented to maintain the performance under the kinematic uncertain and dynamic uncertain generated. In addition, the admittance Cartesian control method is introduced to control the robot, providing compliant behaviour to an external force in its operational space. In this proposed framework, a neural-learning-enhanced disturbance observer is investigated to calculate the external factor operating on the end effector premised on generalised momentum in order to ensure accuracy. Finally, the experiments are implemented using a redundant robot to validate the efficacy of the suggested approach with moving RCM constraints.

Miniature Manipulator Design and Cartesian Control for Minimally Invasive Transluminal Endoscopic Surgery.

This paper presents a miniature manipulator under Cartesian control for minimally invasive transluminal endoscopic surgery. The manipulator had four degrees of freedom (DoFs) and a diameter of only 3.5 mm. The compact size of the manipulator allowed it to pass through the instrument channel of the endoscope, and its high dexterity allowed it to perform most of the operations in endoscopic surgery such as marking, grasping, hanging, etc. The implicit function relationship in the kinematics of the continuum manipulator was analyzed. By introducing the regression analysis method, the analytical form of the inverse kinematics was obtained. The distribution of singularities in the manipulator workspace was analyzed with emphasis. The presence of singularities made Cartesian mapping control between the primary side and secondary side impossible. By introducing the smoothing method of the joint trajectory, the discontinuity of the joint velocity at the singularity was avoided and the primary-secondary mapping under Cartesian control was realized. The trajectory-tracking experiment proved that the smoothness of the joint trajectory could make the manipulator smoothly pass through the singularity. The fixed-point marking experiment proved that the Cartesian control could improve the intuition of operation and the efficiency of task completion. Comprehensive performance experiments showed that the manipulator had enough dexterity to execute complex operations.

Novel Modularization Design and Intelligent Control of a Multifunctional and Flexible Baby Chair

The design and control of baby chairs have attracted great interest due to children’s increasing consumption market. As a human-robot interface, the features of baby chairs, such as their flexibility, comfortableness, safety, etc., are important factors that should be considered. Therefore, in this paper, to provide competent assistance to parents in taking care of their children, we propose a novel design and control scheme for improving children’s living goods and easing parents’ burden. Firstly, a novel modularization design method is introduced to redesign the shape and structure of the baby chair to cater to multifunctional demands. Flexible materials are chosen to adapt to different body shapes for the sake of safety and comfortableness. Moreover, a Cartesian impedance controller enhanced by a radial basis function neural network (RBFNN) is proposed to achieve a safe, smooth and accurate control of the baby chair with children sitting on it in various uncertain situations using integrated actuators. Both target posture control and periodic control of the chair are implemented to meet different practical requirements. The feasibility of both the chair design and its control is verified in the MATLAB simulation environment through reference tracking tasks. The experimental results demonstrate that our controller can achieve satisfactory performance by controlling the position error in a reasonable range and keeping the manipulation stable and smooth. With the increasing demand for baby chairs in the global children’s consumption market, we believe that the methodology proposed in this paper will attract more research and industry interest.

An Interference Inspection Algorithm of Limb and Hexapod Frame in the Treatment of Lower Limb Deformity

Pre-operative correction trajectory planning is one of the important aspects of deformity correction. Avoidance of limb-frame interference is essential to verify the implementability of the preplanned correction trajectory, as well as to maintain the continuity and security of the correction strategy. In this study, a novel interference inspection algorithm is developed to investigate the interaction of the limb and hexapod frame in the treatment of lower limb deformities. The algorithm is built on a minimum distance model of the cone frustum busbar and cylindrical axis using vector analysis. A predefined trajectory is generated by Cartesian coordinate path control. Subsequently, an interference case is performed through numerical simulation and motion simulation. The results show that the conclusion of numerical simulation and motion simulation is consistent, which prove the feasibility of the algorithm. The results also show that it is possible to identify the riskiest struts, which are prone to interfere with the limb, and the riskiest positions. The proposed algorithm can support the clinician in selecting the suitable frame configuration to avoid interference. The algorithm solves the problem that the interference can only be judged by clinical observation in the clinic.

Mix Frame Visual Servo Control Framework for Autonomous Assistive Robotic Arms.

Assistive robotic arms (ARAs) that provide care to the elderly and people with disabilities, are a significant part of Human-Robot Interaction (HRI). Presently available ARAs provide non-intuitive interfaces such as joysticks for control and thus, lacks the autonomy to perform daily activities. This study proposes that, for inducing autonomous behavior in ARAs, visual sensors integration is vital, and visual servoing in the direct Cartesian control mode is the preferred method. Generally, ARAs are designed in a configuration where its end-effector’s position is defined in the fixed base frame while orientation is expressed in the end-effector frame. We denoted this configuration as ‘mixed frame robotic arms’. Consequently, conventional visual servo controllers which operate in a single frame of reference are incompatible with mixed frame ARAs. Therefore, we propose a mixed-frame visual servo control framework for ARAs. Moreover, we enlightened the task space kinematics of a mixed frame ARAs, which led us to the development of a novel “mixed frame Jacobian matrix”. The proposed framework was validated on a mixed frame JACO-2 7 DoF ARA using an adaptive proportional derivative controller for achieving image-based visual servoing (IBVS), which showed a significant increase of 31% in the convergence rate, outperforming conventional IBVS joint controllers, especially in the outstretched arm positions and near the base frame. Our Results determine the need for the mixed frame controller for deploying visual servo control on modern ARAs, that can inherently cater to the robotic arm’s joint limits, singularities, and self-collision problems.

Nonlinear Model Predictive Control of Rotation Floating Space Robots for Autonomous Active Debris Removal

Active Debris removal using robotic manipulators onboard satellites is a promising way of cleaning up the space junk. However, complexities and non-linearities associated with the control of such coupled space-based systems present difficulties in their feasible implementation. Lack of a fixed base arises serious problems in controlling the space manipulators for precision tasks like capture of an orbiting space debris. This paper presents systematic modelling and control approaches for Rotation floating space robots in order to draw a comparison between them while tracking a moving target representing autonomous debris capture. We propose a Nonlinear Model Predictive Controller (NMPC) for the space robot in order to design an optimal path that the end-effector can follow while being controlled to capture the target. To the best of the knowledge of the authors, such a controller has not been tested for a Rotation floating space robot before. Further, the current work implements and reviews one of the most commonly used Transpose Jacobian Cartesian (TJC) controller for Rotation floating space robots through the use of Generalized Jacobian Matrix (GJM). The results provide sufficient evidence of the superior performance of the nonlinear model predictive controller over the TJC controller. Finally, the current work also implements the same nonlinear model predictive controller on a more popular state of the art Free floating space robot and compares it with the Rotation floating space robot.

Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in +X,+Y,−X,−Y directions), while the other four poles are inserted in a way such that each pole makes 45° with two of the axes +X,+Y,−X,−Y. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in X and Y directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient.

Magnetically Levitated Linear Drive Using an Active Gravity Compensation Based on Hybrid Shape Memory Actuators

This article presents a magnetically levitated linear drive for precision engineering with integrated active gravity compensation. The gravity compensation combines permanent magnets with novel hybrid shape memory actuators. The magnetically levitated system uses a homopolar linear drive as well as nine reluctance actuators to levitate a passive armature with no mechanical connection between the stator and armature. The mechanical design is based on geometrically decoupled horizontal and vertical guidance axes. A decoupled Cartesian control scheme is developed, which compensates for the actuator and system nonlinearities in order to achieve high bandwidths. The active gravity compensation adjusts the air gap between the permanent magnets and armature to the required gravity compensation force. This helps to keep the dissipated power and temperature increase in the magnetically levitated drive low (and thus, system precision high). To avoid the generation of particles in clean room applications, the actuators positioning the permanent magnets are solely based on solid-state effects: thermal shape memory alloys actively generate motion, while passive magnetic shape memory alloy elements realize a multistable behavior based on their internal twinning force. The resulting actuator is compact, energy efficient, and abrasion-free. The implementation of the gravity compensation in the levitated linear drive is verified and the functionality of the system is demonstrated in experiments.

Towards Autonomous Robotic Assembly: Using Combined Visual and Tactile Sensing for Adaptive Task Execution

Robotic assembly tasks are typically implemented in static settings in which parts are kept at fixed locations by making use of part holders. Very few works deal with the problem of moving parts in industrial assembly applications. However, having autonomous robots that are able to execute assembly tasks in dynamic environments could lead to more flexible facilities with reduced implementation efforts for individual products. In this paper, we present a general approach towards autonomous robotic assembly that combines visual and intrinsic tactile sensing to continuously track parts within a single Bayesian framework. Based on this, it is possible to implement object-centric assembly skills that are guided by the estimated poses of the parts, including cases where occlusions block the vision system. In particular, we investigate the application of this approach for peg-in-hole assembly. A tilt-and-align strategy is implemented using a Cartesian impedance controller, and combined with an adaptive path executor. Experimental results with multiple part combinations are provided and analyzed in detail.

A Comparison of Different Approaches for Formation Control of Nonholonomic Mobile Robots regarding Object Transport

Controlling the formation of several mobile robots allows for the connection of these robots to a large virtual unit. This enables a group of mobile robots to carry out tasks that a single robot could not perform. For this purpose, the use of nonholonomic mobile robots is especially useful, as they often have a higher payload and are suitable for a wider range of terrains. However, most research in the area of formation control is focused on holonomic robots, since their superior mobility allows for better control and allows for the research on more sophisticated control techniques. The remaining articles explicitly dealing with nonholonomic robots often do cover common controllers, but do not include realistic simulations or comparison of different controls on the same trajectory. Therefore, in this paper, we present a comparative analysis of two frequently used control approaches. We compare the behavior of a l-ψ-controller and a Cartesian reference-based controller with different types of reference value generation and pose determination. The evaluation of all resulting control schemes is based on the task of collaborative object transport. To do so, we selected performance criteria geared towards applicability in real processes. In addition, we used an error model, which takes into account the noise and accuracy of all sensors (IMU and encoder) as well as the drift in odometry caused by the slip of the robot’s wheels. The comparison includes a series of simulations using two trajectories with a changing number of robots and different formation geometries. In the simulations we got slightly better results for the Cartesian control law.

Robust state dependent Riccati equation variable impedance control for robotic force-tracking tasks

Industrial robots are increasingly used in highly flexible interaction tasks, where the intrinsic variability makes difficult to pre-program the manipulator for all the different scenarios. In such applications, interaction environments are commonly (partially) unknown to the robot, requiring the implemented controllers to take in charge for the stability of the interaction. While standard controllers are sensor-based, there is a growing need to make sensorless robots (i.e., most of the commercial robots are not equipped with force/torque sensors) able to sense the environment, properly reacting to the established interaction. This paper proposes a new methodology to sensorless force control manipulators. On the basis of sensorless Cartesian impedance control, an Extended Kalman Filter (EKF) is designed to estimate the interaction exchanged between the robot and the environment. Such an estimation is then used in order to close a robust high-performance force loop, designed exploiting a variable impedance control and a State Dependent Riccati Equation (SDRE) force controller. The described approach has been validated in simulations. A Franka EMIKA panda robot has been considered as a test platform. A probing task involving different materials (i.e., with different stiffness properties) has been considered to show the capabilities of the developed EKF (able to converge with limited errors) and controller (preserving stability and avoiding overshoots). The proposed controller has been compared with an LQR controller to show its improved performance.

Two different control strategies for 16-pole rotor active magnetic bearings system with constant stiffness coefficients

Rotor active magnetic bearing is one of the preferable supporting techniques for the high-speed rotating machinery. This article proposes a comparison between two different control strategies for the constant stiffness coefficients 16-pole rotor active magnetic bearings system (16-pole Rotor-AMBs). The first strategy is the Cartesian control in which the applied currents on the poles depend on the horizontal or vertical displacements of the rotor. The second strategy is the radial control in which the applied currents depend on the radial displacement of the rotor. Both strategies are based on the proportional-derivative (PD) control algorithm to make the rotor's vibrations track a zero reference point. The major novelty here is that we compare the two strategies to explore their advantages and disadvantages in controlling the 16-pole Rotor-AMBs. The analytical and numerical approximate predictions of the rotor's vibrations are extracted to show and verify the nonlinear dynamical behavior of the rotor based on the two methods. The local stability of the extracted solutions is analyzed via Hartman–Grobman theorem to conclude the stable and unstable solutions regions and the boundary between them. Various responses are included to show, in most conditions, that the radial control has a privilege over the Cartesian control in avoiding either the multi-stable solutions or the rub/impact forces occurrence between the rotating disk and the stator pole legs.

Cartesian Control of Sit-to-Stand Motion Using Head Position Feedback.

Sit-to-stand (STS) motion is an indicator of an individual's physical independence and well-being. Determination of various variables that contribute to the execution and control of STS motion is an active area of research. In this study, we evaluate the clinical hypothesis that besides numerous other factors, the central nervous system (CNS) controls STS motion by tracking a prelearned head position trajectory. Motivated by the evidence for a task-oriented encoding of motion by the CNS, we adopt a robotic approach for the synthesis of STS motion and propose this scheme as a solution to this hypothesis. We propose an analytical biomechanical human CNS modeling framework where the head position trajectory defines the high-level task control variable. The motion control is divided into low-level task generation and motor execution phases. We model CNS as STS controller and its Estimator subsystem plans joint trajectories to perform the low-level task. The motor execution is done through the Cartesian controller subsystem that generates torque commands to the joints. We do extensive motion and force capture experiments on human subjects to validate our analytical modeling scheme. We first scale our biomechanical model to match the anthropometry of the subjects. We do dynamic motion reconstruction through the control of simulated custom human CNS models to follow the captured head position trajectories in real time. We perform kinematic and kinetic analyses and comparison of experimental and simulated motions. For head position trajectories, root mean square (RMS) errors are 0.0118 m in horizontal and 0.0315 m in vertical directions. Errors in angle estimates are 0.55 rad, 0.93 rad, 0.59 rad, and 0.0442 rad for ankle, knee, hip, and head orientation, respectively. RMS error of ground reaction force (GRF) is 50.26 N, and the correlation between ground reaction torque and the support moment is 0.72. Low errors in our results validate (1) the reliability of motion/force capture methods and anthropometric technique for customization of human models and (2) high-level task control framework and human CNS modeling as a solution to the hypothesis. Accurate modeling and detailed understanding of human motion can have significant scope in the fields of rehabilitation, humanoid robotics, and virtual characters' motion planning based on high-level task control schemes.

An Augmented Kinematic Model for the Cartesian Control of the Hybrid Wheeled-Legged Quadrupedal Robot CENTAURO

This work deals with the kinematic control of Centauro , a highly redundant, hybrid wheeled-legged robot designed at Istituto Italiano di Tecnologia (IIT) . Given its full wheeled mobility as allowed by its four independently steerable wheels, the choice of some local frame (in addition to the global world) is required in order to express tasks that are naturally defined in a robot-centric fashion. In this work, we show that trivially selecting such a frame as the robot trunk leads to sub-optimal results in terms of motion capabilities; as main contribution, we therefore propose a comparative analysis among three different choices of local frame, and demonstrate that in order to retain all advantages from the whole-body control domain, the kinematic model of the robot must be augmented with an additional virtual frame, which proves to be a useful choice of local frame, enabling e.g. the automatic adaptation of the trunk posture under constraint activation. The resulting Cartesian controller is finally validated by means of an extensive experimental session on the real hardware.